Question

How much mass of water can be lifted by a pump motor of 9.8kw in one minute to a height of 5m?

Answer 1

Answer: The mass of the water is 12000 kg.

Explanation:

The expression for the power in terms of work done and time is as follows,

$P=\frac{W}{t}$                                                    ....... (1)

Here, P is the power, W is the work done and t is the time.

The expression for the work done is as follows,

$W=Fs$

Put F=mg.

$W=mgs$

Put $W=mgs$ in the equation (1).

$P=\frac{mgs}{t}$

As it is given in the problem,  water can be lifted by a pump motor of 9.8kw in one minute to a height of 5m.

Convert time from to second and power from kW to W.

t= 1 min = 60 s

1 kW= 1000 W

$P=9.8\times 1000 W$

Put s=5 m, t=60 s,$P=9.8\times 1000 W$ and g=9.8 meter per second square.

$9.8\times 1000=\frac{m(9.8)(5)}{60}$

$9.8\times 1000 =\frac{m(9.8)(5)}{60}\\m=12000 kg$

Therefore, the mass of the water is 12000 kg.

Answer 2

Work. = Mass * Gravity * height

Power * time = Mass * Gravity * height

9800W * 60s =Mass * 9.8m/s^2 * 50m

Mass = 12000kg