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Question 2.7: Power Transmission by the Shaft of a Car Determine the power...

Power Transmission by the Shaft of a Car

Determine the power transmitted through the shaft of a car when the torque applied is 200 N-m and the shaft rotates at a rate of 4000 revolutions per minute (rpm).

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The torque and the rpm for a car engine are given. The power transmitted is to be determined.

Analysis A sketch of the car is given in Fig. 2-31. The shaft power is determined directly from

\begin{aligned}\dot{W}_{\mathrm{sh}} &=2 \pi \dot{n} \mathrm{~T}=(2 \pi)\left(4000 \frac{1}{\mathrm{~min}}\right)(200 \mathrm{~N} \cdot \mathrm{m})\left(\frac{1 \mathrm{~min}}{60 \mathrm{~s}}\right)\left(\frac{1 \mathrm{~kJ}}{1000 \mathrm{~N} \cdot \mathrm{m}}\right) \\&=83.8 \mathrm{~kW} \quad\quad(\text { or } 112 \mathrm{hp})\end{aligned}

Discussion Note that power transmitted by a shaft is proportional to torque and the rotational speed.

2.31

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