You’re already familiar with two different kinds of potential energy: elastic (like the energy stored in a rubber band) and gravitational (the energy stored in height). Now let’s take a look at electrical potential energy stored in an electric field:
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Ever wonder where the “volt” comes from? We’re going to look at this more in the next section on DC current, but here’s a snapshot overview of electric potential:
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If you have a Fun Fly Stick, then pull it out and watch the video below. If not, don’t worry – you can do most of these experiments with a charged balloon (one that you’ve rubbed on your hair). Let’ play with a more static electricity experiments, including making things move, roll, spin, chime, light up, wiggle and more using static electricity!
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Materials:
This video show you how to get the most out of your Fun Fly Stick. If you don’t have a Fly Stick, simply use an inflated balloon that you’ve rubbed on your head. In the video, the Electrostatic Lab is mounted on a foam meat tray I found at the grocery store.
Download Student Worksheet & Exercises
The triboelectric series is a list that ranks different materials according to how they lose or gain electrons. Near the top of the list are materials that take on a positive charge, such as air, human skin, glass, rabbit fur, human hair, wool, silk, and aluminum. Near the bottom of the list are materials that take on a negative charge, such as amber, rubber balloons, copper, brass, gold, cellophane tape, Teflon, and silicone rubber.
When you turn on your Fun Fly Stick (or rub your head with a balloon), one end of the Fun Fly Stick takes on a positive charge and the other end holds the negative charge. When you rub your head with a balloon, the hair takes on a positive charge and the balloon takes on a negative charge.
When you scuff along the carpet, you build up a static charge (of electrons). Your socks insulate you from the ground, and the electrons can’t cross your sock-barrier and zip back into the ground. When you touch someone (or something grounded, like a metal faucet), the electrons jump from you and complete the circuit, sending the electrons from you to them (or it).
Exercises
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This simple FET circuit is really an electronic version of the electroscope. This “Alien Detector” is a super-sensitive static charge detector made from a few electronics parts. I originally made a few of these and placed them in soap boxes and nailed the lids shut and asked kids how they worked. (I did place a on/off switch poking through the box along with the LED so they would have ‘some’ control over the experiment.)
This detector is so sensitive that you can go around your house and find pockets of static charge… even from your own footprints! This is an advanced project for advanced students.
You will need to get:
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Download Student Worksheet & Exercises
After you’ve made your charge detector, turn it on and comb your hair, holding the charge detector near your head and then the comb. You’ll notice that the comb makes the LED turn off, and your head (in certain spots) makes the LED go on. So it’s a positive charge static detector… this is important, because now you know when the LED is off, the space you’re detecting is negatively charged, and when it’s lit up, you’re in a pocket of positively charged particles. How far from the comb does your detector need to be to detect the charge? Does it matter how humid it is?
You can take your detector outdoors, away from any standing objects like trees, buildings, and people, and hold it high in the air. What does the LED look like? What happens when you lower the detector closer to the ground? Raise it back up again to get a second reading… did you find that the earth is negative, and the sky is more positive?
You can increase the antenna sensitivity by dangling an extra wire (like an alligator clip lead) to the end of the antenna. Because thunderstorms are moving electrical charges around (negative charges downwards and positive charges upwards), the earth is electrified negatively everywhere. During a thunderstorm, the friction caused by the moving water molecules is what causes lightning to strike! (But don’t test your ideas outside in the wide open while lightening is striking!)
Exercises
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What causes lightning, and how can we protect ourselves from strikes? In many textbooks, you’ll read about how clouds become electrically charged through friction in the moist air, but the truth is, scientists still don’t fully understand how and why lightning happens the way it does. But here’s what we do know: lightning happens when the positive and negative charges in a cloud become polarized. That is, the (extra) positive charges move to the top of the cloud and the (extra) negative charges move to the bottom of the cloud, usually by friction of the water vapor molecules in the cloud.
As the water molecules rise, electrons are stripped off and add to the charge of the cloud. The cloud can become ever more polarized if the rising water vapor freezes. The frozen particles clump together and take on a negative charge inside, positive charge on the outside, which rips the clumps apart to further polarize the cloud. The more polarized the cloud is, the more its electric field affects the space around it. The electrons on the surface of the Earth underneath the cloud are repelled by the bottom of the cloud, which creates a positive charge on the surface under the cloud. Trees. houses, cars, and people take on a positive charge as the cloud passes by. Now we’re set up for a lightning strike.
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Even though a bolt of lightning can have 10 coulombs of charge, a coin contains about 250,000 coulombs of positive charge (balanced by the same amount of negative charge). There is a whole lot of electric charge that is in ordinary matter, but since it’s balanced, it’s not as noticeable as the lightning strike!
Yay! You’ve completed this set of lessons! Now it’s your turn to do physics problems on your own.
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The way charges attract or repel each other can be described as a force. A charge can exert a push or pull on another charge depending on if the charges are positive or negative. How much force they exert can be figured out using Coulomb’s Law of Electric Force, which is:
where C = 8.99 x 109 Nm2/C2
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Now Coulomb’s Law looks a lot like Newton’s Law of Gravitation… they both have a constant out in front, and they both have the inverse square relationship relating distance to force. They are different, however in a couple of important ways. Newton’s Law of Gravitation breaks down on the atomic level, and has to be replaced with Quantum Mechanics. Also, gravity is only an attractive force, whereas electric forces are both attractive and repulsive.
Notice the inverse square relationship: if you double the distance two charges are standing apart, the electrical force felt by the charges will decrease by a factor of four. If you triple the distance, the force goes down by a factor of nine.
Teachers and students both like to study, teach and learn subjects in neat, separate little packages, but this isn’t the way the universe works. Things aren’t usually isolated in their own box so they nothing to do with anything else. When we learned about the inverse square law, it wasn’t only for Newton’s Law of Gravitation… it popped up here also! And Newton’s Laws included forces, acceleration, gravity and energy, and now we’re going to add in an electrical force. But what does electrical force have to do with Newton’s Laws?
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You can’t do an experiment on the planet without gravity playing some part of it (albeit sometimes so small you can ignore gravitational effects) since we’re in the Earth’s gravitational field. The electrical forces will add another force vector to our FBD that can be used when we look at how objects move in reaction to the forces.
Let’s take a look at how this works:
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How much charge do you think is inside a penny? What would happen if you could separate the positive and negative charges? How much force would each bundle of charge experience? Here’s how you find out:
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As a physics student, I wondered how much of a pulling force was between the nucleus of an atom and the electrons. Let’s look at the simplest atom (hydrogen) and find the attractive force between the proton and the electron:
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Wasn’t that incredible how much force was present just between the two? After I figured that out, I wanted to know how much “push” was present between two protons in the nucleus. If you think about it, there’s really no reason for the protons to stick together inside the nucleus because they are all positively charged. Let’s take a look at the iron atom as we figure this out…
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There are four types of forces. They are, in order of strength: the strong nuclear force, electromagnetism, weak nuclear force, and gravity. That’s it. Those are all the forces that do all the pushing and pulling in the entire universe. The strong and weak nuclear forces are responsible for holding atoms together. They are quite important as you can imagine!
What kind of forces do protons inside the nucleus of an atom experience? They are both positive charges, and really they don’t have any reason to stay together inside the nucleus as they’d be experiecing a repulsive force with each other. Let’s see exactly how big this repulsive force is:
Of all the forces, gravity is the weakling. It is actually much weaker than the other three. (In fact, in a way the other three have a tendency to pick on gravity, which isn’t very nice.)
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The Triboelectric Effect is a type of electrification that happens when you rub two different materials together and then separate them. Often, one will take on a positive charge and the other a negative. But how do you know which is going to be which?
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A bolt of lightning carries a LOT of extra excess electrons. We can calculate how much using a simple calculation.
No matter how hard you try, if you hae a copper rod that you rub with a cloth, you just can’t get a charge to build up on it. Why is that?
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You can use the idea that like charges repel (like two electrons) and opposites attract to move stuff around, stick to walls, float, spin, and roll. Make sure you do this experiment first.
I’ve got two different videos that use positive and negative charges to make things rotate, the first of which is more of a demonstration (unless you happen to have a 50,000 Volt electrostatic generator on hand), and the second is a homemade version on a smaller scale.
Did you know that you can make a motor turn using static electricity? Here’s how:
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Download Student Worksheet & Exercises
Here’s how the electrostatic machine works – you will need:
How does it work? Different parts of the atom have different electrical charges. The proton has a positive charge, the neutron has no charge (neutron, neutral get it?) and the electron has a negative charge. These charges repel and attract one another kind of like magnets repel or attract. Like charges repel (push away) one another and unlike charges attract one another.
So if two items that are both negatively charged get close to one another, the two items will try to get away from one another. If two items are both positively charged, they will try to get away from one another. If one item is positive and the other negative, they will try to come together.
How do things get charged? Generally things are neutrally charged. They aren’t very positive or negative. However, occasionally (or on purpose as we’ll see later) things can gain a charge. Things get charged when electrons move. Electrons are negatively charged particles. So if an object has more electrons than it usually does, that object would have a negative charge. If an object has less electrons than protons (positive charges), it would have a positive charge.
How do electrons move? It turns out that electrons can be kind of loosey-goosey. Depending on the type of atom they are a part of, they are quite willing to jump ship and go somewhere else. The way to get them to jump ship is to rub things together.
Remember, in static electricity, electrons are negatively charged and they can move from one object to another. This movement of electrons can create a positive charge (if something has too few electrons) or a negative charge (if something has too many electrons). It turns out that electrons will also move around inside an object without necessarily leaving the object. When this happens the object is said to have a temporary charge.
Try this: Blow up a balloon. When you rub the balloon on your head, the balloon is now filled up with extra electrons, and now has a negative charge. Now stick it to a wall— to create a temporary charge on a wall.
Opposite charges attract right? So, is the entire wall now an opposite charge from the balloon? No. In fact, the wall is not charged at all. It is neutral. So why did the balloon stick to it?
The balloon is negatively charged. It created a temporary positive charge when it got close to the wall. As the balloon gets closer to the wall, it repels the electrons in the wall. The negatively charged electrons in the wall are repelled from the negatively charged electrons in the balloon.
Since the electrons are repelled, what is left behind? Positive charges. The section of wall that has had its electrons repelled is now left positively charged. The negatively charged balloon will now “stick” to the positively charged wall. The wall is temporarily charged because once you move the balloon away, the electrons will go back to where they were and there will no longer be a charge on that part of the wall.
This is why plastic wrap, Styrofoam packing popcorn, and socks right out of the dryer stick to things. All those things have charges and can create temporary charges on things they get close to.
Want to purchase an electrostatic machine? Here’s a link to the one used in the video called a Wimshurst Machine which makes sparks up to 4″ long. For younger kids, we recommend this fun hand-held, non-shocking electrostatic generator.
