# A pump lifts 30 kg of water a vertical distance of 20 m each second. what is the power output?

## Question:

A pump lifts 30 kg of water a vertical distance of 20 m each second. what is the power output?

The answer to this question is 5.88 Kw which is approximately 6 kilowatts A pump lifts 30 kg of water a vertical distance of 20 m each second. what is the power output?

#### 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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