Newton's Third Law of pushing a box

[Doc Al]

Don't forget that "action" and "reaction" forces (a better term would be "third law pairs") act on different bodies and thus never "cancel out" directly. The force of 100 N on the box describes a force acting on the box. To determine the motion of the box, you need to examine all the forces acting on the box. Similarly, the "reaction" of the box pushing back on you is a force on you.

 

[rcgldr]

ok, so the box is in dynamic equilibrium...so what's the difference between the force of the box pushing back and the force of friction?

Zero, assuming the box isn't accelerating. Since static friction is normally greater than dynamic friction, it would have taken more than 100N to get the box to start sliding, and once it was sliding the force could be reduced to equal that of dynamic (sliding) friction, which in this case is 100N, and the box would not accelerate.

Newton 3rd law coexistant force pairs: a forward force applied by the pusher onto the box, and and backwards force applied by the box onto the pusher. A forwards force applied by the box onto the surface it slides on, and a backwards force applied by the surface onto the sliding box. Vertical forces: gravity pulls down on the box and upwards on the earth. The surface the box rests on is compressed: the box applies a downwards force onto the surface, the surface applies an upwards force onto the box, at the bottom side of the surface, the surface applies a downwards force onto the earth, the Earth applies an upwards force onto the surface.

 

[Laus102]

I just cannot understand how the forces do not cancel out directly yet do in fact cancel out in some way. I understand that the action and reaction forces act on different bodies, but how then do they end up canceling each other out? Do they never cancel out at all? Does the box push back on me until it can no longer match my force and it has to move since my force has offset gravity and friction? Grrrrrrr...

 

[Doc Al]

I just cannot understand how the forces do not cancel out directly yet do in fact cancel out in some way. I understand that the action and reaction forces act on different bodies, but how then do they end up canceling each other out? Do they never cancel out at all?

That's right: Action and reaction forces never cancel out because they don't act on the same body.

If you are able to push on the box with 100N of force, that means the box is also pushing back on you with 100N of force. These two forces don't cancel out.

An example of forces (not action/reaction pairs) canceling would be this: You push on the box with a force of 100N to the right while friction pushes on the box with a force of 100N to the left. Those forces on the box cancel, giving a net force of zero.