A pump lifts 5000 kg of water to a vertical height of 60 inches in 15 minutes. Calculate the power of the…

Question

A pump lifts 5000 kg of water to a vertical height of 60 inches in 15 minutes. Calculate the power of the pump.

ScanSolve AI Tutor · Accepted Answer

To find the power of the pump, we need to calculate the work done in lifting the water and then divide it by the time taken.

Convert all given values to SI units.
- Mass ( $m$ ) = $5000 \text{ kg}$ (already in SI units)
- Vertical height ( $h$ ) = $60 \text{ in}$ Since $1 \text{ inch} = 0.0254 \text{ meters}$ : $h = 60 \text{ in} \times 0.0254 \text{ m/in} = 1.524 \text{ m}$
- Time ( $t$ ) = $15 \text{ mins}$ Since $1 \text{ minute} = 60 \text{ seconds}$ : $t = 15 \text{ mins} \times 60 \text{ s/min} = 900 \text{ s}$
- Acceleration due to gravity ( $g$ ) = $9.8 \text{ m/s}^2$ (standard value)
Calculate the work done ( $W$ ) by the pump.
The work done in lifting the water is equal to the gravitational potential energy gained by the water.
$W = mgh$ $W = 5000 \text{ kg} \times 9.8 \text{ m/s}^2 \times 1.524 \text{ m}$ $W = 74676 \text{ J}$
Calculate the power ( $P$ ) of the pump.
Power is the rate at which work is done.
$P = \frac{W}{t}$ $P = \frac{74676 \text{ J}}{900 \text{ s}}$ $P \approx 82.973 \text{ W}$
Rounding to three significant figures:
$P \approx 83.0 \text{ W}$
The power of the pump is:
$\text{83.0 W}$

A pump lifts 5000 kg of water to a vertical height of 60 inches in 15 minutes. Calculate the power of the pump.