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 $\mathbf{175}\mathbf{}\mathit{h}\mathit{p}$, estimate the total friction force acting on the car when it is moving at a speed of $\mathbf{29}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}$. One horsepower equals $\mathbf{746}\mathbf{}\mathit{w}$.

Short answer

The total friction force acting on the car when it is moving is: $5\times {10}^{5}N$.

Step-by-step solution

Definition of the power

Power is given by

$P_{output}=f_{total}v$

where

$P_{output}=$Output power

$V=$Body speed

$f_{total}=$Total frictional force exerted on body.

Calculation of the total friction force

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

$$\begin{gathered} P_{output}=f_{total}v\left(P_{input}=P_{output}\right) \\ {P}_{input}=f_{total}v \\ {f}_{total}=\frac{P_{input}}{v} \end{gathered}$$

Byusingtheconceptfromstep(1),wehave

$$\begin{gathered} f_{total}=\frac{P_{input}}{v} \\ {f}_{total}=\frac{175hp}{29m/s}\left(\frac{746w}{1hp}\right)=4.5\times {10}^{5}N=5\times {10}^{5}N \end{gathered}$$

Thus, the total friction force acting on the car when it is moving is: $5\times {10}^{5}N$.