Work and Potential Energy

In Chapter 7 we discussed the relation between work and a change in kinetic energy. Here we discuss the relation between work and a change in potential energy.

Let us throw a tomato upward (Fig. 8-2). We already know that as the tomato rises, the work done on the tomato by the gravitational force is negative because the force transfers energy from the kinetic energy of the tomato. We can now finish the story by saying that this energy is transferred by the gravitational force to the gravitational potential energy of the tomato-Earth system.

The tomato slows, stops, and then begins to fall back down because of the gravitational force. During the fall, the transfer is reversed: The work done on the tomato by the gravitational force is now positive - that force transfers energy from the gravitational potential energy of the tomato-Earth system to the kinetic energy of the tomato.

For either rise or fall, the change in gravitational potential energy is defined to equal the negative of the work done on the tomato by the gravitational force. Using the general symbol for work, we write this as

Fig. 8-2 A tomato is thrown upward. As it rises, the gravitational force does neg­ative work on it, decreasing its kinetic energy. As the tomato descends, the gravitational force does positive work on it, increasing its kinetic energy.

This equation also applies to a block-spring system, as in Fig. 8-3. If we abruptly shove the block to send it moving rightward, the spring force acts leftward and thus does negative work on the block, transferring energy from the kinetic energy of the block to the elastic potential energy

of the spring. The block slows and even­tually stops, and then begins to move leftward because the spring force is still leftward. The transfer of energy is then reversed - it is from potential energy of the spring to kinetic energy of the block.