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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You can find circular motion everywhere, including football, car racing, ice skating, and baseball. An ice skater spins on ice, or a competition speed skater makes a turn… they are both examples of circular motion. A turn happens when there’s a force component directed inward from the circular path. Let me show you a couple of examples:
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What about your car along a circular path? Let’s take a look at two different examples. The first is an unbanked turn with friction:
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The second example is a banked turn, like NASCAR racing:
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We’ve already studied the different types of forces and learned how to draw free body diagrams. We’re going to use those concepts to put forces into two different categories: internal and external forces. Internal forces include forces due to gravity, magnetism, electricity, and springs. External forces include applied, normal, tension, friction, drag and air resistance forces.
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As Phillip holds the ball at the top of the building, the ball has 100 Joules of potential energy (the number is just an example). When he drops it, the potential energy of the ball drops since the height of the ball gets less and less. At the same time, however, kinetic energy increases because the speed of the ball increases. All the way down, the sum of the two energies equals 100. No energy gets lost, it only gets transferred. Energy is conserved.
Now here’s a question you may be asking yourself, “If energy is neither created or destroyed in a closed system then why doesn’t a pendulum swing forever?”
That’s a very good question. Energy is neither created or destroyed, but it can be transferred into non- useful energy.
In the case of a pendulum, every swing loses a little bit of energy,which is why each swing goes slightly less high (achieves slightly less PE) than the swing before it. Where does that energy go? To heat. The second law of thermodynamics states basically that eventually all energy ends up as heat. If you could measure it, you’d find that the string, and the weight have a slightly higher temperature then they did when they started due to friction. The energy of your pendulum is lost to heat!
If you could prevent the loss of energy to useless energy, you could create a perpetual motion machine. A machine that works forever! There have been a lot of folks who have spent a lot of time trying to make a perpetual motion machine. So far, they have all failed. A perpetual motion machine is one that is said to be 100% energy efficient. In other words all the energy that goes into it goes to useful energy.
Your pendulum could be said to be about 90% efficient.Very little energy is converted into useless energy. In most systems, energy is converted to useless heat and sound energy.
This is a nit-picky experiment that focuses on the energy transfer of rolling cars. You’ll be placing objects and moving them about to gather information about the potential and kinetic energy.
We’ll also be taking data and recording the results as well as doing a few math calculations, so if math isn’t your thing, feel free to skip it.
Here’s what you need:
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The setup is simple. Here’s what you do:
1. Set up the track (board or book so that there’s a nice slant to the floor).
2. Put a car on the track.
3. Let the car go.
4. Mark or measure how far it went.
Download Student Worksheet & Exercises
As you lifted the car onto the track you gave the car potential energy. As the car went down the track and reached the floor the car lost potential energy and gained kinetic energy. When the car hit the floor it no longer had any potential energy only kinetic.
If the car was 100% energy efficient, the car would keep going forever. It would never have any energy transferred to useless energy. Your cars didn’t go forever did they? Nope, they stopped and some stopped before others. The ones that went farther were more energy efficient. Less of their energy was transferred to useless energy than the cars that went less far.
Where did the energy go? To heat energy, created by the friction of the wheels, and to sound energy. Was energy lost? NOOOO, it was only changed. If you could capture the heat energy and the sound energy and add it to the the kinetic energy, the sum would be equal to the original amount of energy the car had when it was sitting on top of the ramp.
For K-8 grades, click here to download a data sheet.
For Advanced Students, click here for the data log sheet. You’ll need Microsoft Excel to use this file.
Exercises
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What’s an inclined plane? Jar lids, spiral staircases, light bulbs, and key rings. These are all examples of inclined planes that wind around themselves. Some inclined planes are used to lower and raise things (like a jack or ramp), but they can also used to hold objects together (like jar lids or light bulb threads).
Here’s a quick experiment you can do to show yourself how something straight, like a ramp, is really the same as a spiral staircase.
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Here’s what you need to find:
Cut a right triangle out of paper so that the two sides of the right angle are 11” and 5 ½” (the hypotenuse – the side opposite the right angle – will be longer than either of these). Find a short dowel or use a cardboard tube from a coat-hanger. Roll the triangular paper around the tube beginning at the short side and roll toward the triangle point, keeping the base even as it rolls.
Notice that the inclined plane (hypotenuse) spirals up as a tread as you roll. Remind you of screw threads? Those are inclined planes. If you have trouble figuring out how to do this experiment, just watch the video clip below:
Download Student Worksheet & Exercises
Inclined planes are simple machines. It’s how people used to lift heavy things (like the top stones for a pyramid).
Here’s another twist on the inclined plane: a wedge is a double inclined plane (top and bottom surfaces are inclined planes). You have lots of wedges at home: forks, knives, and nails just name a few.
When you stick a fork in food, it splits the food apart. You can make a simple wedge from a block of wood and drive it under a heavy block (like a tree stump or large book) with a kid on top.
Exercises
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When you toss down a ball, gravity pulls on the ball as it falls (creating kinetic energy) until it smacks the pavement, converting it back to potential energy as it bounces up again. This cycles between kinetic and potential energy as long as the ball continues to bounce.
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But note that when you drop the ball, it doesn’t rise up to the same height again. If the ball did return to the same height, this means you recovered all the kinetic energy into potential energy and you have a 100% efficient machine at work. But that’s not what happens, is it? Where did the rest of the energy go? Some of the energy was lost as heat and sound. (Did you hear something when the ball hit the floor?)
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Note: Do the pendulum experiment first, and when you’re done with the heavy nut from that activity, just use it in this experiment.
You can easily create one of these mystery toys out of an old baking powder can, a heavy rock, two paper clips, and a rubber band (at least 3″ x 1/4″). It will keep small kids and cats busy for hours.
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Here’s what you get:
You’ll need two holds punched through your container – one in the lid and the bottom. Thread your rubber band through the heavy washer and tie it off (this is important!). Poke the ends of the rubber band through one of the holes and catch it on the other side with a paper clip. (Just push a paper clip partway through so the rubber band doesn’t slip back through the hole.) Do this for both sides, and make sure that your rubber band is a pulled mildly-tight inside the can. You want the hexnut to dangle in the center of the can without touching the sides of the container.
Download Student Worksheet & Exercises
Now for the fun part… gently roll the can on a smooth floor away from you. The can should roll, slow down, stop, and return to you! If it doesn’t, check the rubber band tightness inside the can.
