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Work Done When Force Is Varying

A 50kg man wi...

Question

A $50 k g$ man with a $20 k g$ load on his head climbs up $20$ steps of $0.25 m$ height each. The work done in climbing is

$5 J$

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$350 J$

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$100 J$

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$3430 J$

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Solution

The correct option is D
$3430 J$

Step 1: Given data
Mass of the man, $m_{1} = 50 k g$
Mass of the load, $m_{2} = 20 k g$
Height of each step, $h = 0.25 m$
No of steps, $n = 20$
Step 2: Find the total mass
Total mass, $M = 50 k g + 20 k g$
$= 70 k g$
Step 3: Find the total height
Total height, $h = 20 \times 0.25$
$= 5 m$
Step 4: Find the work done to climb a height $h$
Work done to climb a height $h, W = p o t e n t i a l e n e r g y g a i n e d t o r e a c h t h e h e i g h t$
Potential energy gained, $P . E = m g h$
$P . E = 70 k g \times 9.8 m s^{- 2} \times 5 m$
$= 3430 J$
Hence, Option D is correct

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