Question

Find the power of an engine that lifts 90 metrics tonnes of coal per hour from a depth of 200m.

Answer 1

Hint: Power also known as an activity, is defined as the amount of energy transferred or converted per unit of time. We can calculate the energy required for the mass given and thus, find the power required.

Formula Used: $ {\text{Power of engine = }}\dfrac{{{\text{Energy required}}}}{{{\text{Time}}}} $
E=mgh
where m is the mass, g is acceleration due to gravity and h is the height.

Complete step-by-step answer
It is given that the engine lifts 90 metric tonnes of coal per hour from a depth of 200m that is the height to which mass (m) is lifted is h=200m.
The power of the engine will be the energy required by the engine to lift the mass per unit time.
To find the power of the engine, the formula used will be,
 $ {\text{Power of engine = }}\dfrac{{{\text{Energy required}}}}{{{\text{Time}}}} $ ,
 $ P = \dfrac{E}{T} $ ,
Where E=mgh that is the work done and T=1hr.
E=mgh, here m=mass of the object, g= constant related to earth’s gravitational force, and h= height.
Therefore, $ {\text{P = }}\dfrac{{{{(90 \times 1000)(10)(200)}}}}{{{{(60 \times 60)}}}} $
 $ {\text{P = }}\dfrac{{{{(18 \times 1}}{{\text{0}}^{\text{7}}}{{)}}}}{{{{(36 \times 1}}{{\text{0}}^{\text{2}}}{\text{)}}}} $
The final answer will be,
 $ {{P = 5 \times 1}}{{\text{0}}^{\text{4}}}{\text{ W}} $
Therefore, the total power required by the engine to lift the coals is $ {{5 \times 1}}{{\text{0}}^{\text{4}}} $ watt.

Note:
Power is a scalar quantity and has an SI unit as watt (W). In this question for calculating force, the formula of energy is used E=mgh. The time given in the question is in hours whereas the formula has time in minutes, thus we need to multiply one minute with 60 to make it one hour as per the question.