Exercises
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Induction is another way to create a charge in an object. You can charge an object by induction without even touching it. I’ve got a couple of really neat experiments that will show you how this works, but here’s the basic idea: when you have two metal objects, like two soda cans, standing upright on a foam slab and just touching each other (so they are insulated from the table but in contact with each other), you can bring a charged balloon close to one of them and see a really interesting effect: the can closest to the charged balloon (which has a negative charge) will take on a positive charge, and the soda can furthest from the balloon will take on a negative charge. And when you separate the two cans, the charges on each will be evenly distributed over the surface of each can and remain polarized (the further can keeps its negative charge and the closer can keeps its positive charge). That’s charging by induction!
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Note that the net charge of the system was zero when you started, and is still zero when you finish, even though the electrons have moved and the charge on each can is different than when you started. Charge cannot be created or destroyed, however it can be transferred from one object to another by electrons. If you touch the soda can while you’re charging it, the electrons will enter your hand and “go to ground” and discharge your system. Humidity also does this using water vapor – the water molecules will dissipate your static charge build up so it looks like your static electricity experiments don’t work! However, if you bring a positively charged object near the soda cans and then touch the can, electrons will be attracted and actually create a larger static charge on the can.
This idea of “grounding” simply means that the excess charge (either positive or negative) can be removed by transferring electrons from something really big, like the Earth, that acts like a huge ocean of electrons.
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When high energy radiation strikes the Earth from space, it’s called cosmic rays. To be accurate, a cosmic ray is not like a ray of sunshine, but rather is a super-fast particle slinging through space. Think of throwing a grain of sand at a 100 mph… and that’s what we call a ‘cosmic ray’. Build your own electroscope with this video!
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Materials:
Download Student Worksheet & Exercises
Troubleshooting: This device is also known as an electroscope, and its job is to detect static charges, whether positive or negative. The easiest way to make sure your electroscope is working is to rub your head with a balloon and bring it near the foil ball on top – the foil “leaves” inside the jar should spread apart into a V-shape.
Exercises
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Jupiter not only has the biggest lightning bolts we’ve ever detected, it also shocks its moons with a charge of 3 million amps every time they pass through certain hotspots. Some of these bolts are cause by the friction of fast-moving clouds. Today you get to make your own sparks and simulate Jupiter’s turbulent storms.
Electrons are too small for us to see with our eyes, but there are other ways to detect something’s going on. The proton has a positive charge, and the electron has a negative charge. Like charges repel and opposite charges attract.
Materials
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Download Student Worksheet & Exercises
If you rub a balloon on your head, the balloon becomes filled up with extra electrons, and now has a negative charge. Try the following experiment to create a temporary charge on a wall: Bring the balloon close to the wall until it sticks.
Opposite charges attract right? So, is the entire wall now an opposite charge from the balloon? No. In fact, the wall is not charged at all. It is neutral. So why did the balloon stick to it?
The balloon is negatively charged. It created a temporary positive charge when it got close to the wall. As the balloon gets closer to the wall, it repels the electrons in the wall. The negatively charged electrons in the wall are repelled from the negatively charged electrons in the balloon.
Since the electrons are repelled, what is left behind? Positive charges. The section of wall that has had its electrons repelled is now left positively charged. The negatively charged balloon will now “stick” to the positively charged wall. The wall is temporarily charged because once you move the balloon away, the electrons will go back to where they were and there will no longer be a charge on that part of the wall.
This is why plastic wrap, Styrofoam packing popcorn, and socks right out of the dryer stick to things. All those things have charges and can create temporary charges on things they get close to.
If you rub a balloon all over your hair, the Triboelectric Effect causes the electrons to move from your head to the balloon. But why don’t the electrons go from the balloon to your head? The direction of electron transfer has to do with the properties of the material itself. And the balloon-hair combination isn’t the only game in town.
Electrons move differently depending on the materials that are rubbed together. A balloon takes on a negative charge when rubbed on hair. Today, the kids are going to find when a foam plate is rubbed with wool, the plate takes on electrons and creates a negative charge on the plate. To give the plate a positive charge, kids can rub it with a plastic bag.
The Triboelectric Series is a list that ranks different materials according to how they lose or gain electrons. A rubber rod rubbed with wool produces a negative charge on the rod, however an acrylic rod rubbed with silk creates a positive charge on the rod. A foam plate often has a positive charge when you slide one off the stack, but if you rub it with wool it will build up a negative charge.
Near the top of the list are materials that take on a positive charge, such as air, human skin, glass, rabbit fur, human hair, wool, silk, and aluminum. Near the bottom of the list are materials that take on a negative charge, such as amber, rubber balloons, copper, brass, gold, cellophane tape, Teflon, and silicone rubber. Scientists developed this list by doing a series of experiments, very similar to the ones we’re about to do.
Exercises
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Einstein received a Nobel Prize for figuring out what happens when you shine blue light on a sheet of metal. When he aimed a blue light on a metal plate, electrons shot off the surface. (Metals have electrons which are free to move around, which is why metals are electrically conductive. More on this in Unit 10).
When Einstein aimed a red light at the metal sheet, nothing happened. Even when he cranked the intensity (brightness) of the red light, still nothing happened. So it was the energy of the light (wavelength), not the number of photons (intensity) that made the electrons eject from the plate. This is called the ‘photoelectric effect’. Can you imagine what happens if we aim a UV light (which has even more energy than blue light) at the plate?
This photoelectric effect is used by all sorts of things today, including solar cells, electronic components, older types of television screens, video camera detectors, and night-vision goggles.
This photoelectric effect also causes the outer shell of orbiting spacecraft to develop an electric charge, which can wreck havoc on its internal computer systems.
A surprising find was back in the 1960s, when scientists discovered that moon dust levitated through the photoelectric effect. Sunlight hit the lunar dust, which became (slightly) electrically charged, and the dust would then lift up off the surface in thin, thread-like fountains of particles up ¾ of a mile high.
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Materials:
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Ygou can also charge objects by conduction. You’ve actually already done with without really thinking about it. The foil on the wire coat hanger in the electroscope was being charged by conduction. When you touch a charged balloon to the foil ball on the electroscope, that’s a charge by conduction. If you were to get the charged balloon really close but not touching the foil ball, that would be charging by induction. (See the difference?) Charging by conduction just means that you need to touch the electrically neutral object to the one that is charged to transfer the charge. It’s charge by contact.
With charge by induction, it’s the forces due to likes repelling and opposites attracting that cause the charge in objects. With conduction, it’s the actual movement of electrons to the object that make the charge in the object. This is obvious if you think about touching two soda cans together, since they are both made out of a material that allows electrons to move about freely within the material (on the surface of the object). But what about two insulators, like two foam plates? What happens then?
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Insulators do not conduct charge the way that conductors do. Even if two foam plates are touching, charge can not be conducted from one foam plate to another, or even from a foam plate to a soda can. However the foam plate can polarize the soda can through electrical forces (opposite charges attracting and lie charges repelling).
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This experiment is just for advanced students. If you guessed that this has to do with electricity and chemistry, you’re right! But you might wonder how they work together. Back in 1800, William Nicholson and Johann Ritter were the first ones to split water into hydrogen and oxygen using electrolysis. (Soon afterward, Ritter went on to figure out electroplating.) They added energy in the form of an electric current into a cup of water and captured the bubbles forming into two separate cups, one for hydrogen and other for oxygen.
This experiment is not an easy one, so feel free to skip it if you need to. You don’t need to do this to get the concepts of this lesson but it’s such a neat and classical experiment (my students love it) so you can give it a try if you want to. The reason I like this is because what you are really doing in this experiment is ripping molecules apart and then later crashing them back together.
Have fun and please follow the directions carefully. This could be dangerous if you’re not careful. The image shown here is using graphite from two pencils sharpened on both ends, but the instructions below use wire. Feel free to try both to see which types of electrodes provide the best results.
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You will need:
Download Student Worksheet & Exercises
1. Fill the cup with water.
2. Put a tablespoon or so of salt into the water and stir it up. (The salt allows the electricity to flow better through the water.)
2. Put one wire into the test tube and rubber band it to the test tube so that it won’t come out (see picture).
3. Use the masking tape to attach both wires to the battery. Make sure the wire that is in the test tube is connected to the negative (-) pole of the battery and that the other is connected to the positive (+) pole. Don’t let the bare parts of the different wires touch. They could get very hot if they do.
4. Fill the test tube to the brim with the salt water.
5. This is the tricky part. Put your finger over the test tube, turn it over and put the test tube, open side down, into the cup of water. (See picture.)
6. Now put the other wire into the water. Be careful not to let the bare parts of the wires touch.
7. You should see bubbles rising into the test tube. If you don’t see bubbles, check the other wire. If bubbles are coming from the other wire either switch the wires on the battery connections or put the wire that is bubbling into the test tube and remove the other. If you see no bubbles check the connections on the battery.
8. When the test tube is half full of gas (half empty of salt water depending on how you look at it) light the long match or the wooden stick. Then take the test tube out of the water and let the water drain out. Holding the test tube with the open end down, wait for five seconds and put the burning stick deep into the test tube (the flame will probably go out but that’s okay). You should hear an instant pop and see a flash of light. If you don’t, light the stick again and try it another time. For some reason, it rarely works the first time but usually does the second or third.
A water molecule, as you saw before, is two hydrogen atoms and one oxygen atom. The electricity encouraged the oxygen to react with the copper wire leaving the hydrogen atoms with no oxygen atom to hang onto. The bubbles you saw were caused by the newly released hydrogen atoms floating through the test tube in the form of hydrogen gas. Eventually that test tube was part way filled with nothing but pure hydrogen gas.
But how do you know which bubbles are which? You can tell the difference between the two by the way they ignite (don’t’ worry – you’re only making a tiny bit of each one, so this experiment is completely safe to do with a grown up).
It takes energy to split a water molecule. (On the flip side, when you combine oxygen and hydrogen together, it makes water and a puff of energy. That’s what a fuel cell does.) Back to splitting the water molecule – as the electricity zips through your wires, the water molecule breaks apart into smaller pieces: hydrogen ions (positively charged hydrogen) and oxygen ions (negatively charged oxygen). Remember that a battery has a plus and a minus charge to it, and that positive and negative attract each other.
So, the positive hydrogen ions zip over to the negative terminal and form tiny bubbles right on the wire. Same thing happens on the positive battery wire. After a bit of time, the ions form a larger gas bubble. If you stick a cup over each wire, you can capture the bubbles and when you’re ready, ignite each to verify which is which.
If the match burns brighter, the gas is oxygen. If you hear a POP!, the gas is hydrogen. Oxygen itself is not flammable, so you need a fuel in addition to the oxygen for a flame. In one case, the fuel is hydrogen, and hence you hear a pop as it ignites. In the other case, the fuel is the match itself, and the flame glows brighter with the addition of more oxygen.
