In Example 6.10, we compared the gravitational potential energy of a 100-W lightbulb to th...

In Example 6.10, we compared the gravitational potential energy of a 100-W lightbulb to the electrical energy consumed when it is turned on. Repeat that calculation, but now assume the lightbulb is turned on for one day. Find the height h through which the lightbulb would have to fall for the change in gravitational potential energy to equal the electrical energy consumed by the lightbulb. Compare this answer to the height of Mount Everest. Assume you can use the relation PEgrav = >mgh.

Example 6.10

Comparing Mechanical and Electrical Energy

Consider a lightbulb rated for a power consumption of Pbulb = 100 W. This lightbulb consumes a certain amount of electrical energy in 1 second of use. Suppose we want to generate the same amount of energy by dropping the lightbulb from a height h to ground level. If the mass of the lightbulb is m = 0.050 kg, what is h?

RECOGNIZE THE PRINCIPLE

We apply conservation of energy principles to the lightbulb. The change in potential energy of the lightbulb is ΔPE = −mgh. This energy must equal (in magnitude) the energy used by the lightbulb in 1 s.

SKETCH THE PROBLEM

Figure 6.33 describes the problem.

Figure 6.33 Example 6.10. A falling lightbulb.

IDENTIFY THE RELATIONSHIPS

Using the definition of power (Eq. 6.30), the energy consumed by the lightbulb in time t is

W = Pbulbt

Setting this equal to the change in potential energy when the lightbulb falls gives

mgh = Pbulbt

SOLVE

Solving for h, we find

What does it mean?

This result is a surprisingly large height: what we normally consider to be a rather small amount of electrical power consumption (by the lightbulb) corresponds to a substantial amount of mechanical energy. Imagine what h would be if the lightbulb were turned on for 1 day!