# Forces Cancel?

## The Problem:

Often people have the following difficulty with Newton's Third Law:

"If A pushes B, then B pushes A with an equal and opposite force. If these forces are equal and opposite, they cancel, producing a net force of zero. This means that neither object can accelerate, which means that Newton's Laws predict that nothing can ever move."

(See The Horse & Cart Problem.) What's going on?

## The Key Ideas:

• Object A accelerates (or not) because of the forces that push or pull on it. (Newton's 2nd Law) Forces that push or pull on some other object have no effect on object A's motion - even if object A exerts them.

• Only the forces that act on an object can cancel. Forces that act on different objects don't cancel - after all, they affect the motion of different objects!

## The Solution:

Newton's Third Law really does say that if A pushes B, then B pushes A with an equal and opposite force. However, these forces DO NOT CANCEL because they influence the motion of different objects. The force that A exerts on B influences B's motion, and the force that B exerts on A influences A's motion. The force on B can cancel with other forces on B - but NOT with forces on A(and vice versa).

last update March 23, 1998 by JL Stanbrough