When you put the match to it, the energy of the heat causes the hydrogen to react with the oxygen in the air and “POP”, hydrogen and oxygen combine to form what? That’s right, more water. You have destroyed and created water! (It’s a very small amount of water so you probably won’t see much change in the test tube.)
The chemical equations going on during this electrolysis process look like this:
A reduction reaction is happening at the negatively charged cathode. Electrons from the cathode are sticking to the hydrogen cations to form hydrogen gas:
2 H+(aq) + 2e– –> H2(g)
2 H2O(l) + 2e– –> H2(g) + 2 OH–(aq)
The oxidation reaction is occurring at the positively charged anode as oxygen is being generated:
2 H2O(l) –> O2(g) + 4 H+(aq) + 4e–
4 OH–(aq) –> O2(g) + 2 H2O(l) + 4 e-
Overall reaction:
2 H2O(l) –> 2 H2(g) + O2(g)
Note that this reaction creates twice the amount of hydrogen than oxygen molecules. If the temperature and pressure for both are the same, you can expect to get twice the volume of hydrogen to oxygen gas (This relationship between pressure, temperature, and volume is the Ideal Gas Law principle.)
This is the idea behind vehicles that run on sunlight and water. They use a solar panel (instead of a 9V battery) to break apart the hydrogen and oxygen and store them in separate tanks, then run them both back together through a fuel cell, which captures the energy (released when the hydrogen and oxygen recombine into water) and turns the car’s motor. Cool, isn’t it?
Note: We’re going to focus on Alternative Energy in Unit 12 and create all sorts of various energy sources including how to make your own solar battery, heat engine, solar & fuel cell vehicles (as described above), and more!
Exercises
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Let’s try another way to look at this. You’re playing miniature golf and you come to the old wind mill hole. Your friend takes a shot and since the blades of the windmill are going nice and slow he gets the ball right through. Now it’s your turn. Suddenly you hear a zap and a pow and sparks go flying. Something has gone wrong with the wind mill and it starts spinning at amazing speeds. You decide to give it a try and hit the ball towards the wind mill.
Well since it is spinning out of control, those blades now form almost a solid disk so that there is no way your ball can get through the wind mill. Electrons do the same thing. They move so fast that even though there may not be many of them, they form a shell that can’t be penetrated. (To be clear, particles that are smaller than an atom can go through the shells and pop out the other side.)
Let’s go a little further with this shell thing. An atom can have as few as one and as many as seven shells. Imagine our balloon again. Now there can be a balloon inside of a balloon inside a balloon and so on. Up to seven balloons! Each balloon, whoops, I mean shell, can have only so many electrons in it. This simple equation 2n2 tells you how many electrons can be in each shell. The n stands for the number of the shell.
The first shell can have up to 2 x 1(first shell)2 or 2 electrons. The second shell can have up to 2 x 2(second shell)2 or 8 electrons. The third shell can have up to 2 x 32 or 18 electrons. The fourth shell can have up to 2 x 42 or 32 electrons. All the way up to the seventh shell which can have 2 x 72 or 98 electrons!
One last thing about shells, the shells have to be full before the electrons will go to the next shell. A helium atom will have two electrons. Both of them will be in the first shell. A Lithium atom will have three electrons. Two will be in the first shell and one (since the first shell is filled) will be in the second shell.
Electrons provide the size and stability of the atom and, as such, the mass and the structure of all matter. Electrons are also the key to all electromagnetic energy. But wait, that’s not all! It is the number of electrons in an atom that determines if and how atoms come together to form molecules. Electrons determine how and what matter will be.
Atoms like to feel satisfied and they feel satisfied if they are “full”. An atom is “full” if its outer electron shell has as many electrons as it can hold or if there are eight or a multiple of eight (16, 24 etc.) electrons in the outer shell. This is called the octet rule and works most of the time, but is not perfect.
If an atom is not full, it is not satisfied. An unsatisfied atom needs to do something with its electrons to be happy. Luckily atoms are very friendly and love to share. Most atoms are not satisfied as individuals. The oxygen atom has six electrons in its outer shell. It needs eight electrons to be satisfied.
Luckily, two Hydrogen atoms happen by. Each one of them has only one electron in its outer shell and needs one more to be satisfied. If both Hydrogens share their one electron with the Oxygen, the oxygen has eight electrons and is satisfied. Also, if the Oxygen shares an electron with each Hydrogen, then both Hydrogens are satisfied as well. Just like your mother told you, it’s nice to share. It is this sharing of electrons that makes atoms come together to form molecules.
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To summarize, protons and neutrons are in the nucleus of an atom, and tightly bound together. The proton has a positive charge while the neutron has no charge, and both of them are much larger than the electron. The tiny electron is outside the nucleus and weakly bound to the atom and carries a negative a charge.
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Go get a balloon. The rubber latex kind work the best (not the shiny Mylar kind). You’ll need it for the next set of experiments we’re going to talk about below. When you rub a balloon on your head, you charge up the balloon with a negative static charge. But how much charge is it? The units of charge are called the Coulomb (C), just like the units of time are seconds (s). And just like seconds, you can have microseconds (10-6 seconds) and nanoseconds (10-9 seconds), you can have microCoulombs (10-6 C or μC) and nanoCoulombs (10-9 C or nC).
The charge of one electron is -1.6 x 10-19 C… it’s a really small number! The charge of one proton is +1.6 x 10-19 C. The kind of charge (whether positive or negative) is determined by how many extra protons or electrons are present in addition to the ones that are evenly matched to balance the charge. If an object has 15 protons and 17 electrons, then it’s got a negative charge by 2 electrons. Just because an object is not charged (electrically neutral) doesn’t mean it doesn’t have any protons or electrons. Rather it means that the number of electrons and protons are evenly matched to balance the charge of the object. We say that charge is quantized, which means that electric charge isn’t a continuous fluid flow, but instead is made up of tiny packets of charged particles. The charge on one electron is -1.60 x 10-19 C. This is one of the most fundamental concepts in physics!
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Let’s go back to rubbing a balloon on your head. When you do this and bring it close to objects like a thin stream of water trickling out of the faucet, or small its of paper, or bubbles in the air, or even a ping pong ball on the table, did you notice now you can influence things? You can make water flick and spray, paper jump up and down, and bubbles and ping pong balls will follow your every move. But why is that?
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The influence you’re exerting on these objects is called the electric force, which is a non-contact force that can happen over a distance.
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Did you notice that you can exert a force on an object without touching it? Try it now if you haven’t already! Did you notice how opposite charges attract and like charges repel? That’s the fundamental key concept with this section. Electrical force are the attractive for opposite charges and repulsive for like charges. Electrical force is also attractive between a charged and a neutral object.
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Certain materials conduct electricity better than others.
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An electrical circuit is like a NASCAR raceway. The electrons (racecars) zip around the race loop (wire circuit) superfast to make stuff happen. Although you can’t see the electrons zipping around the circuit, you can see the effects: lighting up LEDs, sounding buzzers, clicking relays, etc.
There are many different electrical components that make the electrons react in different ways, such as resistors (limit current), capacitors (collect a charge), transistors (gate for electrons), relays (electricity itself activates a switch), diodes (one-way street for electrons), solenoids (electrical magnet), switches (stoplight for electrons), and more. We’re going to use a combination diode-light-bulb (LED), buzzers, and motors in our circuits right now.
A CIRCUIT looks like a CIRCLE. When you connect the batteries to the LED with wire and make a circle, the LED lights up. If you break open the circle, electricity (current) doesn’t flow and the LED turns dark.
LED stands for “Light Emitting Diode”. Diodes are one-way streets for electricity – they allow electrons to flow one way but not the other.
Remember when you scuffed along the carpet? You gathered up an electric charge in your body. That charge was static until you zapped someone else. The movement of electric charge is called electric current, and is measured in amperes (A). When electric current passes through a material, it does it by electrical conduction. There are different kinds of conduction, such as metallic conduction, where electrons flow through a conductor (like metal) and electrolysis, where charged atoms (called ions) flow through liquids.
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Here’s what you need:
Download Student Worksheet & Exercises
Be alert for:
1. Batteries inserted into the case the wrong way!
2. LED in the wrong way (LEDs are picky about plus and minus – they are POLARIZED)
3. Is there a metal-to-metal connection? (You’re not grabbing ahold of the plastic insulation, are you?)
4. Bad wires can cause headaches – if all else fails, then swap out your alligator clip lead wires for new ones.
Exercises
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Make yourself a grab bag of fun things to test: copper pieces (nails or pipe pieces), zinc washers, pipe cleaners, Mylar, aluminum foil, pennies, nickels, keys, film canisters, paper clips, load stones (magnetic rock), other rocks, and just about anything else in the back of your desk drawer.
Certain materials conduct electricity better than others. Silver, for example, is one of the best electrical conductors on the planet, followed closely by copper and gold. Most scientists use gold contacts because, unlike silver and copper, gold does not tarnish (oxidize) as easily. Gold is a soft metal and wears away much more easily than others, but since most circuits are built for the short term (less than 50 years of use), the loss of material is unnoticeable.
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Modify your basic LED circuit into a Conductivity Circuit by removing one clip lead from the battery and inserting a third clip lead to the battery terminal. The two free ends are your new clips to put things in from the grab bag. Try zippers, metal buttons, barrettes, water from a fountain, the fountain itself, bike racks, locks, doorknobs, unpainted benches… you get the idea!
Here’s what you need:
Why does metal, not plastic, conduct electricity? Imagine you have a garden hose with water flowing through it. The hose is like the metal wire, and the water is like the electric current. Trying to run electricity through plastic is like filling your hose with cement. It’s just the nature of the material.
Download Student Worksheet & Exercises
Exercises
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When an atom (like hydrogen) or molecule (like water) loses an electron (negative charge), it becomes an ion and takes on a positive charge. When an atom (or molecule) gains an electron, it becomes a negative ion. An electrolyte is any substance (like salt) that becomes a conductor of electricity when dissolved in a solvent (like water).
This type of conductor is called an ‘ionic conductor’ because once the salt is in the water, it helps along the flow of electrons from one clip lead terminal to the other so that there is a continuous flow of electricity.
This experiment is an extension of the Conductivity Tester experiment, only in this case we’re using water as a holder for different substances, like sugar and salt. You can use orange juice, lemon juice, vinegar, baking powder, baking soda, spices, cornstarch, flour, oil, soap, shampoo, and anything else you have around. Don’t forget to test out plain water for your ‘control’ in the experiment!
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Here’s what you need:
Download Student Worksheet & Exercises
Exercises
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When I was in 10th grade, my teammate and I designed what we thought was pretty clever: a superconductor roller coaster, which we imagined would float effortlessly above its magnetic track. Of course, our roller coaster was only designed on paper, because yttrium barium copper oxide ceramics had only just been discovered by top scientists.
