# An automobile crankshaft transfers energy from the engine to the axle at the rate of 100 hp (=...

## Question:

An automobile crankshaft transfers energy from the engine to the axle at the rate of {eq}100 \ hp \ (= 74.6 \ kW) {/eq}, when rotating at a speed of {eq}1800 \ rev / min {/eq}.

(a) What torque (in newton-meters) does the crankshaft deliver?

## The torque of Crankshaft :

The formula for the power of the crankshaft in terms of torque is:

• {eq}P=\tau \omega {/eq}

Where,

• {eq}\tau {/eq} is the torque of the crankshaft.
• {eq}\omega {/eq} is the angular velocity of the crankshaft.

Rearrange the above formula for torque and simplify it after substitution the values.

## Answer and Explanation:

Given data:

The power of the crankshaft is:

{eq}P=74.6\ kW\\ =74.6\times 10^{3}\ W {/eq}

The angular speed of the crankshaft is:

{eq}\omega = 1800\ rev/min\\ =1800 \times \frac{2\pi}{60}\ rad/sec\\ =60\pi \ rad/sec {/eq}

Substitute these values in the formula and simplify the expression for torque.

{eq}\begin{align*} 74.6\times 10^{3}&=\tau (60\pi )\\ \tau&=\frac{74.6\times 10^{3}}{60\pi}\\ &=395.76\ N\cdot m \end{align*} {/eq}