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Newton's Third Law

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The third law is in part very straight forward but in another part not easy to buy really into. Remember that we introduced forces as an interaction between two objects. One object has to be exerting a force on a second object. An object cannot do this on its own.

Imagine you are riding a skateboard. To get going you are pushing off the ground. If you push against the ground, you are interacting with it. Your foot is pushing off the gournd backwards, but the skateboard will be moving forward. The change in motion of the skateboard cannot be caused by your push since it is in the wrong direction. Instead it has to be caused by a push in the opposite direction. This push is caused by the ground. Since forces are always an interaction between two objects every force is paired with a second force that is going in the opposite direction.

Imagine you are standing with skates on ice and are pushing off of your friend. The result will be both of you moving in opposite direction. Forces always come in pairs that are in opposite directions.

This aspect of Newton’s third law is fairly easy to understand as you have a lot of experience to back it up. But there is another aspect that is more difficult and not as easy to understand. It compares the magnitude of these two forces in other words we are trying to find out which force is bigger.

Let’s get back to our example of two skaters on ice, but now the skaters are not kids but say Andre the Giant and a tiny figure skater. If Andre pushes off of the figure skater we will find that they are both moving apart. You might also imagine that Andre is not going as far (or fast) as the figure skater. All of this might lead you to conclude that the force by Andre on the skater is greater than the force by the skater on Andre, after all Andre is much stronger and the skater moves farther. This is, however, not true. Both forces are equal.

 

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In order to understand this, you need to look into what causes the figure skater to move farther and faster. Sure, it could be that the force that is applied is greater, what is a fact, however, is that the skater is smaller and has les mass, therefore less resistance to change her motion from rest. Imagine you are asked to push both of them, the skater and Andre with the same force, what would you expect? Surely you would agree that with Andre being much more massive he will not move as easily as the figure skater. So, we see that the same force applied can result in different changes in motion if the masses are not the same. That shows that even though it is counterintuitive it is possible for the forces between the two to be the same. But we do not have proof yet, that they really are.

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Real proof can only come through an experiment, but there are a few things that you can try to think about that might help you understand. Imagine our two helpers form above, but this time they are not pushing but rather holding on to a thin rubber band and pulling. Andre does all the pulling and the skater is simply holding on.  Andre is stronger and does the pulling. How will the rubber band stretch? Will is stretch more on Andre’s side because he does the pulling? I think it will not take a great leap of faith that the rubber band will stretch the same throughout, thus proving that the pulls the same on either end, and that even so the skater does nothing but hold on, she still pulls just as hard as Andre.

 

Imagine our two helpers from above push off each other (Andre still does all the pushing) but now they are each holding a needle and between them is a piece of wax or something soft like it, so the needles can penetrate the wax. The figure skater is holding the needle, which is touching the wax. On the other side Andre is also holding a needle, which is touching the wax on the opposite side. Andre now pushes toward the skater with his needle, which then will go into the wax. The wax will also move and go toward the second needle. Which needle will have penetrated more? It should not take a great leap of faith to see that both needles will have penetrated the same amount, thus showing that the forces are the same.

 

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