Question

(II) How much work can a 2.0-hp motor do in 1.0 h?

Short answer

The obtained value of the work done by the motor is\(5.37 \times {10^6}\;{\rm{J}}\).

Step-by-step solution

The relation expressing power and work

In order to calculate the work done by the motor,you will need to calculate the product of the power of the motor and the provided time.In the standard international system, work is expressed in Joule and power is expressed in Watt.

The relation between power (P) and work (W) for time (t)is given by:

\(P = \frac{W}{t}\)

\(W = P \times t\) … (i)

Given data and required work done

Given data:

The power of the motor is\(P = 2\;{\rm{hp}}\).

The time is\(t = 1\;{\rm{h}}\).

On plugging the values in the equation (i), you get:

\(\begin{aligned}W &= \left( {2\;{\rm{hp}} \times \frac{{746\;{\rm{W}}}}{{1\;{\rm{hp}}}}} \right)\left( {1\;{\rm{h}} \times \frac{{60 \times 60\;{\rm{s}}}}{{1\;{\rm{h}}}}} \right)\\W &= 5.37 \times {10^6}\;{\rm{J}}\end{aligned}\)

Thus,\(W = 5.37 \times {10^6}\;{\rm{J}}\)is the work done by the motor.