Question

A block of mass 30.0 kg is being brought down by a chain. If the block acquires a speed of 40.0 cm/s in dropping down 2.00 m, find the work done by the chain during the process.
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Let T be the force which is applied by the chain.

Given in the question :-
Mass of the block m = 30 kg.
Initial velocity,  u = 0
Final velocity v = 40 cm / sec. = 0.4 m/s
Distance s = 2 m.

Now weight of the block ,
= mg
= 30 × 9.8
= 294 N (Which is downward) 
Now change in Kinetic energy = 1/2 (mv²)
= 1/2 ( 30 × 0.4²)
= 4.80/2
= 2.40 J.

Therefore,  the Net force on the block wrt gravity
F= 294 - T  (downward)
Hence work done by this force is :-
W = F × s
W = (294 -T) × 2
2.4 = (294-T) × 2
T = 294 - 1.2
T= 292.8 N.
Therefore work done by the chain during the process :-
W = -T ×s   [ Force & displacement in opposite direction ]
W = 292.8 × 2
W = -585.6 J.

Hence the work done by the chain during this process is -585.6 J



Hope it Helps.