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 10 m. 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 20 m. 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.
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The plot of the forces applied b the woman and the frictional forcesf versus displacement is,
x=20m,f=50N(
=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
=1000×10+
2
1
(1000+50)×10
1000+750=1750J
Now, the work done by the frictional force is:
Area of the rectangle AGHI
W
f
=(−50)×20=1000N
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