Did you notice how it was smoking in the video? That’s because it was so cold! The usual problem with superconductors is that they need to be incredibly cold in order to exhibit superconductive properties. Yttrium barium copper oxide (YBa2Cu3O7) was the first compound that used liquid nitrogen for cooling, making superconductors a lot less expensive to work with – you no longer needed a cryogenic lab in order to levitate objects above a magnet.
Recently, scientists have found a way to make an amazing superconductor by taking a single crystal sapphire wafer and coating it with a thin (~1µm thick) ceramic material (yttrium barium copper oxide). Normally, the ceramic layer has no interesting magnetic or electrical properties, but that’s when you’re looking at it at room temperature. If you cool this material below -185ºC (-301ºF), it turns out that the ceramic material becomes a superconductor, meaning that it conducts electricity without resistance, with no energy loss. Zero. That’s what makes it a ‘superconductor’.
To further understand superconductivity, it’s helpful to understand what normally happens to electricity as it flows through a wire. As you may know, energy cannot be created or destroyed, but can be changed from one form to another.
In the case of wires, some of the electrical energy is changed to heat energy. If you’ve ever touched a wire that had been in use for a while, and discovered it was hot, you’ve experienced this. The heat energy is a waste. It simply means that less electricity gets to its final destination.
This is why superconductivity is so cool (no pun intended.) By cooling things down to temperatures near absolute zero, which is as low as temperatures can get, you can create a phenomenon where electricity flows without having any of it converted to heat.
Scientists also figured out that superconductors and magnetic field really do not like each other. The Meissner effect happens when a superconductor expels all its magnetic fields from inside.
However, if you make your superconductor thin enough, you can get the magnetic field to penetrate in discrete quantities (this is real quantum physics now) called flux tubes (the blue lines that go through the disc).
Inside each of the magnetic flux tubes, the superconductivity is destroyed, but the superconductor tries to keep the magnetic tubes pinned in weak areas and any movement of the superconductor itself (like if you pushed it) causes the flux tubes to move, and this is what traps (or locks) the superconductor in midair.
If you’d like to experiment with superconductors yourself, check out this information.
Have you ever had a bad hair day? Did you happen to notice if the air was drier or wetter weather on those days? Usually folks have bad hair days when the air is drier, which is when static charge can build up more easily. Some folks notice every time they touch a doorknob, slide down a plastic slide, or scuff along the carpet in socks that they get zapped. Since there’s less water vapor in the air on drier days, there’s more of a chance for static charge to build up. The water molecule dissipates the static charge, and the more wet the air is (humid), the less static build up there is. Static electricity experiments are really hard to do on humid days, especially if it’s raining outside!
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Can you rub a balloon and stick it to the wall? Why does that work? The wall isn’t positively charged, is it?
No… the wall is not charged at all. It’s electrically neutral. However, when you bring a negatively charged balloon near it, two important things happen: the negative charge on the balloon repels the negative charges in the wall, pushing them further away. At the same time, the positive charges in the wall are attracted to the balloon and move toward it. The result is that the balloon sticks to the wall, and you have just moved charges around in the wall without even realizing it. Polarization means that you separate the charges in an object. The wall became polarized when you brought the balloon close to it.
Like charges repel and opposites attract.This happens in neutrally charged objects, like the yardstick in the electrostatic motor that you’ve done previously on this page. If the object is a conductor, like a metal, the charges move quickly from one side of the object to the other quite freely along the surface.
However if the object is an insulator, the electrons simply redistribute themselves within the atom, since the charges can’t move along the surface as they would with a conductor. The electrons live in an electron cloud that surrounds the nucleus of the atom, which normally is uniform and symmetrical. When an electrical charge is applied to insulators, that cloud will distort and become non-symmetrical as the electrons move in response. In this way, insulators can be polarized.
Water is a polar molecule. In a molecule, the atoms stay together to form the molecule through bonds that are formed between the negative and positive charges on the individual atoms. For water, the oxygen and hydrogen have a polar bond because the protons in one are attracted to the electrons in the other. The electrons are shared and their electron clouds overlap.
For water however, the electrons within the clouds are not equally shared which makes the electron cloud distorted, making one side of the water molecule more negatively electrically charged than the other. This makes water a polar molecule because the electron cloud is shifted more toward the oxygen than the hydrogen atoms.
When you bring a charged balloon near a thin trickle of water streaming from the faucet, the stream is deflected and sprayed by the presence of the balloon because the water molecules are polar and align to the balloon.
Just a quick tip: don’t mix up the concepts of polarizing and charging. Charging is when there’s an imbalance of electric charge, like rubbing the balloon on your head. The balloon now has an excess number of electrons, so it’s negatively charged. Objects that are polarized have their charges separated either on the surface or within the atom itself. The overall charge of a polarized object is balanced (electrically neutral), even if the negative charges are at one end and positive charges are on the other.
Scientific Concepts for Atoms:
Scientific Concepts for Electrons:
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Johannes Kepler, a German mathematician and astronomer in the 1600s, was one of the key players of his time in astronomy. Among his best discoveries was the development of three laws of planetary orbits. He worked for Tycho Brahe, who had logged huge volumes of astronomical data, which was later passed onto to Kepler. Kepler took this information to design and develop his ideas about the movements of the planets around the Sun.
Kepler’s 1st Law states that planetary orbits about the Sun are not circles, but rather ellipses. The Sun lies at one of the foci of the ellipse.
Well, almost.
Newton’s Laws of Motion state that the Sun can’t be stationary, because the Sun is pulling on the planet just as hard as the planet is pulling on the Sun. They are yanking on each other. The planet will move more due to this pulling because it is less massive. The real trick to understanding this law is that both objects orbit around a common point that is the center of mass for both objects. If you’ve ever swung a heavy bag of oranges around in a circle, you know that you have to lean back a bit to balance yourself as you swing around and around. It’s the same principle, just on a smaller scale.
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In our solar system the Sun has 99.85% of the mass, so the center of mass between the Sun and any other object actually lies inside the Sun (although not at the center).
Kepler’s 2nd Law states that a line connecting the Sun and an orbiting planet will sweep out equal areas in for a given amount of time. The planet’s speed decreases the further from the Sun it is located (actually, the speed varies inversely with the square‐root of the distance, but you needn’t worry about that).
You can see this for yourself by tying a ball to the end of a string and whirl it around in a circle. After a few revolutions, let the string wind itself up around your finger. As the string length shortens, the ball speeds up. As the planet moves inward, the planet’s orbital speed increases.
Embedded in the second law are two very important laws: conservation of angular moment and conservation of energy. Although those laws might sound scary, they are not difficult to understand. Angular momentum is distance multiplied by mass multiplied by speed. The angular momentum for one case must be the same for the second case (otherwise it wouldn’t be conserved). As the planet moves in closer to the Sun, the distance decreases. The speed it orbits the Sun must increase because the mass doesn’t change. Just like you saw when you wound the ball around your finger.
Energy is the sum of both the kinetic (moving) energy and the potential energy (this is the “could” energy, as in a ball dropped from a tower has more potential energy than a ball on the ground, because it “could” move if released). For conservation of energy, as the planet’s distance from the Sun increases, so does the gravitational potential energy. Again, since the energy for the first case must equal the energy from the second case (that’s what conservation means), the kinetic energy must decrease in order to keep the total energy sum a constant value.
Kepler’s 3rd Law is an equation that relates the revolution period with the average orbit speed.
The important thing to note here is that mass was not originally in this equation. Newton came along shortly after and did add in the total mass of the system, which fixed the small error with the equation. This makes sense, as you might imagine a Sun twice the size would cause the Earth to orbit faster. However, if we double the mass of the Earth, it does not affect the speed with which it orbits the Sun. Why not? Because the Earth is soooo much smaller than the Sun that increasing a planet’s size generally doesn’t make a difference in the orbital speed. If you’re working with two objects about the same size, of course, then changing one of the masses absolutely has an effect on the other.
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Kepler’s Laws of planetary orbits explain why the planets move at the speeds they do. You’ll be making a scale model of the solar system and tracking orbital speeds.
Kepler’s 1st Law states that planetary orbits about the Sun are not circles, but rather ellipses. The Sun lies at one of the foci of the ellipse. Kepler’s 2nd Law states that a line connecting the Sun and an orbiting planet will sweep out equal areas in for a given amount of time. Translation: the further away a planet is from the Sun, the slower it goes.
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Download Student Worksheet & Exercises
What are the planets in our solar system starting closest to the Sun? On a sheet of paper, write down a planet and label it with the name. Do this for each of the eight planets.
Of course, we don’t travel to planets in straight lines – we use curved paths to make use of the gravitational pull of nearby objects to slingshot us forward and save on fuel.
Now for the fun part! You’ll need a group of friends to work together for this lab, so you have at least one student for each planet, one for the Sun, and two for the asteroid belts, and five for the dwarf planets. You can assign additional students to be moons of Earth (Moon), Mars (Phobos and Deimos), Jupiter (assign only 4 for the largest ones: Ganymede, Callisto, Io, and Europa), Saturn (again, assign only 4: Titan, Rhea, Iapetus, and Dione), Uranus (Oberon, Titania), and Neptune (Triton). If you still have extra students, assign one to Charon (Pluto’s binary companion) and one each to Hydra and Nix, which orbit Pluto and Charon. While you ask the students to walk around in a later step, the moons can circle while they orbit.
Johannes Kepler, a German mathematician and astronomer in the 1600s, was one of the key players of his time in astronomy. Among his best discoveries was the development of three laws of planetary orbits. He worked for Tycho Brahe, who had logged huge volumes of astronomical data, which was later passed onto to Kepler. Kepler took this information to design and develop his ideas about the movements of the planets around the Sun.
Kepler’s 1st Law states that planetary orbits about the Sun are not circles, but rather ellipses. The Sun lies at one of the foci of the ellipse. Well, almost. Newton’s Laws of Motion state that the Sun can’t be stationary, because the Sun is pulling on the planet just as hard as the planet is pulling on the Sun. They are yanking on each other. The planet will move more due to this pulling because it is less massive. The real trick to understanding this law is that both objects orbit around a common point that is the center of mass for both objects. If you’ve ever swung a heavy bag of oranges around in a circle, you know that you have to lean back a bit to balance yourself as you swing around and around. It’s the same principle, just on a smaller scale.
In our solar system the Sun has 99.85% of the mass, so the center of mass between the Sun and any other object actually lies inside the Sun (although not at the center).
Kepler’s 2nd Law states that a line connecting the Sun and an orbiting planet will sweep out equal areas in for a given amount of time. The planet’s speed decreases the further from the Sun it is located (actually, the speed varies inversely with the square‐root of the distance, but you needn’t worry about that). You can demonstrate this to the students by tying a ball to the end of a string and whirl it around in a circle. After a few revolutions, let the string wind itself up around your finger. As the string length shortens, the ball speeds up. As the planet moves inward, the planet’s orbital speed increases.
