A force is something that can cause matter to start moving, stop moving, speed up or slow down. In other words, if a force is applied to some piece of matter it will change the way it is moving or not moving.

The problem with this is that it seems to violate our common experience. We see moving objects slow down and stop all of the time without any apparent force applied. To make matters worse, there are lots of times that we know a force is being applied and yet objects don’t start moving at all. To appreciate forces, and to understand how they work, we need to imagine an “ideal” world—that is a world where we can control all forces.

As a simple example, think about a puck on an air hockey table. This essentially eliminates friction, the force that slows things down as they slide along the floor or a table. Now, imagine the puck moving along the table. It glides, not speeding up, not slowing down and not changing direction until some force is applied, that is until something pushes it or pulls on it in some way. This could be when it bangs into the wall, when it gets hit by a paddle or even if you blow on it. Any of these things could stop the puck, change its direction, slow it down, speed it up, or some combination of these. What is important to recognize is that once the puck is moving, force no longer needs to be applied to keep it moving, but that to change the movement in any way (speed or direction) a force must be applied.

Now imagine that both you and your opponent are pushing on the puck at the same time. If you push in the same direction, the puck will move faster and faster in that direction. However, if you push in opposite directions, and if you both push equally hard, the puck will not move. In this instance we say that there are equal and opposite forces on the puck. Now, here’s the weird part. If both of you were invisible, there would be no way for someone looking at the puck, seeing it not moving, to tell whether it was being pushed in opposite directions, or not being pushed at all.

The upshot of this is that when something is not moving, there are two possibilities. One, that there is no force acting on it at all, and two, that there are equal and opposite forces acting on it.In our very real world with friction, gravity, etc. the second is much more common.

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