The hexnut is a weight that twists up the rubber band as the can rolls around it. The kinetic energy (the rolling motion of the can) transforms into potential (elastic) energy stored in the rubber band the free side twists around. The can stops (this is the point of highest potential energy) and returns to you (potential energy is being transformed into kinetic). The farther the toy is rolled the more elastic potential energy it stores.
Exercises
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This is a very simple yet powerful demonstration that shows how potential energy and kinetic energy transfer from one to the other and back again, over and over. Once you wrap your head around this concept, you’ll be well on your way to designing world-class roller coasters.
For these experiments, find your materials:
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Here’s what you do:
1. Make the string into a 2 foot or so length.
2. Tie the string to the washer, or weight.
3. Tape the other end of the string to a table.
4. Lift the weight and let go, causing the weight to swing back and forth at the end of the pendulum.
Download Student Worksheet & Exercises
Watch the pendulum for a bit and describe what it’s doing as far as energy goes. Some questions to think about include:
Remember, potential energy is highest where the weight is the highest.
Kinetic energy is highest were the weight is moving the fastest. So potential energy is highest at the ends of the swings. Here’s a coincidence, that’s also where kinetic energy is the lowest since the weight is moving the least.
Where’s potential energy the lowest? At the middle or lowest part of the swing. Another coincidence, this is where kinetic energy is the highest! Now, wait a minute…coincidence or physics? It’s physics right?
In fact, it’s conservation of energy. No energy is created or destroyed, so as PE gets lower KE must get higher. As KE gets higher PE must get lower. It’s the law…the law of conservation of energy! Lastly, where did the energy come from in the first place? It came from you. You added energy (increased PE) when you lifted the weight.
(By the way, you did work on the weight by lifting it the distance you lifted it. You put a certain amount of Joules of energy into the pendulum system. Where did you get that energy? From your morning Wheaties!)
For this next experiment, we’ll be using magnets to add energy into the system by having a magnetic pendulum interact with magnets carefully spaced around the pendulum. Watch the video to learn how to set this one up. You’ll need a set of magnets (at least one of them is a ring magnet so you can easily thread a string through it), tape, string, and a table or chair. Are you ready?
Exercises
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This experiment is for Advanced Students.There are several different ways of throwing objects. This is the only potato cannon we’ve found that does NOT use explosives, so you can be assured your kid will still have their face attached at the end of the day. (We’ll do more when we get to chemistry, so don’t worry!)
These nifty devices give off a satisfying *POP!!* when they fire and your backyard will look like an invasion of aliens from the French Fry planet when you’re done. Have your kids use a set of goggles and do all your experimenting outside.
Here’s what you need:
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Where is the potential energy the greatest? How much energy did your spud have at this point? Hmmm… let’s see if we can get a few actual numbers with this experiment. In order to calculate potential energy at the highest point of travel, you’ll need to figure out how high it went.
Here are instructions for making your own height-gauge:
Once you get your height gauge working right, you’ll need to track your data. Start a log sheet in your journal and jot down the height for each launch. Let’s practice a sample calculation:
If you measured an angle of 30 degrees, and your spud landed 20 feet away, we can assume that the spud when highest right in the middle of its flight, which is halfway (10 feet). Use basic trigonometry to find the height 45 degrees up at a horizontal distance ten feet away to get:
height = h = (10′) * (tan 30) = 5.8 feet
(Convert this to meters by: (5.8 feet) * (12 inches/foot) / (39.97 inches/meter) = 1.8 meters)
I measured the mass of my spud to be 25 grams (which is 0.025 kg).
Now, let’s calculate the potential energy:
PE = mgh = (0.025 kg) * (1.8 meters) * (10 m/s2) = 0.44 Joules
How fast was the spud going before it smacked into the ground? Set PE = KE to solve for velocity:
mgh = 0.5 mv2 gives v = (2gh)1/2
Plug in your numbers to get:
v = [(2) * (10) * (1.8)]2 = 6 m/s (or about 20 feet per second). Cool!
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Bobsleds use the low-friction surface of ice to coast downhill at ridiculous speeds. You start at the top of a high hill (with loads of potential energy) then slide down a icy hill til you transform all that potential energy into kinetic energy. It’s one of the most efficient ways of energy transformation on planet Earth. Ready to give it a try?
This is one of those quick-yet-highly-satisfying activities which utilizes ordinary materials and turns it into something highly unusual… for example, taking aluminum foil and marbles and making it into a racecar.
While you can make a tube out of gift wrap tubes, it’s much more fun to use clear plastic tubes (such as the ones that protect the long overhead fluorescent lights). Find the longest ones you can at your local hardware store. In a pinch, you can slit the gift wrap tubes in half lengthwise and tape either the lengths together for a longer run or side-by-side for multiple tracks for races. (Poke a skewer through the rolls horizontally to make a quick-release gate.)
Here’s what you need:
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If you’re finding that the marbles fall out before the bobsled reaches the bottom of the slide, you need to either crimp the foil more closely around the marbles or decrease your hill height.
Check to be sure the marbles are free to turn in their “slots” before launching into the tube – if you’ve crimped them in too tightly, they won’t move at all. If you oil the bearings with a little olive oil or machine oil, your tube will also get covered with oil and later become sticky and grimy… but they sure go faster those first few times!
Download Student Worksheet & Exercises
Exercises Answer the questions below:
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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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Most real life situations do involve friction. But how does it fit in with kinetic and potential energy equations? Here’s how:
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Springs can launch projectiles huge distances, and they’re really easy to model on paper using the conservation of energy:
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Here’s how you can model a car suspension system using a simple spring model and a couple of energy equations:
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A lot of people’s worst nightmare is an elevator cable breaking while they are in the elevator. Let’s find out exactly how bad this type of accident can be from a physics perspective:
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Do you like water slides? Did you know that you can find your speed that you hit the water without even knowing the shape of the slide? Here’s how…
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Nothing says summer time fun than a home-built go-kart that can race down the driveway with just as much thrill as two story roller coasters.
A go-karts (also called “go-cart”) can be gravity powered (without a motor) or include electric or gas powered motors. The gravity powered kind are also known as Soap Box Derby racers, and are the simplest kind to make since all you need is wheels, a frame, and a good hill (and a helmet!).
