Question below, how does the way someone pushes two boxes affect the action reaction forces on each box?

Two trunks sit side by side on the floor. The large trunk (52kg) is to the left of the smaller trunk (34kg). A person pushes on the larger trunk horizontally toward the right. The coefficient of static friction between the trunks and the floor is 0.35. Does the force that the larger trunk exerts on the smaller trunk change if the person pushed in the opposite direction (on the smaller trunk)?

Oct 7, 2017

The force does depend on which way one pushes the trunks. See below for details.

Explanation:

If you push on the larger trunk, the force applied by the larger trunk on the smaller crate is based on the value of the static coefficient and the normal force acting on the smaller trunk (which is equal to the weight of the smaller trunk).

(Don't be confused here - the force being applied by the person pushing both trunks is dependent on the weight of both trunks, and would not change if we changed directions. But the force being exerted by the large trunk on the smaller one depends only on the weight of the smaller one. It is as though the person and the larger trunk become one object that is causing the force one the smaller trunk.)

Now, if we reverse direction, and push on the smaller trunk instead, the amount of force between the trunks is based on the value of the static coefficient and the normal force acting on the larger trunk, as it is now the one that we are attempting to move. So, the force is larger than before.

We might be inclined to think that this larger force is the actually the small trunk pushing on the big trunk, but by Newton's third law, this must be equal to the force of the big trunk on the small trunk. I mention this only in the hope of making it clear that the force of the larger trunk on the smaller, or of the smaller trunk on the larger are the type of "equal and opposite" forces as described in Newton's third law.