Question

An engine generates a power of $75\text{kW}$ having efficiency of $80\%$ and the car moves with a constant velocity of $20\text{m/s}$. Find the force generated by the engine. (Assume the engine applies a constant force on the car)

• A. $2000\text{N}$
• B. $3000\text{N}$
• C. $6000\text{N}$
• D. $1500\text{N}$

Answer 1

The correct option is B $3000\text{N}$

Given Power$=75\text{kW}$
Efficiency of engine, $\eta =80\%$
$\eta =\frac{\text{Actual delivered power to the car}}{\text{Power generated by the engine}}$
i.e $0.80=\frac{P_{actual}}{75}$
$\Rightarrow P_{actual}=0.80\times 75\text{kW}=60000\text{W}$

We know that Power$P=\overrightarrow{F}.\overrightarrow{v}=Fv\cos \theta =Fv\cos 0^{\circ }=Fv$
$\Rightarrow 60000=F\times 20$
$\therefore F=\frac{60000}{20}=3000\text{N}$