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Materials:
Hardware Bits and Pieces:
Wood:
Tools:
Make sure you wear your HELMET and get someone to help you with the power tools!
The go-kart we’re going to make is long enough to hold two passengers, so feel free to shorten it up a bit if you’re only needing it for one passenger. You’ll need only a couple of tools like a drill and a saw, and also some experienced adult help and you’ll be off and riding this vehicle in under two hours, from start to finish.
After you’ve got this working, you’re probably going to be more than a little popular, especially with younger kids that might be too small to ride safely. Here’s a smaller version you can build them with only a few parts. You’ll not only get points for making something really cool, but it’ll keep them busy so you can ride your new go-kart!
And yes, you must INSIST that everyone wears helmets, or you’ll take the wheels off. Helmet hair is way more fashionable than squashed brain cells.
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If you’ve ever thrown a ball down into the sand, you know it can bury itself below the surface. Here’s how you figure out the non-conservative forces into the equation of the sand exerting a force on the ball as it slows down and stops deep in the sand.
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Friction can be tricky to deal with, especially since it’s a non-conservative force (meaning that you can’t recover the energy from it for a useful purpose the way you can with potential and kinetic energy).
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Have you learned how to drive yet, or are you excited to learn? Here’s a question on the driver’s test that is really kind of scary from a physics point of view, but it will make a lot of sense once you see how it works. And might even keep you from speeding, now that you understand what can happen if you lock up your brakes while going too fast.
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How do you calculate the energies of particles going near the speed of light? It’s a little tricky, but you can do it if you have the right equation. Since the kinetic energy equation comes from Newton’s Laws of Motion, which don’t apply to particles moving near the speed of light, we have to add a correction factor from Einstein’s Theory of Relativity in order to compensate and make the equations accurate. Here’s the equation for particles going close to light speed:
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Yay! You’ve completed this set of lessons! Now it’s time for you to work your own physics problems.
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Work is not that hard… it’s force that can be difficult. Imagine getting up a 10-step flight of stairs without a set of stairs. Your legs don’t have the strength or force for you to jump up… you’d have to climb up or find a ladder or a rope. The stairs allow you to, slowly but surely, lift yourself from the bottom to the top. Now imagine you are riding your bike and a friend of yours is running beside you.
Who’s got the tougher job? Your friend, right? You could go for many miles on your bike but your friend will tire out after only a few miles. The bike is easier (requires less force) to do as much work as the runner has to do. Now here’s an important point, you and your friend do about the same amount of work.
You also do the same amount of work when you go up the stairs versus climbing up the rope. The work is the same, but the force needed to make it happen is much different. Don’t worry if that doesn’t make sense now. As we move forward, it will become clearer. Before we start solving physics problems, we first have to accurately define a couple of terms we’re going to be using a lot that you might already have a different definition for.
Here are three concepts we’re going to be working with in this section:
Energy is the ability to do work. Work is done on an object when a force acts on it so the object moves somewhere. It can be a large or small displacement, but as long as it’s not in its original position when it’s done, work is said to be done on the object. An example of work is when an apple falls off the tree and hits the ground. The apple falls because the gravitational force is acting on it, and it went from the tree to the ground. If you carry a heavy box up a flight of stairs, you are doing work on the box.
An example of what is not work is if you push really hard against a brick wall. The wall didn’t go anywhere, so you didn’t do any work at all (even though your muscles may not agree!). Mathematically, work is a vector, and is defined as the force multiplied by the distance like this: W = F d
If there’s an angle between the force and displacement vectors, then you’ll need to also multiply by the cosine of the angle between the two vectors. This is an important concept: Notice that the force has to cause the displacement. If you’re carrying a heavy box across the room (no stairs) at a constant speed, then you are not doing work on the box.
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The box is traveling in the horizontal direction at a constant speed. You are holding the heavy box up in the vertical direction. The force you are applying to the box is not causing it to be displaced in the same direction. There has to be a component of the force in the horizontal direction if you’re doing work on the box ((Remember F=ma? Constant speed means no acceleration!) Mathematically, the work equation would have angle between the force and the displacement vectors at 90 degrees, and the cosine of 90 degrees is zero, thus cancelling the work out to zero.
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We’ll cover power in a little bit, but first we need to have a unit of measurement for work. The units for work and energy are the same, but note that energy and work are not the same. (Remember, energy is the ability to do work.)
For energy, a couple of units are the Joule (J) and the calorie (cal or Cal). A Joule is the energy needed to lift one Newton one meter. A Newton is a unit of force. One Newton is about the amount of force it takes to lift 100 grams or 4 ounces or an apple.
It takes about 66 Newtons to lift a 15-pound bowling ball and it would take a 250-pound linebacker about 1000 Newtons to lift himself up the stairs! So, if you lifted an apple one meter (about 3 feet) into the air you would have exerted one Joule of energy to do it.
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The calorie is generally used to talk about heat energy, and you may be a bit more familiar with it due to food and exercise. A calorie is the amount of energy it takes to heat one gram of water one degree Celsius. Four Joules are about one calorie. A 100-gram object takes about one Newton of force to lift. Since it took one Newton of force to lift that object, how much work did we do? Remember work = force x distance so in this case work = 1 Newton x 20 meters or work = 20 Joules.
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This experiment is for Advanced Students. We’re going to really get a good feel for energy and power as it shows up in real life. For this experiment, you need:
This might seem sort of silly but it’s a good way to get the feeling for what a Joule is and what work is.
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Download Student Worksheet & Exercises
1. Grab your 100 gram object, put it on a table.
2. Now lift it off the table straight up until you lift it one meter (one yard).
3. Lift it up and down 20 times.
A 100 gram object takes about one Newton of force to lift. Since it took one Newton of force to lift that object, how much work did we do? Remember work = force x distance so in this case work = 1 Newton x 20 meters or work = 20 Joules.
You may ask “but didn’t we move it 40 meters, 20 meters up and 20 down?” That’s true, but work is moving something against a force. When you moved the object down you were moving the object with a force, the force of gravity. Only in lifting it up, are you actually moving it against a force and doing work. Four Joules are about 1 calories so we did 5 calories of work.
“Wow, I can lift an apple 20 times and burn 5 calories! Helloooo weight loss!” Well…not so fast there Richard Simmons. When we talk about calories in nutrition we are really talking about kilo calories. In other words, every calorie in that potato chip is really 1000 calories in physics. So as far as diet and exercise goes, lifting that apple actually only burned .005 calories of energy,…rats.