Embedded in the second law are two very important laws: conservation of angular moment and conservation of energy. Although those laws might sound scary, they are not difficult to understand. Angular momentum is distance multiplied by mass multiplied by speed. The angular momentum for one case must be the same for the second case (otherwise it wouldn’t be conserved). As the planet moves in closer to the Sun, the distance decreases. The speed it orbits the Sun must increase because the mass doesn’t change. Just like you saw when you wound the ball around your finger.
Energy is the sum of both the kinetic (moving) energy and the potential energy (this is the “could” energy, as in a
ball dropped from a tower has more potential energy than a ball on the ground, because it “could” move if released). For conservation of energy, as the planet’s distance from the Sun increases, so does the gravitational potential energy. Again, since the energy for the first case must equal the energy from the second case (that’s what conservation means), the kinetic energy must decrease in order to keep the total energy sum a constant value.
Kepler’s 3rd Law is an equation that relates the revolution period with the average orbit speed. The important thing to note here is that mass was not originally in this equation. Newton came along shortly after and did add in the total mass of the system, which fixed the small error with the equation. This makes sense, as you might imagine a Sun twice the size would cause the Earth to orbit faster. However, if we double the mass of the Earth, it does not affect the speed with which it orbits the Sun. Why not? Because the Earth is soooo much smaller than the Sun that increasing a planet’s size generally doesn’t make a difference in the orbital speed. If you’re working with two objects about the same size, of course, then changing one of the masses absolutely has an effect on the other.
Exercises
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If one of Kepler’s Laws describe the orbits of satellites as being an elliptical orbit, you might be wondering what an ellipse is! Here’s a really neat way to make an ellipse using a pencil and a rubber band:
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Let’s try a few practice problems so you get more familiar with how to use and apply Kepler’s Laws to real world physics problems…
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A satellite is an object that orbits the sun, earth or other massive body like a planet, moon, asteroid, or even galaxy. There are two kinds of satellites: natural, like the moon, and man-made, like the Hubble Space Telescope.
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But physics doesn’t care if a satellite is man-made or not. The laws of physics and math equations still apply no matter where the satellite came from.
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An important concept to understand is that a satellite is a projectile, meaning that only the force of gravity is acted on it (once it’s launched). In order to maintain it’s orbit, a satellite needs to fall continuously at the same rate that the earth is curving away from it.
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The Hubble Space Telescope (HST) zooms around the Earth once every 90 minutes (about 5 miles per second), and in August 2008, Hubble completed 100,000 orbits! Although the HST was not the first space telescope, is the one of the largest and most publicized scientific instrument around. Hubble is a collaboration project between NASA and the ESA (European Space Agency), and is one of NASA’s “Great Observatories” (others include Compton Gamma Ray Observatory, Chandra X-Ray Observatory, and Spitzer Space Telescope). Anyone can apply for time on the telescope (you do not need to be affiliated with any academic institution or company), but it’s a tight squeeze to get on the schedule.
Hubble’s orbit zooms high in the upper atmosphere to steer clear of the obscuring haze of molecules in the sea of air. Hubble’s orbit slowly decays over time and begins to spiral back into Earth until the astronauts bump it back up into a higher orbit.
But how does a satellite stay in orbit? Try this experiment now:
Materials:
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Download Student Worksheet & Exercises
Troubleshooting: Expect to find marbles flying everywhere with this experiment! This quick activity demonstrates the idea of centripetal (centrifugal) acceleration. What happens when you circle the cone too slow or too fast? The marble itself is the satellite (like HST), and the cone’s apex (tip) is the Earth. When the marble zooms around too slow, it falls back into the Earth. So what keeps it up in “orbit”?
The faster an object moves, the greater the acceleration against the force of gravity (toward the Earth in this case). Think back to the Physics lab – when a marble went too slow through the roller coaster loop, it crashed back to the floor. When it went too fast, it flew off the track. There was a certain speed that was needed for the marble to stay in the loop and on course. The same is true for satellites in outer space.
If you have trouble with this experiment, just replace the paper cone with a disposable cup with a lid and try again (with the lid in place), and see if you can keep the marble circling around the top rim.
Exercises
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Kepler’s Law of Periods relates the period T of any planet around the sun to the cube of the semi-major axis a of the orbit:
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If T is in earth years, a is in AU (1 AU = distance from the sun to the earth), and M = solar mass, then the equation above reduces to: T2 = a3.
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A satellite is an object that does around a planet, a star, or other similar object. Here’s how you can figure out the net force of a satellite as well as the velocity of the satellite, since the only force applied to the satellite is from gravity:
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For a satellite orbiting around the earth at a given distance. What is the speed and acceleration of the satellite? Do you think you need to know the masses of the satellite and the earth, or just one?
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Here’s an overview of all the equations we’ve been using so far for our study in uniform circular motion:
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How fast does the moon travel around the earth? And how far away is the moon really? Here’s a way to figure out!
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Callisto is one of Jupiter’s moons. Would it be really cool to be able to approximate the size of Jupiter based on watching the motion of Callisto? For example, if you knew how long it took Callisto to orbit around Jupiter, and the furthest distance it traveled away from it (both of which you could measure from a backyard telescope)? Here’s how:
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One of the questions I get asked a lot is how fast does the International Space Station travel around the Earth? Here’s how to figure this out (hint: it’s a lot like the one we did previously with Jupiter and Callisto!)
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Finding the Mass of the Earth Now let’s estimate the mass of the Earth. You already know what it is (because we’ve been using it a lot in our previous calculations), so let’s pretend we don’t know and figure out first-hand.
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Comet Hally takes 76 years to orbit around the sun, and in 1986 it came as close as it possibly could to the sun (89,000,000 km). Can we figure out how far the comet gets from the sun based on this information? Sure! Here’s how:
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So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change but since weight is a measure for how much gravity is pulling on you, weight will change. Did you notice that I put weightless in quotation marks? Wonder why?
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Weightlessness is a myth! Believe it or not, one is never weightless. A person can be pretty close to weightless in very deep space but the astronauts in a space ship actually do have a bit of weight.
Think about it for a second. If a space ship is orbiting the Earth what is it doing? It’s constantly falling! If it wasn’t moving forward at 10’s of thousands of miles an hour it would hit the Earth. It’s moving fast enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us.
Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling too! The astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
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Now let’s have fun with an elevator and a bathroom scale, since we can’t easily jump ourselves into orbit.
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Now let’s bust the myth of weightlessness in space for good…
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A binary system exists when objects approach each other in size (and gravitational fields), the common point they rotate around (called the center of mass) lies outside both objects and they orbit around each other. Astronomers have found binary planets, binary stars, and even binary black holes.
The path of a planet around the Sun is due to the gravitational attraction between the Sun and the planet. This is true for the path of the Moon around the Earth, and Titan around Saturn, and the rest of the planets that have an orbiting moon.
Materials
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Download Student Worksheet & Exercises
The path of a planet around the Sun is due to the gravitational attraction between the Sun and the planet. This is true for the path of the Moon around the Earth, and Titan around Saturn, and the rest of the planets that have an orbiting moon.
Charon and Pluto orbit around each other due to their gravitational attraction to each other. However, Charon is not the moon of Pluto, as originally thought. Pluto and Charon actually orbit around each other. Pluto and Charon also are tidally locked, just like the Earth-Moon system, meaning that one side of Pluto is always faces the same side of Charon.
Imagine you have a bucket half full of water. Can you tilt a bucket completely sideways without spilling a drop? Sure thing! You can swing it by the handle, and even though it’s upside down at one point, the water stays put. What’s keeping the water inside the bucket?
Before we answer this, imagine you are a passenger in a car, and the driver is late for an appointment. They take a turn a little too fast, and you forgot to fasten your seat belts. The car makes a sharp left turn. Which way would you move in the car if they took this turn too fast? Exactly – you’d go sliding to the right. So, who pushed you?
No one! Your body wanted to continue in a straight line, but the car is turning, so the right side car door keeps pushing you to turn you in a curve – into the left turn. The car door keeps moving in your way, turning you into a circle. The car door pushing on you is called centripetal force. Centripetal means “center-seeking.” It’s the force that points toward the center of the circle you’re moving on. When you swing the bucket around your head, the bottom of the bucket is making the water turn in a circle and not fly away. Your arm is pulling on the handle of the bucket, keeping it turning in a circle and not letting it fly away. That’s centripetal force.
Think of it this way: If I throw a ball in outer space, does it go in a straight line or does it wiggle all over the place? Straight line, right? Centripetal force is the force needed to keep an object following a curved path.
Remember how objects will travel in a straight line unless they bump into something or have another force acting on them, such as gravity, drag force, and so forth? Well, to keep the bucket of water swinging in a curved arc, the centripetal force can be felt in the tension experienced by the handle (or your arm, in our case). Swinging an object around on a string will cause the rope to undergo tension (centripetal force), and if your rope isn’t strong enough, it will snap and break, sending the mass flying off in a tangent (straight) line until gravity and drag force pull the object to a stop. This force is proportional to the square of the speed – the faster you swing the object, the higher the force.
Exercises
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Today you get to learn how to read an astronomical chart to find out when the Sun sets, when twilight ends, which planets are visible, when the next full moon occurs, and much more. This is an excellent way to impress your friends.
The patterns of stars and planets stay the same, although they appear to move across the sky nightly, and different stars and planets can be seen in different seasons.
Materials:
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Download Student Worksheet & Exercises
This is one of the finest charts I’ve ever used as an astronomer, as it has so much information all in one place. You’ll find the rise and set times for all eight planets, peak times for annual meteor showers, moon phases, sunrise and set times, and it gives an overall picture of what the evening looks like over the entire year. Kids can clearly see the planetary movement patterns and quickly find what they need each night. I keep one of these posted right by the door for everyone to view all year long.
Exercises
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What would happen if our solar system had three suns? Or the Earth had two moons? You can find out all these and more with this lesson on orbital mechanics. Instead of waiting until you hit college, we thought we'd throw some university-level physics at you... without the hard math.
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To get you experienced with the force of gravity without getting lost in the math, there's an excellent computer program that allows you to see how multi-object systems interact. Most textbooks are limited to the interaction between a very large object, like the Earth, and much smaller objects that are very close to it, like the Moon. This seriously cuts out most of the interesting solar systems that are out there in the real universe.
The University of Colorado at Boulder designed a great system to do the hard math for you. Don't be fooled by the simplistic appearance - the physics behind the simulation is rock-solid... meaning that the results you get are exactly what scientists would predict to happen.
Go to the My Solar System simulation on the PhET website and carefully follow the instructions for each activity. Answer the questions and record your results before going on to the next activity. Click here to RUN the simulation. If that link doesn't work try this alternative.
