Why Action and Reaction

Forces Don't Cancel - 2

In the previous chapter, there was a very simple example problem - to avoid too much flipping back and forth, here it is:

A net force of 10 Newtons acts on a box which has a mass of 2 kg. What will be the acceleration of the box?


This is about as straightforward as it can get - Newton's Second Law says that the acceleration of an object equals the net force on it divided by its mass:

Example 1 solution

This is pretty simple, right? The acceleration of the box just equals the net force on the box divided by the mass of the box. In this example, we didn't stop to consider where the 10 N force came from - but now we know that forces are interactions between objects - some object exerted the 10 N force on the box. Suppose this object was a person's hand:

diagram of hand pushing box

Newton's Third Law says that isolated forces do not exist - forces always occur in pairs. if the "action force" in this situation is "Hand pushes box.", the reaction force is "Box pushes hand.", right?

Diagram for Newton's Third Law

So, what is the acceleration of the box? It is still 5 m/s2! Of course! Even though these two forces are equal and opposite, they do not cancel. The force that the hand exerts on the box accelerates the box (at 5 m/s2). The force that the box exerts on the hand accelerates the hand. (Actually, it is the net force on the hand that accelerates the hand, but the box's force contributes to the net force on the hand.)

Only forces on you accelerate you.

Forces you exert on other objects accelerate the other objects.

last update April 6, 2000 by JL Stanbrough