Statement:
A body is under the action of a force F such that the force-displacement graph of the body is semicircle as shown above. The work done on the body by the force in moving through 24 meters.
To find out:
The work done by the body.
Solution:
- Here force is F and let us consider the displacement as s.
- We know, work done = Fs.
- Here the area under the curve is Fs, i.e., work done.
- We know, area of a semicircle = [tex] \frac{\pi \: {r}^{2} }{2} [/tex]where r is the radius.
- Here, radius (r) = 24 m
- Therefore, work done
[tex] = \frac{\pi \: {r}^{2} }{2} \\= \frac{(24) ^{2}\pi }{2} {m}^{2} \\ = \frac{576\pi}{2} {m}^{2} \\ = 288\pi \: {m}^{2} [/tex]
Answer:
The work done is 288π m².
Hope you could understand.
If you have any query, feel free to ask.