Here's what you should see and do:
Exercises:
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If you watch the moon, you’d notice that it rises in the east and sets in the west. This direction is called ‘prograde motion’. The stars, sun, and moon all follow the same prograde motion, meaning that they all move across the sky in the same direction.
However, at certain times of the orbit, certain planets move in ‘retrograde motion’, the opposite way. Mars, Venus, and Mercury all have retrograde motion that have been recorded for as long as we’ve had something to write with. While most of the time, they spend their time in the ‘prograde’ direction, you’ll find that sometimes they stop, go backwards, stop, then go forward again, all over the course of several days to weeks.
Here are videos I created that show you what this would look like if you tracked their position in the sky each night for an year or two.
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This is a video that shows the retrograde motion of Venus and Mercury over the course of several years. Venus is the dot that stays centered throughout the video (Mercury is the one that swings around rapidly), and the bright dot is the sun. Note how sometimes the trace lines zigzag, and other times they loop. Mercury and Venus never get far from the sun from Earth’s point of view, which is why you’ll only see Mercury in the early dawn or early evening.
You’ve probably heard of epicycles people used to use to help explain the retrograde motion of Mars. Have you ever wondered what the fuss was all about? Here’s a video that traces out the path Mars takes over the course of several years. Do you see our Moon zipping by? The planets, Sun, and Moon all travel along line called the ‘ecliptic’, as they all are in about the same plane.
Download Student Worksheet & Exercises
Exercises
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In our physics problems so far, we’ve kept the objects close to the earth so that the acceleration due to gravity g remains constant, and we defined the potential energy of an object on the surface of the earth to be zero. What if we look up and see three stars in a system and want to find out the gravitational potential energy of the system?
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Globular clusters have a HUGE amount of gravitational potential energy.
This image above is known as Messier 13 (M13) or NGC 6205, also called the Hercules Globular Cluster, is a home to 300,000 stars in the constellation of Hercules. Can you start to see how there’s an enormous amount of gravitational potential energy in the universe?
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Let’s determine the gravitational potential energy of the earth-moon system as well as the speed needed to escape the Earth’s gravitational pull:
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Here’s how you put it all together and figure out the total energy of the system. This is useful when you’re trying to figure out something that you can’t otherwise solve for… let me show you with a set of videos here. Remember, for satellites the only force we have on the object is due to gravity, so the external work force term always goes to zero like this:
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A geosynchronous orbit is an orbit that a satellite has when viewed from the earth, looks like the satellite is stationary.
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How do you find the gravitational potential energy between two objects that are really far apart, like two stars or two galaxies? Here’s how:
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Imagine you and I are racing rocketships in orbit around the Earth. I can slow down and still beat you around the Earth. Want to see how?
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Einstein once said: “I was sitting in a chair in the patent office at Bern when all of the sudden a thought occurred to me: If a person falls freely, he will not feel his own weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.”
This led Einstein to develop his general theory of relativity, which interprets gravity not as a force but as the curvature of space and time. This topic is out of the scope for our lesson here, but you can explore more about it in this lesson.
The fundamental principle for relativity is the principle of equivalence, which says that if you were locked up in a box, you wouldn’t tell the difference between being in a gravitational field and accelerating (with an acceleration value equal to g) in a rocket.
The same thing is also true if you were either locked in a box, floating in outer space or in an elevator shaft experiencing free-fall. Any experiments you could do in either of those cases wouldn’t be able to tell you what was really happening outside your box. The way a ball drops is exactly the same in either case, and you would not be able to tell if you were falling in an elevator shaft or drifting in space.
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Have you ever seen an icicle? They usually grown downward toward the center of the earth (the direction of free-fall). But icicles on a car wheel grow radially outward because the wheel spins and flings the water toward the outside of the wheel where it freezes into spikes. The icicles can’t tell if the wheel is rotating and that’s why they grow radially, or it’s at rest at the gravitational field is in the radial direction!
Here’s a questions for you: these two astronauts (below) are inside the space station, which is currently in orbit around the earth. Which astronaut is upside down? Can you tell?
The principle of equivalence has some consequences! Navigation systems for ships, airplanes, missiles and submarines rely on acceleration information to calculate their velocity and position. However, the instruments that measure acceleration also react with unexpected variations in the earth’s gravitational field, and there’s no direct way to separate these two effect to avoid errors.
Highlights for Kepler’s Laws:
Yay! You completed this set of lessons on circular motion! Now it’s time for you to work your own physics problems!
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Gravity is the reason behind books being dropped and suitcases feeling heavy. It’s also the reason our atmosphere sticks around and oceans staying put on the surface of the earth. Gravity is what pulls it all together, and we’re going to look deeper into what this one-way attractive force is all about.
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Galileo was actually one of the first people to do science experiment on gravity.Galileo soon figured out that objects could be the same shape and different weights (think of a golf ball and a ping pong ball), and they will still fall the same. It was only how they interacted with the air that caused the fall rate to change. By studying ramps (and not just dropping things), he could measure how long things took to drop using not a stopwatch but a water clock (imagine having a sink that regularly dripped once per second).
Whenever I teach a class about gravity, I’ll drop something (usually something large). After the heads whip around, I ask the hard question: “Why did it fall?”
You already know the answer – gravity. But why? Why does gravity pull things down, not up? And when did people first start noticing that we stick to the surface of the planet and not float up into the sky? No one can tell you why gravity is – that’s just the way the universe is wired. Gravitation is a natural thing that happens when you have mass.
Would it sound strange to you if I said that gravity propagates at the speed of light? If we suddenly made the sun disappear, the Earth’s orbit wouldn’t be instantaneously affected… it would take time for that information to travel to the earth. What does that mean? By the end of this section, you’ll be able to tell me about it. Let’s get started!
So far, saying the force of gravity is pretty comfortable. When you throw a ball high in the air, the force of gravity slows it down and as it falls back to the earth the force of gravity speeds the ball up. The force of gravity causes an acceleration during this flight, and is called the acceleration of gravity. The acceleration of gravity g is the acceleration experienced by an object when the only force acting on it is the force of gravity. This value of g is the same no matter how massive the object is. It’s always 9.81 m/s2.
Johannes Kepler, a German mathematician and astronomer in the 1600s, was one of the key players of his time in astronomy. Among his best discoveries was the development of three laws of planetary orbits. He worked for Tycho Brahe, who had logged huge volumes of astronomical data, which was later passed onto to Kepler. Kepler took this information to design and develop his ideas about the movements of the planets around the Sun. We’re going to go into deeper discussion about Kepler’s Laws in the next section, but here they are in a nutshell:
Did you notice that while Kepler’s Laws describe the motion of the planets around the sun, they don’t say why these paths are there? Kepler only hinted at an interaction between the sun and the planets to drive their motion, but not between the planets themselves, and it really was only a teensy hint.
Newton wasn’t satisfied with this explanation. He was determined to figure out the cause for the elliptical motion, especially since it wasn’t a circle or a straight line (remember Newton’s First Law: Objects in motion tend to stay in motion unless acted upon by an unbalanced force?) And circular motion needs centripetal force to keep the object following a curved path. So what force was keeping the planets in an ellipse around the sun?
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One of Newton’s biggest contributions was figuring out how to show that gravity was the same force that caused both objects like an apple to fall to the earth at a rate of 9.81 m/s2 AND the moon being accelerated toward the earth but at a different rate of 0.00272 m/s2. If these are both due to the same force of gravity, why are they different numbers then? Why is the acceleration of the moon 1/3600th the acceleration of objects near the surface of the earth? It has to do with the fact that gravity decreases the further you are from an object. The moon is in orbit about 60 times further from the earth’s center than an object on the surface of the earth, which indicates that gravity is proportional to the inverse of the square of the distance (also called the inverse square law). So the force of gravity acts between any two objects and is inversely proportional to the square of the distance between the two centers. The further apart the objects are, the less they force of gravity is between the two of them. If you separate the objects by twice the distance, the gravitational force goes down by a factor of 4.
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All objects are attracted to each other with a gravitational force. You need objects the size of planets in order to detect this force, but everything, everywhere has a gravitational field and force associated with it. If you have mass, you have a gravitational attractive force. Newton’s Universal Law of Gravitation is amazing not because he figured out the relationship between mass, distance, and gravitational force (which is pretty incredible in its own right), but the fact that it’s universal, meaning that this applies to every object, everywhere.
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Newton suggested that every particle everywhere attracts every other particle with a force given by the following equation. If you have mass, then this force applies to you. Newton’s Universal Law of Gravitation is: 
That G is called the universal gravitation constant and is determined by doing experiments.
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Lord Henry Cavendish in 1798 (about a century after Newton) performed experiments with a torsion balance to figure out the value of G. It’s a very small number, so Cavendish had to carefully calibrate his experiment! The reason the number is so small is because we don’t see the effects of gravity until objects are very massive, like a moon or a planet in size.
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Cavendish used an experiment where two small lead spheres were fastened to the ends of a rod which had a very fine string (actually a quartz fiber) attached to the middle so it could be lifted off the ground. This is called a torsion balance, meaning that you can carefully measure the twist in the string by measuring how much the rod spins around. (Torsion balances can be made from other materials that have a stiffer spring constant value, like metal rods.) Back to his experiment: Cavendish placed two large lead spheres next to the smaller spheres, which moved the larger spheres and exerted a torque on the rod, and Cavendish was able to calculate the value of G.
The value of G is always the same, everywhere you go and any situation you apply it to. Once you know the masses and distances between objects, you can always calculate the force due to gravity with this one equation.
Although Newton’s Law of Gravitation applies only to particles, you can apply it to real objects as long as the sizes of the objects is small when you compare it to the distances between them.
You can concentrate an objects mass by shrinking it down to a particle using the idea of the center of mass like this:
Let’s practice it now…
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How do astronomers find planets around distant stars? If you look at a star through binoculars or a telescope, you’ll quickly notice how bright the star is, and how difficult it is to see anything other than the star, especially a small planet that doesn’t generate any light of its own! Astronomers look for a shift, or wobble, of the star as it gets gravitationally “yanked” around by the orbiting planets. By measuring this wobble, astronomers can estimate the size and distance of larger orbiting objects.
Doppler spectroscopy is one way astronomers find planets around distant stars. If you recall the lesson where we created our own solar system in a computer simulation, you remember how the star could be influenced by a smaller planet enough to have a tiny orbit of its own. This tiny orbit is what astronomers are trying to detect with this method.
Materials
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Download Student Worksheet & Exercises
Nearly half of the extrasolar (outside our solar system) planets discovered were found by using this method of detection. It’s very hard to detect planets from Earth because planets are so dim, and the light they do emit tends to be infrared radiation. Our Sun outshines all the planets in our solar system by one billion times.
