Suppose you and a friend, who has exactly twice your mass, are on skates. You push away from your friend....?

Question

How does the force with which you push your friend compare to the force with which your friend pushes you? How do your accelerations compare?

Answer 1

The forces are equal and opposite, but your friend with twice your mass will accelerate at only half the rate you do. Newton's Third Law of Motion specifies that any action (i.e., force) has an equal and opposite reaction, in this case the force with which your friend pushes on you when you push on him. Newton's Second Law of Motion says that the rate of change of momentum is proportional to an applied force. This is usually rendered F = ma, where F is force, m is mass, and a is acceleration. As you can see, to keep F constant when m is doubled, a must be divided in half.