No Friction Involved

To compete in a bowling-ball hurling contest, you first squat and cup your hands under the ball on the floor. Then you rapidly straighten up while also pulling your hands up sharply, launching the ball upward at about face level. During your upward motion, your applied force on the ball obviously does work; that is, it is an external force that transfers energy, but to what system?

To answer, we check to see which energies change. There is a change in the ball's kinetic energy and, because the ball and Earth become more separated, there is a change in the gravitational potential energy of the ball-Earth system. To include both changes, we need to consider the ball-Earth system. Then your force is an external force doing work on that system, and the work is

, (8-23)

Or (work done on system, no friction involved), (8-24)

where is the change in the mechanical energy of the system. These two equations, which are represented in Fig. 8-12, are equivalent energy statements for work done on a system by an external force when friction is not involved.