Question

Solve the following problem.

While decreasing linearly from 5 N to 3 N, a force displaces an object from 3 m to 5 m. Calculate the work done by this force during this displacement.

Answer 1

For a variable force, work done is given by the area under the curve of force v/s displacement graph. From the given data, the graph can be plotted as follows:

∴ Work done, W = Area of `square`ABCD

∴ W = A(Δ AEB) + A `(square "EBCD")`

`= (1/2 xx "EB" xx "AE") + ("DE" xx "EB")`

`= (1/2 xx 2 xx 2) + (3 xx 2)`

= 8 J

Answer 2

Work done, W = Area of trapezium ADCB

∴ W = `1/2`(AD + CB) × DC

∴ W = `1/2`(5N + 3N) × (5m - 3m)

`= 1/2 xx 8 xx 2` = 8J