First slide

Power

Question

When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the car by the air and the road. If the power developed by an engine is 175 hp, estimate the total friction force (approx.) acting on the car when it is moving at a speed of 25 m/s. One horsepower equals 746 W.

Moderate

A

360 kN
B

373 kN
C

250 kN
D

500 kN

Solution

When the car moves at constant speed on a level roadway, the power used to overcome the total friction force equals the power input from the engine, or $P_{output} = f_{total} v = P_{input} . This gives$
$f_{total} = \frac{P_{input}}{v} = \frac{175 hp}{25 m / s} (\frac{746 W}{1 hp})$
= 5.22 $\times 10^{5} N or about 5 \times 10^{5} N or 500 kN (aprrox .)$

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