Question

A chain 65 meters long whose mass is 27 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 4 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared.

Answer 1

Answer:1050.35 J

Explanation:

Given

length of chain=65 m

mass of chain=27 kg

we know work done is given by$=\int_{a}^{b}F.dx$

Let $\lambda$is mass density

$\lambda =\frac{m}{L}=\frac{27}{65}$

$\lambda =0.415 kg/m$

for dx length mass is dm

dm=$\lambda dx$

We need to see the change in potential energy only as gravity is uniform and chain is freely suspended

$=\int_{a}^{b}\lambda g.(65-x)dx$

$=\int_{0}^{4}\left ( 65-x\right )dx=\lambda g\left [ 65x-\frac{x^2}{2} \right ]^4_0$

=1050.35 J