The efficiency of a pump is 50%. It lifts 2 tonnes of water by 60 m in 20 minutes. Find the input power (in kW) of the pump.
2
CONCEPT:
- Power : The rate of work done is called power. It is denoted by P.
Power (P) = Work done (W)/Time (t)
- Potential energy: The energy of a body due to its position is called potential energy.
Potential energy (PE) = m g h
Where m is mass, g is the acceleration due to gravity and h is height.
Efficiency (η) = Output power/Input power
CALCULATION:
Given that:
Mass (m) = 2 tonnes = \(2\times10^3Kg\) .
Height (h) = 60 meters.
Acceleration due to gravity (g) = 10 m/s.
Time (t) = 20 minutes = \(20\times60\ seconds\)
Efficiency= 50%= \({1 \over2}\)
\(Power(Output) = {Work \over Time}\longrightarrow\) ①
\(Work= m\times g\times h\longrightarrow\) ②
Substitute ② in ①
\(Output \ Power = {2\times10^3\times10\times60 \over 20\times60}\)
\(Output\ Power=10^3 watts\)
\(Efficiency = {Output \ Power \over Input\ Power}\)
\({1 \over 2}={10^3\over Input\ Power}\)
∴ \(Input\ Power=2\times10^3 watts = 2\ kW\)
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Important Questions from Work Power Energy
- Which of the following is a clear example of potential energy?
An object having the capability to do work is said to possess____________.
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