Newton’s Second Law of Motion

To review, Newton’s First Law deals with objects that have balanced forces on it and predicts how they will behave. It’s sometimes called the law of inertia, and it’s the law that is responsible for helping you figure out which egg is raw or hard-boiled without having to crack it open. (If you haven’t done this, you really need to. All you have to do is set the egg spinning on the counter, then gently touch the top with a finger for a second, then release. The egg that stops dead is hard-boiled, and the one that starts spinning again in raw. Don’t know why this works? The raw egg has a liquid center that isn’t connected to the hard shell. When you stopped the shell for a split second, the innards didn’t have time to stop, and they have inertia. When you removed your finger, the liquid exerts a force on the shell and starts it spinning again. The hard-boiled egg is solid all the way through, so when you stopped the shell, the whole thing stops. Newton’s First Law in action.)

Newton’s Second Law of Motion deals with the behavior of objects that have unbalanced forces.  The acceleration of an object depends on two things: mass and the net force actin on the object. As the mass of an object increases, like going from a marshmallow to a bowling ball, the acceleration decreases. Or a rocket burning through its fuel loses mass, so it accelerates and goes faster as time progresses. There’s a math equation for the second law, and it’s stated like this: F = ma, where F is the net force, m is the mass, and a is the acceleration.  It’s important to note that F is the vector sum of all forces applied to the object. If you miss one or double count one of them, you’re in trouble. Also note that F is the external forces exerted on the object by other objects, not the internal forces because those cancel each other out.

Remember when we studied Free Fall Motion and we assumed that all objects fall with the same acceleration of g or 9.81 m/s² ?

Well, that wasn’t the whole truth, because not all objects fall with the same acceleration. But it’s a good place to start out when we’re getting our feet wet with physics. (You’ll find this happens a lot when you get to more advanced concepts… you learn the easier stuff first by ignoring a lot of other things until you can learn how to incorporate more things into your equations.) So why do objects stop accelerating and reach terminal velocity, and how why do more massive objects fall faster than less massive? To answer this, we’ll take a look at air resistance and Newton’s Second Law using the F = ma equation.

This lesson may give you a sinking sensation but don’t worry about it. It’s only because we’re talking about gravity. You can’t go anywhere without gravity. Even though we deal with gravity on a constant basis, there are several misconceptions about it. Let’s get to an experiment right away and I’ll show you what I mean.

If I drop a ping pong ball and a golf ball from the same height, which one hits the ground first? How about a bowling ball and a marble?

Here’s what you need:

There are situations where you have two objects interacting with each other, which means that you’ll have two unknown variables you’ll solve for (usually acceleration). You can solve these types of problems in a couple different ways. First, you can look at the entire system and consider both objects as only one object. For example, the Earth and Moon might be combined into one object if we’re looking at objects that orbit the sun, so the mass of the Earth and Moon would be combined into a single mass, m, and would also have the same acceleration, a. This approach is used if you really don’t care about what’s going on between the two objects. Or you could treat each object as it’s own separate body and draw FBD for each one. This second approach is usually used if you need to know the forces acting between the two objects.