Question

A crane raises a load of 4 tonnes through a vertical height of 10m in 50 seconds. Calculate the power of crane in K.W.

Answer 1

Answer:

Given:

Load = 4 tonnes

Height = 10 metres

Time taken = 50 seconds.

To find:

Power of crane in kilowatts.

Formulas used:

$power = \frac{work}{time}$

Conversion:

4 tonnes = 4 × 1000 kg = 4000 kg

Calculation:

Work done = mgh

=> work done = 4000 × 10 × 10

=> work done = 4 × 10^5 joules.

Power = work/time

=> power = (4 × 10^5)/50

=> power = 0.8 × 10^4 watts

=> power = 8 × 10³ watts

=> power = 8 kilowatts.

Answer 2

$\huge{\underline{\underline{\red{\sf{Answer :}}}}}$

$\large \tt Given \begin{cases} \sf{Load \: = \: 4 \: tonnes} \\ \sf{ Height \: = \: 10 \: m} \\ \sf{Time \: = \: 50 \: s} \end{cases}$

Solution :

Convert Tonnes into kg by multiplying it by 1000,

load = 4 tonnes = 4000 kg

Now, we have formula for work done,

$\Large{\underline{\boxed{\sf{Work \: Done \: = \: mgh}}}}$

Put Values

⇒Work Done = 4000*10*10

⇒Work Done = 400000

∴ Work done is 400000 J

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Formula for Power is :

$\Large{\underline{\boxed{\sf{Power \: = \: \frac{Work \: Done}{Time}}}}}$

Put Values

⇒Power = 400000/50

⇒Power = 8000

⇒ Power = 8 KW

∴ Power in lifting load is 8 KW

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