A woman pushes a trunk on a railway platform which has a rough surface. She supplies a force of 100 N over a distance of 10 m. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to 50 N. The total distance by which the trunk has been moved is 20 m.

If frictional force between trunk and rough surface is 50 N, then calculate the net work done by the two forces over 20 m.

1. 1000 J
2. 500 J
3. 750 J
4. 1500 J

750 J

Reason — From graph,

Work done by woman (W_w) = area of rectangle ABCD + area of trapezium CEID

= (100 x 10) + [$\dfrac{1}{2}$ x (100 + 50) x 10]

= 1000 + 750

= 1750 J

Frictional force opposes motion, so it acts in opposite direction.

Work done by frictional force (W_f) = - area of rectangle AGHI

= - AG x AI

= -50 x 20

= -1000 J

Hence, net work done = 1750 - 1000 = 750 J