Question

An engine develops 2kw of power. How much time will it take to lift a mass of 50kg to a height of 40m? \[\left( {g = 10m{\rm{ }}{s^{ - 2}}} \right)\]

Answer 1

Hint: According to the question it is given that the given engine develops the amount of power is 2kw. And the question asks what time it will take to lift a mass of 50kg up to a height of 40m. To solve this question, we will simply insert the formula and enter values and we will get the required solution.

Formula used:
${\rm{P}} = \dfrac{{{\rm{mgh}}}}{{\rm{t}}}$
Where,
P is power developed by the engine.
h is the height at which the object is to be raised
g is the acceleration due to gravity
m is the mass of the given object which is to be lifted and
t is known as the time taken to lift the body.

Complete answer:
The mass of the given object is 50kg
The power of the engine is 2kw which is nothing but $2 \times {10^3}{\rm{W}}$
\[g = 10m{\rm{ }}{s^{ - 2}}\]
The given Height at which the body is to be raised is 40m

Now substituting these above values in the formula,
\[2 \times {10^3} = \dfrac{{50 \times 10 \times 40}}{t}\]
\[ \Rightarrow t = \dfrac{{50 \times 10 \times 40}}{{2 \times {{10}^3}}}\]
\[ \Rightarrow t = 10{\rm{sec}}\]

Hence, the required time to lift the object of 50kg at a height of 40m is 10 seconds.

Note: A common mistake that usually students make mistakes is not converting the unit which results in different and wrong answers. Power is always a function of labour output, therefore if a person works at a variable rate depending on the time of day, his power will likewise vary.