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Introduction to Newton's Laws of Motion

Newton's Third Law of Motion


To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
- Newton's Third Law of Motion, translated from the Principia's Latin
We represent the Third Law by looking at two bodies A and B that are interacting. We define FA as the force applied to body A by body B and FA as the force applied to body B by body A. These forces will be equal in magnitude and opposite in direction. In mathematical terms, it is expressed as:
FB = - FA


FA + FB = 0

This is not the same thing as having a net force of zero, however. If you apply a force to an empty shoebox sitting on a table, the shoebox applies an equal force back on you. This doesn't sound right at first - you're obviously pushing on the box, and it is obviously not pushing on you. But remember that, according to the Second Law, force and acceleration are related - but they aren't identical!

Because your mass is much larger than the mass of the shoebox, the force you exert causes it to accelerate away from you and the force it exerts on you wouldn't cause much acceleration at all.

Not only that, but while it's pushing on the tip of your finger, your finger in turn pushes back into your body, and the rest of your body pushes back against the finger, and your body in turn pushes on the chair or floor (or both), all of which keeps your body from moving and allows you to keep your finger moving to continue the force. There's nothing pushing back on the shoebox to stop it from moving.

If, however, the shoebox is sitting next to a wall and you push it toward the wall, the shoebox will push on the wall - and the wall will push back. The shoebox will, at this point, stop moving. You can try to push it harder, but the box will break before it goes through the wall because it isn't strong enough to handle that much force.

Tug of War: Newton's Laws in Action

Most people have played tug of war at some point. A person or group of people grab the ends of a rope and try to pull the person or group at the other end, usually past some marker (sometimes into a mud pit in really fun versions), thus proving that one of the groups is stronger. All three of Newton's Laws can be seen very obviously in tug of war.

There frequently comes a point in tug of war - sometimes right at the beginning but sometimes later - where neither side is moving. Both sides are pulling with the same force and therefore the rope does not accelerate in either direction. This is a classic example of Newton's First Law.

Once a net force is applied, such as when one group begins pulling a bit harder than the other, an acceleration begins, and this follows the Second Law. The group losing ground must then try to exert more force. When the net force begins going in their direction, the acceleration is in their direction. The movement of the rope slows down until it stops and, if they maintain a higher net force, it begins moving back in their direction.

The Third Law is a lot less visible, but it's still there. When you pull on that rope, you can feel that the rope is also pulling on you, trying to move you toward the other end. You plant your feet firmly in the ground, and the ground actually pushes back on you, helping you to resist the pull of the rope.

Next time you play or watch a game of tug of war - or any sport, for that matter - think about all the forces and accelerations at work. It's truly impressive to realize that you could, if you worked at it, understand the physical laws that are operating in your favorite sport.

Newton's Three Laws of Motion

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