It is interesting to think of calories as the unit of energy for humans or as the fuel we use. The average human uses about 2000 calories (food calories that is, 2,000,000 actual calories) a day of energy. Running, jumping, sleeping, eating all uses calories/energy. Running 15 minutes uses 225 calories. Playing soccer for 15 minutes uses 140 calories. (Remember those are food calories, multiply by 1000 to get physics calories). This web site has a nice chart for more information: Calories used in exercise.
Everything we eat refuels that energy tank. All food has calories in it and our body takes those calories and converts them to calories/energy for us to use. How did the food get the energy in it? From the sun! The sun’s energy gives energy to the plants and when the animals eat the plants they get the energy from the sun as well.
So, if you eat a carrot or a burger you are getting energy from the sun! Eating broccoli gives you about 50 calories. Eating a hamburger gives you about 450 calories! We use energy to do things and we get energy from food. The problem comes when we eat more energy than we can use. When we do that, our body converts the energy to fat, our body’s reserve fuel tank. If you use more energy then you’ve taken in, then your body converts fat to energy. That’s why exercise and diet can help reduce your weight.
Let’s take the concept of work a little bit farther. If Bruno carries a 15 pound bowling ball up a 2 meter (6 foot) flight of stairs, how much work does he do on the bowling ball? It takes 66 Newtons of force to lift a 15 pound bowling ball 1 meter. Remember work = force x distance.
So, work = 66 Newtons x 2 meters. In this case, Bruno does 132 Joules of work on that bowling ball. That’s interesting, but what if we wanted to know how hard poor Bruno works? If he took a half hour to go up those stairs he didn’t work very hard, but if he did it in 1 second, well then Bruno’s sweating!
That’s the concept of power. Power is to energy like miles per hour is to driving. It is a measure of how much energy is used in a given span of time. Mathematically it’s Power = work/time. Power is commonly measured in Watts or Horsepower. Let’s do a little math and see how hard Bruno works.
In both cases mentioned above Bruno, does 132 Joules of work, but in the first case he does the work in 30 minutes (1800 seconds) and in the last case he does it in 1 second. Let’s first figure out Bruno’s power in Watts. A Watt is 1 Joule/second so:
For the half hour Bruno’s Power = 132 Joules/1800 seconds = .07 Watts
For the second Bruno’s Power = 132 joules/1 second = 132 Watts
You can see that the faster you exert energy the more power you use. Another term for power is horsepower. You may have heard the term horsepower in car ads. The more powerful car can exert more energy faster, getting the car moving faster. A Dodge Viper has 450 horsepower which can accelerate a 3,300 pound car from 0 to 60 mph in 4.1 seconds…WOW!
One horsepower is 745 Watts or one Watt is .001 horsepower. So converting Watts to horsepower poor Bruno exerts:
.07 x .001 = .00007 horsepower over the half hour
132 x .001 = .132 horsepower over the second (not exactly a Dodge Viper!)
Exercises
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A peanut is not a nut, but actually a seed. In addition to containing protein, a peanut is rich in fats and carbohydrates. Fats and carbohydrates are the major sources of energy for plants and animals.
The energy contained in the peanut actually came from the sun. Green plants absorb solar energy and use it in photosynthesis. During photosynthesis, carbon dioxide and water are combined to make glucose. Glucose is a simple sugar that is a type of carbohydrate. Oxygen gas is also made during photosynthesis.
The glucose made during photosynthesis is used by plants to make other important chemical substances needed for living and growing. Some of the chemical substances made from glucose include fats, carbohydrates (such as various sugars, starch, and cellulose), and proteins.
Photosynthesis is the way in which green plants make their food, and ultimately, all the food available on earth. All animals and nongreen plants (such as fungi and bacteria) depend on the stored energy of green plants to live. Photosynthesis is the most important way animals obtain energy from the sun.
Oil squeezed from nuts and seeds is a potential source of fuel. In some parts of the world, oil squeezed from seeds-particularly sunflower seeds-is burned as a motor fuel in some farm equipment. In the United States, some people have modified diesel cars and trucks to run on vegetable oils.
Fuels from vegetable oils are particularly attractive because, unlike fossil fuels, these fuels are renewable. They come from plants that can be grown in a reasonable amount of time.
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Materials
Download Student Worksheet & Exercises
Procedure
ASK AN ADULT TO HELP YOU WITH THIS EXPERIMENT. DO NOT DO THIS EXPERIMENT BY YOURSELF. The fuel from the peanut can flare up and burn for a longer time than expected.
Close the drain in the kitchen sink. Fill the sink with water until the bottom of the sink is just covered.
Using a small pair of pliers, hold the peanut over the sink containing water. Ask an adult to hold the flame of a lit match or lighter directly under the peanut. When the peanut starts to burn, the lit match or lighter can be removed.
Allow the peanut to burn for one minute. MAKE SURE AN ADULT REMAINS PRESENT AND MAKE SURE TO HOLD THE PEANUT OVER THE SINK. To extinguish the burning peanut, drop it into the water. After you have extinguished the peanut, allow it to cool and then examine it carefully.
Observations
How long does it take for the peanut to start to burn? Does the peanut burn with a clean flame or a sooty flame? What color is the flame? What color does the peanut turn when it burns? Did the size of the peanut change after it has burned for several minutes?
Discussion
You should find that the peanut ignites and burns after a lit match or lighter is held under it for a few seconds. Although you only let the peanut burn for one minute as a safety measure, the peanut would burn for many minutes.
In this experiment, when the peanut burns, the stored energy in the fats and carbohydrates of the peanut is released as heat and light. When you eat peanuts, the stored energy in the fats and carbohydrates of the peanut is used to fuel your body.
Other Things to Try
Hold one end of a piece of uncooked spaghetti in a pair of pliers. Ask an adult to hold the flame of a lit match or lighter under the other end of the spaghetti. When the spaghetti starts to burn, place it in an aluminum pie pan that is in the sink. Make sure to extinguish the burning spaghetti with water when you are finished with the experiment. How does the burning of the spaghetti compare with the burning of the peanut?
Exercises
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This experiment is for advanced students. Did you know that eating a single peanut will power your brain for 30 minutes? The energy in a peanut also produces a large amount of energy when burned in a flame, which can be used to boil water and measure energy.
