First slide

Concept of potential energy

Question

A man places a chain (of mass m and length l) on a table slowly. Initially, the lower end of the chain just touches the table. The man brings down the chain by length l/2. Work done by the man in this process is

Moderate

A

$- m g \frac{1}{2}$
B

$- \frac{m g l}{4}$
C

$- \frac{3 m g l}{8}$
D

$- \frac{m g l}{8}$

Solution

The work done by the man is negative of the magnitude of decrease in potential energy of the chain $w o r k d o n e i n l i f t i n g c h a i n = \frac{m g l}{2 n^{2}} m i s m a s s o f c h a i n, g a c c e l e r a t i o n d u e t o g r a v i t y, l i s l e n g t h o f c h a i n, n i s f r a c t i o n o f c h a i n t h a t i s h a n g i n g h e r e, w o r k d o n e = \frac{m g l}{2^{}} [\frac{1}{{n^{2}}_{1^{}}} - \frac{1}{{n^{2}}_{2^{}}}] = \frac{m g l}{2^{}} - \frac{m g l}{8^{}} = \frac{3 m g l}{8^{}} b u t w i t h a n e g a t i v e s i g n, a s w o r k i s d o n e b y m a n a g a i n s t g r a v i t y$

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