Question

An electric motor exerts a force of \[40{\text{ N}}\] on a cable and pulls it by a distance of \[30{\text{ m}}\] in one minute. The power supplied by the motor (in watts) is:
A. \[{\text{2}}0{\text{ }}\]
B. \[{\text{200}}\]
C. \[{\text{2}}\]
D. \[{\text{10}}\]

Answer 1

Hint: The amount of force exerted by an electric motor on the cable is \[40{\text{ N}}\]. This force is able to move it a distance of \[30{\text{ m}}\] in one minute, we will calculate the work done in doing so. Then we will find the rate of work done which is equal to power supplied by the motor.

Formula Used:
\[\text{Power} = {\text{ }}\dfrac{{{\text{Work done }}}}{{{\text{Time (s)}}}}\]

Complete step by step answer:
Whenever we exert a force on an object then it gets displaced from its original position and in doing so some work is done. This work done by the force is equal to the product of force and distance by which the object gets displaced.

Therefore we will calculate the work done by the motor on moving the cable by a distance of \[30{\text{ m}}\]. Therefore the amount of work done when a force of \[40{\text{ N}}\] is applied on moving the cable by \[30{\text{ m}}\] can be calculated as,
\[\text{Work done} = \] Force × Displacement
\[\Rightarrow \text{Work done} = {\text{ }}\left( {{\text{40 }} \times {\text{ 30}}} \right){\text{ N m}}\]
\[\Rightarrow \text{Work done} = {\text{ 1200 N m}}\]

We know that power is defined as the rate of work done by any object. Hence the power supplied by the motor in doing the above calculated work in one minute will be calculated as,
\[\text{Power} = {\text{ }}\dfrac{{{\text{Work done }}}}{{{\text{Time (s)}}}}\]
We will convert time into seconds for finding power supplied by an electric motor.
Power supplied by electric motor \[ = {\text{ }}\dfrac{{{\text{1200 N m }}}}{{60{\text{ s}}}}\]
Power supplied by electric motor \[ = {\text{ 20 Watts}}\]

Hence the correct option is A.

Note: We will convert the time into seconds for finding power delivered. We can also find the power supplied by the motor by multiplying the force exerted by the motor and the velocity of the cable during that time. The answer would be the same for both cases.