Power

Power is the rate at which energy is produced, consumed, or transformed, that is,
 ….(8)

Example-1

A car (1000 kg) traveling 55 mph has a forward cross-sectional area of about 4 m2. What is the power dissipated by air resistance? (Use 1 mph  0.45 m/s. Recall that the formula for air resistance is Fair CAv2, where , the density of air, is 1.29 kg/m3 and C  0.2.)

Solution

First, we DRAW A DIAGRAM (Figure 9-10).

Figure 9-10

We have only one formula to work with (P = ΔEt), but we have neither an energy nor a time. But we have several formulas for energy, so let's try to connect it with the force given in the problem. We have

since cosφ = –1. We can substitute for Fair. And the expression Δx/Δt reminds us of velocity, so we have

P = –Fairv = –(CρAv2)v

= –1.6 x 104 W.

The minus sign indicates that the energy is dissipated by the force.

Example-2

The same car is traveling 65 mph. What is the power dissipated by air resistance?

Solution

P = –2.6 x 104 W.

Why is there such a large difference?