This method uses the idea that an orbiting planet exerts a gravitational force on the Sun that yanks the Sun around in a tiny orbit. When this is viewed from a distance, the star appears to wobble. Not only that, this small orbit also affects the color of the light we receive from the star. This method requires that scientists make very precise measurements of its position in the sky.
Exercises
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Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” in space. You are still made of stuff, but there’s no gravity to pull on you so you have no weight. The larger a body is, the more gravitational pull (or in other words the larger a gravitational field) it will have.
The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17 pounds on the Moon). The Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the Sun!).
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As a matter of fact, the dog and I both have gravitational fields! Since we are both bodies of mass, we have a gravitational field which will pull things toward us. All bodies have a gravitational field. However, my mass is so small that the gravitational field I have is miniscule. Something has to be very massive before it has a gravitational field that noticeably attracts another body.
So what’s the measurement for how much stuff you’re made of? Mass. Mass is basically a weightless measure of how much matter makes you you. A hamster is made of a fairly small amount of stuff, so she has a small mass. I am made of more stuff, so my mass is greater than the hamster’s. Your house is made of even more stuff, so its mass is greater still.
So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change, but since weight is a measure for how much gravity is pulling on you, weight will change.
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At some point in the future you may ask yourself this question, “How can gravity pull harder (put more force on some things, like bowling balls) and yet accelerate all things equally?”
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Now that we have studied Newton’s laws, you can see that the above statement doesn’t make any sense at all! More force equals more acceleration is basically Newton’s Second law. The explanation for this is inertia.
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If you could stand on the Sun without being roasted, how much would you weigh? The gravitational pull is different for different objects. Let’s find out which celestial object you’d crack the pavement on, and which your lightweight toes would have to be careful about jumping on in case you leapt off the planet.
Weight is nothing more than a measure of how much gravity is pulling on you. Mass is a measure of how much stuff you’re made out of. Weight can change depending on the gravitational field you are standing in. Mass can only change if you lose an arm.
Materials
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Download Student Worksheet & Exercises
Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” in space. You are still made of stuff, but there’s no gravity to pull on you so you have no weight. The larger a body is, the more gravitational pull (or in other words the larger a gravitational field) it will have.
The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17 pounds on the Moon).The Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the Sun!).
As a matter of fact, the dog and I both have gravitational fields! Since we are both bodies of mass, we have a gravitational field which will pull things toward us. All bodies have a gravitational field. However, my mass is so small that the gravitational field I have is miniscule. Something has to be very massive before it has a gravitational field that noticeably attracts another body.
So what’s the measurement for how much stuff you’re made of? Mass. Mass is basically a weightless measure of how much matter makes you you. A hamster is made of a fairly small amount of stuff, so she has a small mass. I am made of more stuff, so my mass is greater than the hamster’s. Your house is made of even more stuff, so its mass is greater still. So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change, but since weight is a measure for how much gravity is pulling on you, weight will change.
Did you notice that I put weightless in quotation marks? Wonder why?
Weightlessness is a myth! Believe it or not, one is never weightless. A person can be pretty close to weightless in very deep space, but the astronauts in a space ship actually do have a bit of weight.
Think about it for a second. If a space ship is orbiting the Earth, what is it doing? It’s constantly falling! If it wasn’t moving forward at tens of thousands of miles an hour it would hit the Earth. It’s moving fast enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us.
Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling, too! The astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
Either now, or at some point in the future you may ask yourself this question, “How can gravity pull harder (put more force on some things, like bowling balls) and yet accelerate all things equally?” When we get into Newton’s laws in a few lessons, you’ll realize that doesn’t make any sense at all. More force equals more acceleration is basically Newton’s Second law.
Well, I don’t want to take too much time here since this is a little deeper then we need to go but I do feel some explanation is in order to avoid future confusion. The explanation for this is inertia. When we get to Newton’s First law we will discuss inertia. Inertia is basically how much force is needed to get something to move or stop moving.
Now, let’s get back to gravity and acceleration. Let’s take a look at a bowling ball and a golf ball. Gravity puts more force on the bowling ball than on the golf ball. So the bowling ball should accelerate faster since there’s more force on it. However, the bowling ball is heavier so it is harder to get it moving. Vice versa, the golf ball has less force pulling on it but it’s easier to get moving. Do you see it? The force and inertia thing equal out so that all things accelerate due to gravity at the same rate of speed!
Gravity had to be one of the first scientific discoveries. Whoever the first guy was to drop a rock on his foot, probably realized that things fall down! However, even though we have known about gravity for many years, it still remains one of the most elusive mysteries of science. At this point, nobody knows what makes things move toward a body of mass.
Why did the rock drop toward the Earth and on that guy’s foot? We still don’t know. We know that it does, but we don’t know what causes a gravitational attraction between objects. Gravity is also a very weak force. Compared to magnetic forces and electrostatic forces, the gravitational force is extremely weak. How come? No one knows. A large amount of amazing brain power is being used to discover these mysteries of gravity. Maybe it will be you who figures this out!
Exercises
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What happens to gravity if you’re in a rocket moving up through the atmosphere to a satellite in orbit?
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Does it remain the same or does it change during your flight? Here’s information about the earth:
The International Space Station, an object about 72 meters long by 108 meters wide and 20 meters high stays in an orbital altitude of between 330 km (205 miles) and 410 km (255 miles), and moves at a rate of 27,724 kph(17,227 mph).
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First we’re going to assume the earth is like a ball in that it’s a perfect sphere, and also that the density of the earth is even and it depends only how far from the center of the earth you are. Let’s also assume the earth isn’t rotating. Once we have these things in mind, then the magnitude of the force of gravity acting on an object goes like this…
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Material properties, introduction to forces and motion, plants and animals, and basic principles of earth science.
States of matter, weather, sound energy, light waves, and experimenting with the scientific method.
Chemical reactions, polymers, rocks and minerals, genetic traits, plant and animal life cycles, and Earth's resources.
Newton's law of motion, celestial objects, telescopes, measure the climate of the Earth and discover the microscopic world of life.
Electricity and magnetism, circuits and robotics, rocks and minerals, and the many different forms of energy.
Chemical elements and molecules, animal and plant biological functions, heat transfer, weather, planetary and solar astronomy.
Heat transfer, convetion currents, ecosystems, meteorology, simple machines, and alternative energy.
Cells, genetics, DNA, kinetic and potential, thermal energy, light and lasers, and biological structures.
Acceleration, forces projectile motion chemical reactions, deep space astronomy, and the periodic table.
Alternative energy, astrophysics, robotics, chemistry, electronics, physics and more. For high school & advanced 5-8th students.
Tips and tricks to getting the science education results you want most for your students.
Hovercraft, Light Speed, Fruit Batteries, Crystal Radios, R.O.V Underwater Robots and more!
There are three main differences between assuming the earth is round, uniformly dense, and not rotating as we did before.
First, the crust is not uniform. There are lumps and clumps everywhere that vary the density add up to make small variations in the force of gravity that we can actually measure with objects in free-fall motion. It’s actually how scientists find pockets of oil in the earth. They measure the surface gravity and plot it out, and if there’s a large enough deviation, it means there’s something interesting underground.
This image of the Mors salt dome in Denmark was studied for radioactive waste disposal. It’s a surface gravity survey that measures the acceleration due to gravity that shows something interesting is underground! The dots are the places where gravity was actually measured. You can read more about how gravity is measured from advanced lecture notes here. The unit of measurement for these deviations is called the “milligal” for Galileo, where 1 gal = 1,000 mgal = 1 cm/s3.
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The second problem with our assumption sis that the earth is not a sphere. It’s flattened a bit at the poles and bulges out at the equator. The ring around equator is larger than a ring around the poles by 21 km, which makes the poles closer to the center of the earth than the equator! Free-fall at the poles is slightly more than free-fall at the equator.
But before you book a trip to skydive in Ecuador, Colombia, Brazil, Sao Tome, Gabon, the Republic of the Congo, the Democratic Republic of the Congo, Uganda, Kenya, Somalia, Maldives, Indonesia or Kiribati, let’s talk about the assumption we made… The earth really does rotate. That’s not a surprise. How does this affect the value of g then? The bottom line is that gravity changes with altitude from 9.78 to 9.84 m/s2., mostly due to the earth spinning, but some to the earth not being a perfect sphere.
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Here are the Scientific Concepts to remember about Gravity:
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Circular motion is a little different from straight-line motion in a few different ways. Objects that move in circles are roller coasters in a loop, satellites in orbit, DVDs spinning in a player, kids on a merry go round, solar systems rotating in the galaxy, making a left turn in your car, water through a coiled hose, and so much more.
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Imagine driving your car in a circle, like you would when take a clover-leaf type of freeway exit, or make a right turn on a green light. Here’s how the forces play out during the motion:
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For any object that goes in a circle (or you can approximate it to a circle), you’ll want to use this approach when solving problems. You can feel the effect of circular motion if you’ve ever been in a car that suddenly turns right or left. You feel a push to the opposite side, right? If you are going fast enough and you take the turn hard enough, you can actually get slammed against the door. So my question to you is: who pushed you? Let’s find out!
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An object that moves in a circle with constant speed (like driving your car in a big circle at 30 mph) is called uniform circular motion. Although the speed is constant (30 mph), the velocity, which is a vector and made up of speed and direction, is not constant. The velocity vector has the same speed (magnitude), but the direction keeps changing as your car moves around the circle. The direction is an arrow that’s tangent to the circle as long as the car is moving on a circular path. This means that the tangent arrow is constantly changing and pointing in a new direction.
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It’s a common assumption that if the speed is constant, then there’s no acceleration… right?
Nope!
If the velocity is constant, then there’s no acceleration. But for circular motion, it’s speed, not velocity that is constant. Velocity is changing as the car turns a corner because the direction is changing, which also means that there is acceleration also! An accelerating object changes it’s velocity… it can be changing it’s speed, direction, or both. So objects moving in a circle are accelerating because they are always changing their direction.
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Now this next experiment is a little dangerous (we’re going to be spinning flames in a circle), so I found a video by MIT that has a row of five candles sitting on a rotating platform (like a “lazy susan”) so you can see how it works.
The candles are placed inside a dome (or a glass jar) so that when we spin them, they aren’t affected by the moving air but purely by acceleration. So for this video above, a row of candles are inside a clear dome on a rotating platform. When the platform rotates, air inside the dome gets swung to the outer part of the dome, creating higher density air at the outer rim, and lower density air in the middle. The candle flames point inwards towards the middle because the hot gas in the flames always points towards lower density air. Source: http://video.mit.edu
Now you’re beginning to understand how an object moving in a circle experiences acceleration, even if the speed is constant.
So what direction is the acceleration vector?
It’s pointed straight toward the center of that circle.
