A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of 100 N over a distance of 10m. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to 50 N. The total distance through which the trunk has been moved is 20m. Plot the force applied by the woman and the frictional force, which is 50 N versus displacement. Calculate the work done by the two forces over 20 m.

Explanation

The plot of the applied force is shown in Fig. 6.4. At `x= 20 m, F= 50 N (ne 0)`. We are given that the frictional force f is `|f|= 50 N`. It opposes motion and acts in a direction opposite to F. It is therefore, shown on the negative side of the force axis.
The work done by the woman is `W_(F) to` area of the rectangle ABCD + area of the trapezium CEID
`W_(F)= 100 xx 10+(1)/(2)(100+50)xx10`
`= 1000+750 = 1750 J`
The work done by the frictional force is `W_(f) to` area of the ractangle AGHI
`W_(f)= (-50) xx 20= -1000 J`
The area of the negative side of the force axis has a negative sign.