5. Solve the following examples.
a. An electric pump has 2 kW power.
How much water will the pump lift
every minute to a height of 10 m?
Answers
Given:-
- Power,P = 2 kW = 2000 W [ 1 kW = 1000 ]
- Time taken = 1 minute
- Height,h = 10 m
- Acceleration due to gravity,g = 9.8 m/s²
To be calculated:-
How much water will the pump lift every minute ?
Formula used:-
- Power = Work done/Time taken
- Work done = m × g × h
Solution:-
First of all, We should convert the given time into proper unit.
Time taken = 1 minute = 60 seconds
According to the question,
Power = work done/Time taken
we know that,
★ Work done = m × g × h
⇒ Work done = m × 9.8 × 10
⇒ Work done = m × 98......( i )
Now,
Power = work done/Time taken
⇒ 2000 = m × 98 / 60
⇒ 2000 × 60 = m × 98
⇒ 120000 = m × 98
⇒ m = 120000/98
⇒ m = 1,224.48 kg
Thus, 1224.48 kg of water will the pump lift every minute.
Additional information:-
Power: The rate of doing work is called Power.
- Power is scalar quantity [ It has only magnitudes but no direction ]
- S.I unit of Power is Watt ( W ).
- 1 watt = 1 joules per second
Answer: 1225 kg.
Explanation:
Power of pump = 2kW = 2000 W = 2000 J/s
t = 1 min
Height = 10 m
We know,
P = W/t
=> P = mgh/1 min
=> 2000 J/s = (m(9.8)(10) m²/s²)/60 s
=> 2000 × 60 kg m²/s³ = 98 m²/s³·m
=> m = 2000 × 60 × 1/98
=> m = 1225 kg
Therefore,
It will lift about 1225 kg of water every minute.