Question

A pump is used to lift 300 kg of water from a depth of 50 m in 10 s. Calculate
a. the work done by the pump.
b. the power at which the pump works.
[An​

Answer 1

Answer:

Ans. a. W = 147000 J b. P = 14700 W

Answer 2

Provided that:

• Mass = 300 kg
• Depth (distance,s) = 50 m
• Time = 10 seconds

To calculate:

• Work done
• Power

Solution:

• Work done = 150000 J or 150 kJ.
• Power = 15000 Watts or 15 kW.

Using concepts:

• Work done formula
• Power formula

Using formulas:

• Work done formula:

• Force × Displacement

• Power formula:

• Work done/Time

Required solution:

~ By using forum to calculate work done let us solve this question's part!

»»» Work done = Force × Displacement

»»» Work = F × s

»»» Work = ma × s

»»» Work = 300 × 10 × 50

We take it as 10 in approx except of proper value of g ( acceleration due to gravity ) that is 9.8 metre per second sq.

But we can take it as 9.8 too!

»»» Work = 3000 × 50

»»» Work = 1,50,000 Joules

• Henceforth, work done = 1,50,000 Joules or 150 kJ!

~ Now by using power formula let us calculate the power!

»»» Power = Work done/Time

»»» P = W/t

»»» P = 150000/10

»»» P = 15000 Watts

»»» Power = 15000 Watts

• Henceforth, power = 15000 Watts or 15 kilowatts!

Additional information:

$\begin{gathered}\boxed{\begin{array}{c}\\ {\pmb{\sf{Some \: formulas!}}} \\ \\ \sf \star \: Power \: = \dfrac{Work \: done}{Time} \\ \\ \sf \star \: Time \: = \dfrac{Work \: done}{Power} \\ \\ \sf \star \: Power \times Time = Work \: done \end{array}}\end{gathered}$

Power = Force × Speed too! How?

$:\implies \sf Power \: = \dfrac{Work \: done}{Time} \\ \\ :\implies \sf Power \: = \dfrac{Force \times displacement}{Time} \\ \\ :\implies \sf Power \: = Force \times Velocity \\ \\ {\pmb{\sf{Henceforth, \: derived!}}}$