Peanuts are part of the bean family, and actually grows underground (not from trees like almonds or walnuts). In addition to your lunchtime sandwich, peanuts are also used in woman’s cosmetics, certain plastics, paint dyes, and also when making nitroglycerin.
What makes up a peanut? Inside you’ll find a lot of fats (most of them unsaturated) and antioxidants (as much as found in berries). And more than half of all the peanuts Americans eat are produced in Alabama. We’re going to learn how to release the energy inside a peanut and how to measure it.
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Materials:
Download Student Worksheet & Exercises
What’s Going On? There’s chemical energy stored inside a peanut, which gets transformed into heat energy when you ignite it. This heat flows to raise the water temperature, which you can measure with a thermometer. You should find that your peanut contains 1500-2100 calories of energy! Now don’t panic… this isn’t the same as the number of calories you’re allowed to eat in a day. The average person aims to eat around 2,000 Calories (with a capital “C”). 1 Calorie = 1,000 calories. So each peanut contains 1.5-2.1 Calories of energy (the kind you eat in a day). Do you see the difference?
But wait… did all the energy from the peanut go straight to the water, or did it leak somewhere else, too? The heat actually warmed up the nearby air, too, but we weren’t able to measure that. If you were a food scientist, you’d use a nifty little device known as a bomb calorimeter to measure calorie content. It’s basically a well-insulated, well-sealed device that catches nearly all the energy and flows it to the water, so you get a much more accurate temperature reading. (Using a bomb calorimeter, you’d get 6.1-6.8 Calories of energy from one peanut!)
Let’s take an example measurement. Suppose you measured a temperature increase from 20 °C to 100 °C for 10 grams of water, and boiled off 2 grams. We need to break this problem down into two parts – the first part deals with the temperature increase, and the second deals with the water escaping as vapor.
The first basic heat equation is this:
Q = m c T
Q is the heat flow (in calories)
m is the mass of the water (in grams)
c is the specific heat of water (which is 1 degree per calorie per gram)
and T is the temperature change (in degrees)
So our equation becomes: Q = 10 * 1 * 80 = 800 calories.
If you measured that we boiled off 2 grams of water, your equation would look like this for heat energy:
Q = L m
L is the latent heat of vaporization of water (L= 540 calories per gram)
m is the mass of the water (in grams)
So our equation becomes: Q = 540 * 2 = 1080 calories.
The total energy needed is the sum of these two:
Q = 800 calories + 1080 calories = 1880 calories.
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We’re going to learn how to calculate the amount of work done by forces by looking at how the force acts on the object, and if it causes a displacement. Have you spotted the three things you need to know in order to calculate the work done?
The easiest way to do this is to show you by working a set of physics problems. So take out your notebook and a pencil, and do these problems right along with me. Here we go!
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How do we calculate the work done by friction? Here’s a classic problem that shows you how to handle friction forces in your physics problems.
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Ever get out of breath while climbing stairs? How much work do you think you did? Let’s find out…
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Work done by friction is never conserved, since it’s turned into heat or sound, and we can’t get that back. It’s a non-conservative force. Other forces like gravity and speed are said to be conservative, since we can transfer that energy to a different form for a useful purpose. When you pull back a swing and then let go, you’re using the energy created by the gravitational force on the swing and transforming it into the forward motion of the swing as it moves through its arc. Energy from friction forces cannot be recovered, so we say that it’s an external energy, or work done by an external force.
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All the different forms of energy (heat, electrical, nuclear, sound, and so forth) can be broken down into two main categories: potential and kinetic energy. Kinetic energy is the energy of motion. Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it describes the amount of work the object could do as a result of its motion. Whether something is zooming, racing, spinning, rotating, speeding, flying, or diving… if it’s moving, it has kinetic energy.
How much energy it has depends on two important things: how fast it’s going and how much it weighs. A bowling ball cruising at 100 mph has a lot more kinetic energy than a cotton ball moving at the same speed.
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Imagine an arrow is shot from a bow and by the time it hits an apple it is traveling with 10 Joules of kinetic energy (kinetic energy is the energy of motion). What’s meant by kinetic energy is that when it hits something, it can do that much work on whatever is hit.
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Soooo, back to the arrow... if the arrow hits that apple it can exert 10 Joules of energy on that apple. It takes about 1 Newton of force to move that apple so the arrow can move the apple 10 meters. One Joule equals one Newton x one meter so 10 Joules would equal one Newton x 10 meters.
It could also exert a force of 10 Newtons over one meter or any other mathematical calculation you’d like to play with there. (This, by the way, is completely hypothetical. With the apple example we are conveniently ignoring a bunch of stuff like the fact that the arrow would actually pierce the apple, and that there’s friction, heat, sound, and a variety of other forces and energies that would take place here.)
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Here’s a fun experiment that uses a penny in free fall to practice calculating kinetic energy.
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Energy changes to other forms of energy all the time. The electrical energy coming out of a wall socket transfers to light energy in the lamp. The chemical energy in a battery transfers to electrical energy which transfers to sound energy in your personal stereo. In the case of the ball falling, gravitational potential energy transfers to kinetic energy, the energy of motion.
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Think of potential energy as the “could” energy. The battery “could” power the flashlight. The light “could” turn on. I “could” make a sound. That ball “could” fall off the wall. That candy bar “could” give me energy. Potential energy is the energy that something has that can be released. Objects can store energy as a result of their position.
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There are many different kinds of potential energy. We’ve already worked with gravitational potential energy, so let’s take a look at elastic potential energy.
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Materials: a rubber band
A simple way to demonstrate elastic energy is to stretch a rubber band without releasing it. The stretch in the rubber band is your potential energy. When you let go of the rubber band, you are releasing the potential energy, and when you aim it toward a wall, it’s converted into motion (kinetic energy).
Here’s another fun example: the rubber band can also show how every is converted from one form to another. If you place the rubber band against a part of you that is sensitive to temperature changes (like a cheek or upper lip), you can sense when the band heats up. Simply stretch and release the rubber band over and over, testing the temperature as you go. Does it feel warmer in certain spots, or in just one location?
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In this experiment, you’re looking for two different things: first you’ll be dropping objects and making craters in a bowl of flour to see how energy is transformed from potential to kinetic, but you’ll also note that no matter how carefully you do the experiment, you’ll never get the same exact impact location twice.
