# An automobile engine develops a torque of 270 N m at 3500 rpm. What is the power in watts and in...

## Question:

An automobile engine develops a torque of {eq}270\ N \cdot m {/eq} at {eq}3500 {/eq} rpm. What is the power in watts and in horsepower?

## Power

Power {eq}(P){/eq} is the measure of work {eq}(W){/eq} done, or the applied force {eq}(F){/eq} at some distance{eq}(d){/eq}, in a certain amount of time {eq}(t){/eq}.

{eq}P=\dfrac{F\cdot d}{t}{/eq}

This is commonly used when an object is moving in a straight line. Hence, power can also be determined for objects moving around the axis. Now, torque {eq}\tau{/eq} acts as the force within the angle traveled.

{eq}P=\dfrac{F \cdot 2\pi r}{t}{/eq}

where {eq}r{/eq} is the radius, {eq}f=1/t{/eq} and {eq}F\cdot r=\tau{/eq}.

{eq}P=\tau \cdot 2\pi f=\tau \omega{/eq}.

where {eq}P{/eq} is in Watts (W), {eq}\tau{/eq} is Nm, and {eq}\omega{/eq} is in rad/s.

## Answer and Explanation:

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View this answerWe are given with a torque {eq}\tau = 270 N\cdot m{/eq} and speed {eq}\omega=3500~rpm{/eq}. But since {eq}\omega{/eq} must be in rad/s, we need to...

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Chapter 4 / Lesson 11You've probably heard of torque before, perhaps while discussing cars. Now learn what it really is and what it has to do with rotational equilibrium. Then, work through an example problem that combines the two.