Question

a pump lifts 1000 kg of water to a height of 10m in 1 minute calculate the power of the pump​

Answer 1

Given :

Mass of the water = 1000 kg

Height = 10 m

Time interval = 1 min = 60 s

To Find :

Power of the pump.

Solution :

❖ Power is defined as the work done per unit time. It is a scalar quantity having only magnitude. SI unit of power is watt (W).

Formula :- $\underline{\boxed{\bf{\purple{Power=\dfrac{Work}{Time}}}}}$

• In this case work done will be equal to the change in potential energy of water.

Potential energy of body of mass m at a height of h is given by, U = mgh

where g denotes acceleration due to gravity.

• Potential energy at ground or reference point is taken zero.

$\sf:\implies\:P=\dfrac{W}{t}=\dfrac{U_2-U_1}{t}$

$\sf:\implies\:P=\dfrac{mgh-0}{t}$

By substituting the given values;

$\sf:\implies\:P=\dfrac{(1000)(10)(10)}{60}$

$\sf:\implies\:P=\dfrac{10000}{6}$

$:\implies\:\underline{\boxed{\bf{\gray{P=1666.67\:W}}}}$