To get started, you’ll need to gather your materials for this experiment. Here’s what you need:
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Are you ready?
1. Fill the container about 2 inches or so deep with the flour.
2. Weigh one of the balls (If you can, weigh it in grams).
3. Hold the ball about 3 feet (one meter) above the container with the flour.
4. Drop the ball.
5. Whackapow! Now take a look at how deep the ball went and how far the flour spread. (If all your balls are the same size but different weights it’s worth it to measure the size of the splash and the depth the ball went. If they are not, don’t worry about it. The different sizes will effect the splash and depth erratically.
6. Try it with different balls. Be sure to record the mass of each ball and calculate the potential energy for each ball.
Each one of the balls you dropped had a certain amount of potential energy that depended on the mass of the ball and the height it was dropped from. As the ball dropped the potential energy changed to kinetic energy until, “whackapow”, the kinetic energy of the ball collided with and scattered the flour. The kinetic energy of the ball transferred kinetic energy and heat energy to the flour.
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Calculate the gravitational potential energy of the ball. Take the mass of the ball, multiply it by 10 m/s2 and multiply that by 1 meter. For example, if your ball had a mass of 70 grams (you need to convert that to kilograms so divide it by 1000 so that would be .07 grams) your calculation would be
PE=.07 x 10 x 1 = .7 Joules of potential energy.
So, how much kinetic energy did the ball in the example have the moment it impacted the flour? Well, if all the potential energy of the ball transfers to kinetic energy, the ball has .7 Joules of kinetic energy.
Create a table in your science journal or use ours. (You’ll need Microsoft Excel to use this file.)
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We didn’t finish with our three concepts of energy, work, and power yet! The important concept of Power is work done over time, and is measured in watts (W), which is a Joule per second (J/s).
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Work doesn’t have anything to do with time, but power does. Sometimes work is done slow, and other times faster. Someone hiking a mountain can reach the peak way before a rock climber, even though they are both traveling the same vertical distance. A hiker in our example has a higher power rating than a rock climber. Power is the rate that work is done.
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Is power a vector or a scalar quantity? Power is a scalar, but it’s made up of two vector quantities of force and velocity like this:
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What if you’re wanting to get a motor for a winch on the front of your jeep? What size motor do you need? Here’s how to calculate the minimum power so you don’t spend more cash than you need to for a motor that will still do the job. (Near the end of the video below, I’ll show you how to convert watts to horsepower.)
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I love to water ski (no kidding!). Here’s a neat problem about how to determine some things about the boat and deal with weird units like knots in your calculations.
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If you put an ice cube in a glass of lemonade, the ice cube melts. The thermal energy from your lemonade moves to the ice cube. Increasing the temperature of the ice cube and decreasing the temperature of your lemonade. The movement of thermal energy is called heat. The ice cube receives heat from your lemonade. Your lemonade gives heat to the ice cube. Heat can only move from an object of higher temperature to an object of lower temperature.
We’re going to learn about temperature, heat energy, atoms, matter, phase changes, and more in our unit on Thermodynamics as we build steam boats, fire-water balloons, hero engines, thermostats, Stirling engines, and more!
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NEW! Download the complete packet for this section here.
Does this sound familiar? “I’m too cold. Get me a sweater!” “This soup’s too hot!” “Phew, I’m sweating.” “Yowtch, that pan handle burned me!” If you’ve ever made any of the above comments, then you were talking about thermal energy. Very clever of you, don’t you think? Thermal energy is basically the energy of the molecules moving inside something. The faster the molecules are moving, the more thermal energy that something has. The slower they are moving, the less thermal energy that something has.
I’m sure at some point you’ve said, “Wow, my internal thermal energy is way high! I need a liquid with a low thermal energy.” What... you’ve never said that?! Oh, wait. I bet it sounded like this when you said it, “Wow, I’m hot! I need a cool drink.”
Whenever we talk about the temperature of something we are talking about its thermal energy. Objects whose molecules are moving very quickly are said to have high thermal energy or high temperature. The higher the temperature, the faster the molecules are moving. You may remember that temperature is just a speedometer for molecules.
You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down…what happens to the stuff these molecules are are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.
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Here’s a teleclass to get you started on learning about Thermodynamics.
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The next set of lessons will take you in more detail on each topic covered in the teleclass (and more)!
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Temperature is a way of talking about, measuring, and comparing the thermal energy of objects. We use three different kinds of scales to measure temperature. Fahrenheit, Celsius, and Kelvin. (The fourth, Rankine, which is the absolute scale for Fahrenheit, is the one you’ll learn about in college.)
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Mr. Fahrenheit, way back when (18th century) created a scale using a mercury thermometer to measure temperature. He marked 0° as the temperature ice melts in a tub of salt. (Ice melts at lower temperatures when it sits in salt. This is why we salt our driveways to get rid of ice). To standardize the higher point of his scale, he used the body temperature of his wife, 96°.
As you can tell, this wasn’t the most precise or useful measuring device. I can just imagine Mr. Fahrenheit, “Hmmm, something cold…something cold. I got it! Ice in salt. Good, okay there’s zero, excellent. Now, for something hot. Ummm, my wife! She always feels warm. Perfect, 96°. ” I hope he never tried to make a thermometer when she had a fever. Just kidding, I’m sure he was very precise and careful, but it does seem kind of weird.
Over time, the scale was made more precise and today body temperature is usually around 98.6°F. Later, (still 18th century) Mr. Celsius came along and created his scale. He decided that he was going to use water as his standard. He chose the temperature that water freezes at as his 0° mark. He chose the temperature that water boils at as his 100° mark. From there, he put in 100 evenly spaced lines and a thermometer was born.
Last but not least Mr. Kelvin came along and wanted to create another scale. He said, I want my zero to be ZERO! So he chose absolute zero to be the zero on his scale.
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Absolute zero is the theoretical temperature where molecules and atoms stop moving. They do not vibrate, jiggle or anything at absolute zero. In Celsius, absolute zero is -273 ° C. In Fahrenheit, absolute zero is -459°F (or 0°R). It doesn’t get colder than that!
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As you can see, creating the temperature scales was really rather arbitrary: “I think 0° is when water freezes with salt.” “I think it’s just when water freezes.” “Oh, yea, well I think it’s when atoms stop!” Many of our measuring systems started rather arbitrarily and then, due to standardization over time, became the systems we use today. So that’s how temperature is measured, but what is temperature measuring?
