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Standard IX

Physics

Displacement

A person push...

Question

A person pushes a box on a rough horizontal platform surface. He applies a force of $200 N$ over a distance of $15 m$ . Thereafter, he gets progressively tired and his applied force reduces linearly with distance to $100 N$ . The total distance through which the box has been moved is $30 m$ . What is the work done by the person during the total movement of the box ?

$5690 J$

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$5250 J$

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$2780 J$

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$3280 J$

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Solution

The correct option is B
$5250 J$

By applying the formula of the work done, $W$
$W = \int \vec{f} . d s$
$W = A r e a u n d e r t h e f o r c e - d i s p l a c e m e n t g r a p h$
From graph, $W = A r e a o f t r a p a z i u m A B C D + A r e a o f r e c \tan g l e O D C E$ $W = \frac{1}{2} \times 45 \times 100 + 100 \times 30$
$W = 5250 J$
Therefore, the work done by the person during the total movement of the box is $5250 J$ .
Hence, the correct option is $(B)$ .

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