Question

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

Answer 1

The plot of the forces applied b the woman and the frictional forces$f$ versus displacement is,

$x=20m,f=50N(\ne 0)$

Since we have $f=|f|=50N$

It opposes the motion and acts in the direction opposite to $f$,

So, the negative side of the force axis,

The work-done by the woman is:

$W_f=$area of rectangle ABCD+area of trapezium CEID

$W_f=1000\times 10+\frac{1}{2}(1000+50)\times 10$

$1000+750=1750J$

Now, the work done by the frictional force is:

Area of the rectangle AGHI

$W_f=(-50)\times 20=1000N$