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Temperature is measuring thermal energy which is how fast the molecules in something are vibrating and moving. The higher the temperature something has, the faster the molecules are moving. Water at 34°F has molecules moving much more slowly than water at 150°F. Temperature is really a molecular speedometer. When something feels hot to you, the molecules in that something are moving very fast. When something feels cool to you, the molecules in that object aren’t moving quite so fast.
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Have you ever wondered how an ice-cold glass of water gets waterdrops on the outside of the cup? Where does that water come from? Does it ease it’s way through the glass? Did someone come by and squirt the glass with water? No of course not.
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Some of the gaseous water molecules in the air came close enough to the cold glass to lose some molecular speed. Since they lost speed, they formed bonds between each other and liquefied. They condensed on the cold surface of the glass.
Imagine though, if you will, that you live several hundred years ago and the process of condensation wasn’t understood. You happen to be an inquisitive, highly perceptive, person (which of course you are) and you notice this film of water showing up on cold things. Water appearing out of apparently nowhere! You’d be pretty amazed wouldn’t you?!?
Personally, I still find it amazing that every time I pick up a cold can of soda there are molecular interactions happening right in front of my eyes! This is why science is so wonderful. It provides the skills to see these amazing things and the skills to investigate and perhaps understand them.
Here’s an experiment you can do to baffle your senses: Fill one glass with hot water (not boiling), another with ice water, and a third with room temperature water. Place a finger in the hot water and a finger in the ice cold water for a minute or two. Then stick both fingers in the room temperature cup.
How does that feel?
Did it seem that each finger detected a different temperature when placed in the room temperature cup? Weird! So what gives?
Materials:
Download Student Worksheet & Exercises
Your skin contains temperature sensors that work by detecting the direction heat flow (in or out of your body), not temperature directly. These sensors change temperature depending on their surroundings. So when you heated up one finger, and then placed it in cooler water, the heat flowed out of your body, telling your brain it was getting cooler. The ice water finger was detecting a heat flow into your body… and presto! You have one confused brain.
In order for heat to flow, you need to have a temperature difference. But why then do the metal legs of a table feel colder than the wood tabletop when both are at the same room temperature? The metal will feel colder because heat flows away from your skin faster into the metal than the wood. We’ll talk about heat capacity in a later experiment, but this is why scientists had to invent the thermometer, because the human body isn’t designed to detect temperature, only heat flow.
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You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down… what happens to the stuff these molecules are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.
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Is it warmer upstairs or downstairs? If you’re thinking warm air rises, then it’s got to be upstairs, right? If you’ve ever stood on a ladder inside your house and compared it to the temperature under the table, you’ve probably felt a difference.
So why is it cold on the mountain and warm in the valley? Leave it to a science teacher to throw in a wrench just when you think you’ve got it figured out. Let’s take a look at whether hot air or cold air takes up more space. Here’s what you do:
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Materials:
Download Student Worksheet & Exercises
1. Pour a couple of inches of water into an empty soda bottle and cap with a 7-9″ balloon. You can secure the balloon to the bottle mouth with a strip of tape if you want, but it usually seals tight with just the balloon itself.
2. Fill a saucepan with an inch or two of water, and add your bottle. Heat the saucepan over the stove with adult help, keeping a close eye on it. Turn off the heat when your balloon starts to inflate. Since water has a high heat capacity, the water will heat before the bottle melts. (Don’t believe me? Try the Fire-Water Balloon Experiment first to see how water conducts heat away from the bottle!)
3. When you’re finished, stick the whole thing in the freezer for an hour. What happened to the balloon?
What’s going on? So now what do you think? Does the same chunk of air take up more or less space when it’s hot? Cold? When you heat air, it expands because the air molecules move around a lot more when you add energy. The molecules zip around and wiggle like crazy, bouncing off each other more often than when they are cooler.
Getting back to our original question, the upstairs in a house is warmer because the pockets of warm air rise because they are less dense than cool air. The more the molecules move around, the more room they need, and the further they get spaced out. Think of a swimming pool and a piece of aluminum foil. If you place a sheet of foil in the pool, it floats. If you take the foil and crumple it up, it sinks. The more compactly you squish the molecules together, the more dense it becomes. You can read more about density in Unit 3.
As for why mountains and valleys are opposite, it has to do with the Earth being a big massive ball of warm rock which heats up the lower atmosphere in addition to winds blowing on mountains and changes in pressure as you gain altitude… in a nutshell, it’s complicated! What’s important to remember is that the Earth system is a lot bigger than our bottle-saucepan experiment, and can’t be represented in this way.
Exercises
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Making indoor rain clouds demonstrates the idea of temperature, the measure of how hot or cold something is. Here’s how to do it:
Take two clear glasses that fit snugly together when stacked. (Cylindrical glasses with straight sides work well.)
Fill one glass half-full with ice water and the other half-full with very hot water (definitely an adult job – and take care not to shatter the glass with the hot water!). Be sure to leave enough air space for the clouds to form in the hot glass.
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Place the cold glass directly on top of the hot glass and wait several minutes. If the seal holds between the glasses, a rain cloud will form just below the bottom of the cold glass, and it actually rains inside the glass! (You can use a damp towel around the rim to help make a better seal if needed.)
Materials:
Download Student Worksheet & Exercises
On a stormy, rainy afternoon, try bottling clouds — using the refrigerator! Here’s what you do: Place an empty, clean 2-liter soda bottle in the fridge overnight. Take it out and get an adult to light a match, letting it burn for a few seconds, then drop it into the bottle. Immediately cap the bottle and watch what happens (you should see smoke first, then clouds forming inside). Squeeze the sides of the bottle. The clouds should disappear. When you release the bottle, the clouds should reappear. Materials:
Advanced Idea: You can substitute rubbing alcohol and a bicycle pump for the matches to make a more solid-looking cloud. Swirl a bit of rubbing alcohol around inside the bottle, just enough to coat the insides, and then pour it out. Cap your bottle with a rubber stopper fitted with a needle valve (so the valve is poking out of the bottle), and apply your pump. Increase the pressure inside the bottle (keep a firm hand on the stopper or you’ll wind up firing it at someone) with a few strokes and pull out the stopper quickly. You should see a cloud form inside.