Velocity is always tangent to the circle in the direction of the motion, and acceleration is always directed radially inward. Because of these two things, the acceleration that arises from traveling in a circle is called centripetal acceleration (a word created by Sir Isaac Newton). There’s no direct relationship between the acceleration and velocity vectors for a moving particle.
Do you remember when I asked you “Who pushed you?” when you were riding in a car that took a sharp turn? Well, the answer has to do with centripetal force. Centripetal (translation = “center-seeking” ) is the force needed to keep an object following a curved path.
Remember how objects will travel in a straight line unless they bump into something or have another force acting on it like gravity, friction, or drag force? Imagine a car moving in a straight line at a constant speed. You’re inside the car, no seat belt, and the seat is slick enough for you to slide across easily. Now the car turns and drives again at constant speed but now on a circular path. When viewed from above the car, we see the car following a circle, and we see you wanting to keep moving in a straight line, but the car wall (door), moves into your path and exerts a force on you to keep you moving in a circle. The car door is pushing you into the circle.
According to Newton’s second law of motion, if you are experiencing an acceleration you must also be experiencing a net force (F=ma). The direction of the net force is in the same direction as the acceleration, so for the example with you inside the car, there’s an inward force acting on you (from the car door) keeping you moving in a circle.
If you have a bucket of water and you’re swinging it around your head, in order to keep a bucket of water swinging in a circle, the centripetal force can be felt in the tension experienced by the handle. Swinging an object around on a string will cause the rope to undergo tension (centripetal force), and if your rope isn’t strong enough, it will snap and break, sending the mass flying off in a tangential straight line until gravity and drag force pull the object to a stop.
This force is proportional to the square of the speed, meaning that the faster you swing the object, the higher the magnitude of the force will be.
Remember Newton’s First Law? The law of inertia? It states that objects in motion tend to stay in motion with the same speed and direction unless acted upon by an unbalanced/external force. Which means that objects naturally want to continue going their straight and merry way (like you did in a straight line when you were inside the car) until an unbalanced force causes it to turn speed up or stop. Can you see how an unbalanced force is required for objects to move in a circle? There has to be a force pushing on the object, keeping in on a circular path because otherwise, it’ll go off in a straight line!
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Every object moving in a circle will experience a force pushing or pulling it toward the center of the circle. Whether it’s a car making a turn and the friction force from the road are acting on the wheels of the car, or a bucket is swung around your head and the tension of the rope keeps it moving in a circle, they all have to have a force keeping them moving in that circle, and that force is called centripetal force. Without it, objects could never change their direction. Because centripetal force is tangent to the velocity vector, the force can change the direction of an object without changing the magnitude.
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Centrifugal (translation = “center-fleeing”) force has two different definitions, which causes even more confusion. The inertial centrifugal force is the most widely referred to, and is purely mathematical, having to do with calculating kinetic forces using reference frames, and is used with Newton’s laws of motion. It’s often referred to as the ‘fictitious force’.
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Reactive centrifugal force happens when objects move in a curved path. This force is actually the same magnitude as centripetal force, but in the opposite direction, and you can think of it as the reaction force to the centripetal force. Think of how you stand on the Earth. Your weight pushes down on the Earth, and a reaction force (the “normal” force) pushes up in reaction to your weight, keeping you from falling to the center of the Earth.
A centrifugal governor (spinning masses that regulate the speed of an engine) and a centrifugal clutch (spinning disk with two masses separated by a spring inside) are examples of this kind of force in action.
Here’s anther example: imagine driving a car along a banked turn. The road exerts a centripetal force on the car, keeping the car moving in a curved path (the “banked” turn). If you neglected to buckle your seat belt and the seats have a fresh coat of Armor-All (making them slippery), then as the car turns along the banked curve, you get “shoved” toward the door. But who pushed you? No one – your body wanted to continue in a straight line but the car keeps moving in your path, turning your body in a curve. The push of your weight on the door is the reactive centrifugal force, and the car pushing on you is the centripetal force.
What about the fictitious (inertial) centrifugal force? Well, if you imagine being inside the car as it is banking with the windows blacked out, you suddenly feel a magical ‘push’ toward the door away from the center of the bend. This “push” is the fictitious force invoked because the car’s motion and acceleration is hidden from you (the observer) in the reference frame moving within the car.
James Watt invented a “centrifugal governor”, which is a closed loop mechanical device you’ll find in lawn mowers, cruise controls, and airplane propellers to automatically control the speed of these things. The heavy brass balls spin around, and the faster they go, the more they rise up, which increases the rotational energy of this device, and since it’s connected to the throttle of something like a lawn mower engine, it can be carefully set to maintain the same speed or output power of the engine. It’s an automatic feedback system that is purely mechanical. Source: Mirko Junge, Science Museum London.
For circular motion, there are a couple of equations we will need to tackle physics problems that involve speed (v), acceleration (a), and force (F):
Here’s the equation for calculating centripetal force:
There’s another equation that relates the rotational speed (w) with the velocity like this:
Here’s a cool experiment you can do that will really show you how objects that move in a circle experience centripetal force. You can lift at least 10 balls by using only one! All you need are balls, fishing line or dental floss, and an old pen.
Video note: Oops! I made a mistake. Around 5:00 it should be sqrt(10rg) not sqrt(20rg).
Let’s calculate the velocity of the above experiment using our new circular motion equations. Let’s say you timed yourself, and you can get one ball to lift five identical balls when the one ball swings around once every second. Let’s calculate the acceleration, force, and speed.
The net force acting on the ball is directed inwards. There might be more than one force acting on an object moving in a circle, but it’s the net force that adds them all up. The net force is proportional to the square of the speed (look at the equations again!). So if your speed increases three times, then the force increases by a factor of nine.
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Let’s do a sample problem involving a car:
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Now let’s do a similar problem but this time with a kid instead of a car:
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I love amusement park rides, even though I know what’s going on from the science side of things! Here’s one that’s always been a favorite of mine:
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Before we go any further, we need to take a look at how friction gets handled in these types of problems:
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You’ve come so far with your analysis that I really want to give you the “real way” to solve these types of problems. Normally, this method isn’t introduced to you until your second year in college, and that’s only if you’re an engineer taking Statics and Dynamics classes (the next level after this course).
Here’s a step-by-step method that really puts all the pieces we’ve been working on all together into one:
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Do you see how easy that is? It puts the FBD (free body diagram) together with the MAD (mass-acceleration diagram) and uses Newton’s Laws to solve for the things you need to know. Using pictures and equations, you can solve anything now!
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Let’s do something fun now… want to know about the physics of real roller coasters?
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It’s really important to know how much centrifugal force people experience, whether its in cars or roller coasters! In fact roller coaster loops used to be circular, but now they use clothoid loops instead to keep passengers happy during their ride so they don’t need nearly the acceleration that they’d need for a circular loop (which means less g-force so passengers don’t black out).
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There’s two main types of maneuvers a roller coaster can do that’s easy for us to analyze with uniform circular motion: camel-backs are the first one:
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…and loops are the second type of maneuver:
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We’re going to build monster roller coasters in your house using just a couple of simple materials. You might have heard how energy cannot be created or destroyed, but it can be transferred or transformed (if you haven’t that’s okay – you’ll pick it up while doing this activity).
Roller coasters are a prime example of energy transfer: You start at the top of a big hill at low speeds (high gravitational potential energy), then race down a slope at break-neck speed (potential transforming into kinetic) until you bottom out and enter a loop (highest kinetic energy, lowest potential energy). At the top of the loop, your speed slows (increasing your potential energy), but then you speed up again and you zoom near the bottom exit of the loop (increasing your kinetic energy), and you’re off again!
Here’s what you need:
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To make the roller coasters, you’ll need foam pipe insulation, which is sold by the six-foot increments at the hardware store. You’ll be slicing them in half lengthwise, so each piece makes twelve feet of track. It comes in all sizes, so bring your marbles when you select the size. The ¾” size fits most marbles, but if you’re using ball bearings or shooter marbles, try those out at the store. (At the very least you’ll get smiles and interest from the hardware store sales people.) Cut most of the track lengthwise (the hard way) with scissors. You’ll find it is already sliced on one side, so this makes your task easier. Leave a few pieces uncut to become “tunnels” for later roller coasters.
Read for some ‘vintage Aurora’ video? This is one of the very first videos ever made by Supercharged Science:
Download Student Worksheet & Exercises
Loops Swing the track around in a complete circle and attach the outside of the track to chairs, table legs, and hard floors with tape to secure in place. Loops take a bit of speed to make it through, so have your partner hold it while you test it out before taping. Start with smaller loops and increase in size to match your entrance velocity into the loop. Loops can be used to slow a marble down if speed is a problem.
Camel-Backs Make a hill out of track in an upside-down U-shape. Good for show, especially if you get the hill height just right so the marble comes off the track slightly, then back on without missing a beat.
Whirly-Birds Take a loop and make it horizontal. Great around poles and posts, but just keep the bank angle steep enough and the marble speed fast enough so it doesn’t fly off track.
Corkscrew Start with a basic loop, then spread apart the entrance and exit points. The further apart they get, the more fun it becomes. Corkscrews usually require more speed than loops of the same size.
Jump Track A major show-off feature that requires very rigid entrance and exit points on the track. Use a lot of tape and incline the entrance (end of the track) slightly while declining the exit (beginning of new track piece).
Pretzel The cream of the crop in maneuvers. Make a very loose knot that resembles a pretzel. Bank angles and speed are the most critical, with rigid track positioning a close second. If you’re having trouble, make the pretzel smaller and try again. You can bank the track at any angle because the foam is so soft. Use lots of tape and a firm surface (bookcases, chairs, etc).
Troubleshooting Marbles will fly everywhere, so make sure you have a lot of extras! If your marble is not following your track, look very carefully for the point of departure – where it flies off.
-Does the track change position with the weight of the marble, making it fly off course? Make the track more rigid by taping it to a surface.
-Is the marble jumping over the track wall? Increase your bank angle (the amount of twist the track makes along its length).
-Does your marble just fall out of the loop? Increase your marble speed by starting at a higher position. When all else fails and your marble still won’t stay on the track, make it a tunnel section by taping another piece on top the main track. Spiral-wrap the tape along the length of both pieces to secure them together.
HOT TIPS for ULTRA-COOL PARENTS: This lab is an excellent opportunity for kids to practice their resilience, because we guarantee this experiment will not work the first several times they try it. While you can certainly help the kids out, it’s important that you help them figure it out on their own. You can do this by asking questions instead of rushing in to solve their problems. For instance, when the marble flies off the track, you can step back and say:
“Hmmm… did the marble go to fast or too slow?”
“Where did it fly off?”
“Wow – I’ll bet you didn’t expect that to happen. Now what are you going to try?”
Become their biggest fan by cheering them on, encouraging them to make mistakes, and try something new (even if they aren’t sure if it will work out).
Exercises
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