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.

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. (A) 360 kN (B) 373 kN (C) 250 kN (D) 500 kN

Tardigrade Admin · Accepted Answer

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 h p}{25 m / s} (\frac{746 W}{1 h p})

= 5.22 \times 1 0^{5} N

or about

5 \times 1 0^{5} N

or

500 k N

(approx.)

360 kN

373 kN

250 kN

500 kN

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 Poutput​=ftotal​v=Pinput​This gives ftotal​=vPinput​​ =25m/s175hp​(1hp746W​) =5.22×105N or about 5×105N or 500kN (approx.)