What’s going on? Invisible water vapor is all around us, all the time, but they normally don’t stick together. When you squeezed the sides of the bottle, you increased the pressure and squeezed the molecules together. Releasing the bottle decreases the pressure, which causes the temperature to drop. When it cools inside, the water molecules stick to the smoke molecules, making a visible cloud inside your bottle.
Did you know that most drops of water actually form around a dust particle? Up in the sky, clouds come together when water vapor condenses into liquid water drops or ice crystals. The clouds form when warm air rises and the pressure is reduced (as you go up in altitude). The clouds form at the spot where the temperature drops below the dew point.
The alcohol works better than the water because it evaporates faster than water does, which means it moves from liquid to vapor more easily (and vividly) than regular old water.
Questions to ask:
Exercises
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This spooky idea takes almost no time, requires a dime and a bottle, and has the potential for creating quite a stir in your next magic show. The idea is basically this: when you place a coin on a bottle, it starts dancing around. But there’s more to this trick than meets the scientist’s eye.
Here’s how you do it:
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Materials:
Download Student Worksheet & Exercises
Remove the cap of an empty plastic water or soda bottle and replace it with a dime and stick the whole things upright in the freezer overnight. First thing in the morning, take it out and set it on the table. What happens?
If you’re a budding magician, here’s how to modify this experiment to use in your next show. Get a glass container of soda and stick it in the coldest part of your fridge overnight. I know they are getting harder to find these days, but the glass will keep its temperature longer than plastic and enable you to do this trick. In a pinch, you can refill a cleaned glass bottle from a previous use if you can’t locate a fresh glass soda bottle.
As soon as you’re ready to do your trick (practice first!), take it out of the fridge (have it in an ice chest if you’re on stage) and chug the whole thing. (You can ask your audience for help on this – you just want an empty cold bottle for the next part.)
When the bottle is empty but still cold, cap it with a wet dime. Place both hands on the bottle while you “wax eloquent” (make up an engaging story, like “North Winds, come have a taste of soda…”) but be sure to keep your hands on the bottle to warm it up. In about 20 seconds or so, the dime will click up and down, dancing around mysteriously. Keep your hands on the bottle for another 20 seconds or so, and then set it gently on the table with it still dancing, and you’ll find it dancing right on without your hands being there.
How does that work? Was the bottle really empty when you placed it in the freezer? Actually, no… it had air inside of it. The air in the bottle shrank down a bit as it cooled, allowing more air to go into the bottle. When you remove the bottle from the freezer and cap it with the coin, you now have a bottle with more air in it than you started. The air warms and expands, pushing the excess air out the top, making the coin dance. Learn more about air with this Air Expands experiment.
Exercises
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Clouds are made of hundreds of billions of tiny little droplets of liquid water that have condensed onto particles of some sort of dust. Now let’s turn the heat down a bit more and see what happens. As the temperature drops and the molecules continue to slow, the bonds between the molecules can pull them together tighter and tighter.
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Eventually the molecules will fall into a matrix, a pattern, and stick together quite tightly. This would be the solid state. The act of changing from a liquid to a solid is called freezing and the temperature at which it changes is called (say it with me now) freezing point.
Think about this for a second – is the freezing point and melting point of an object at the same temperature? Does something go from solid to liquid or from liquid to solid at the same temperature? If you said yes, you’re right! The freezing point of water and the melting point of water are both 32° F or 0° C. The temperature is the same. It just depends on whether it is getting hotter or colder as to whether the water is freezing or melting. The boiling and condensation point is also the same point.
Now I’m going to mess things up a little bit. Substances can change state at temperatures other than their different freezing or boiling points. Many liquids change from liquid to gas and from gas to liquid relatively easily at room temperatures. And, believe it or not, solids can change to liquids and even gases and vice versa at temperatures other than the usual melting, freezing, or boiling points. So what’s the point of the points?
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At a substance’s boiling, freezing, etc, points, all of the substance must change to the next state. The condition of the bonds cannot remain the same at that temperature. For example, at 100° C water must change from a liquid to a gas. That is the speed limit of liquid water molecules. At 100° C the liquid bonds can no longer hold on and all the molecules convert to gas.
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Believe it or not, the concept of heat is really a bit tricky. What we call heat in common language, is really not what heat is as far as physics goes.
Heat, in a way, doesn’t exist. Nothing has heat. Things can have a temperature. They can have a thermal energy but they can’t have heat. Heat is really the transfer of thermal energy. Or, in other words, the movement of thermal energy from one object to another.
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If you put an ice cube in a glass of lemonade, the ice cube melts. The thermal energy from your lemonade moves to the ice cube. Increasing the temperature of the ice cube and decreasing the temperature of your lemonade. The movement of thermal energy is called heat. The ice cube receives heat from your lemonade. Your lemonade gives heat to the ice cube. Heat can only move from an object of higher temperature to an object of lower temperature.
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If you’ve completed the Soaking Up Rays experiment, you might still be a bit baffled as to why there’s a difference between black and white. Here’s a great way to actually “see” radiation by using liquid crystal thermal sheets.
You’ll need to find a liquid crystal sheet that has a temperature range near body temperature (so it changes color when you warm it with your hands.)
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The liquid crystal sheet is temperature-sensitive. When the sheet received heat from the bulb, the temperature goes up and changes color. The plastic sheets remain black except for the temperature range in which they display a series of colors that reflect the actual temperature of the crystal.
Materials:
1. Color half of the back side of the thermal paper (the side that doesn’t change color) with the highlighter (or cover half of it with foil).
2. Hold it in a position where you can easily see the color-changing side while keeping the light source on the back side.
3. Which side changes color? Is there a difference between the silver and black halves?
You’ll notice that the black half almost immediately changes color, while the silver side stays black. The silver coating reflects the heat, keeping it cool. The black side absorbs the heat and raises its temperature.
Why do liquid crystals change color with temperature? Your liquid crystal sheet is not just one sheet, but a stack of several sheets that are slightly offset from each other. The distance between each layer changes as the sheet warms up – the hotter the temperature, the closer the stacks twist together. The color they emit depends on the distance between the sheets.
The molecules that make up the sheets are long and thin, like hot dogs. When the sheets are cooler, these molecules move around less and don’t twist up as much, which corresponds to reflecting back a redder light. When the temperature rises, the molecules move around more and twist together, and they reflect a bluer light. When the liquid crystal sheet is black, all the light is absorbed (no light gets reflected).
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