Question:
A pump lifts 30 kg of water a vertical distance of 20 m each second. what is the power output?
Answer
The answer to this question is 5.88 Kw which is approximately 6 kilowatts
Explanation
Data
Mass of the pump, m = 30 kg
Vertical distance, h = 20 m
Time, t = 1 s
Acceleration due to gravity, g = 9.8 ms-2
Unknown
Power = ?
Formula
Here is how to conclude on the right formula to apply and solve the question.
We will first look at the definition of power, which is the rate of doing work
and we can write Power, P = Work (w) / time (t)
But work (w) = force (f) x distance (h)
where force = mass (m) x acceleration due to gravity (g)
Hence, after applying f = mg into w = f x h, we will get work done as
Work (w) = mg x h
This implies that
w = mgh
But power (P) = work (w) / time (t)
Thus,
Power, P = mgh / t
Therefore, we will apply the formula P = mgh / t to solve the problem
Solution
We will insert our data into P = mgh / t to obtain
P = mgh / t = (30 x 20 x 9.8) / 1 = 5,880 / 1 = 5,880 watts
We can further convert the unit into kilowatt
Power, P = 5880 / 1000 = 5.88 Kw
Therefore, the power of the pump is approximately 6 kilowatts
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