Question

The two blocks in an Atwood machine has masses 2.0 kg and 3.0 kg. Find the work done by gravity during the fourth second after the system is released from rest.
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Given in the question :-
Here the given Masses are 
M =  3 kg .
m = 2 kg.
For the tension in the string T.
Tension in the string is the sum of the force due to gravity & force acting on the block.
T = ma + mg 
T = m ( a + g) --------→eq (i)

Similarly,
T = M (g -a)------------→eq (ii)

Now equating both the equation , we get,
mg + ma = Mg - Ma
a ( M +m ) =(M -m )g
a = [(M - m)g / (M +m )]
a = [(3 -2) g / (3 +2)]
a= g/5 m/s²

Using the equation of motion , 
S = ut + 1/2 [a(2t - 1)]
where t = 4 sec, u = 0 , [Since block is at rest]
S = 0 + 1/2 [(g/5) × 2×4 -1 ]
S = 7g / 10 m .

Therefore, work done by the gravity is :-
=Mgs - mgs
=gS(M-m)
=g(7g/10) (3-2)
=7g²/10
= (7 × 9.8² )/10
= 672.28 /10
= 67.28 J.

Hence the work done by the gravity is 67.28 J.


Hope it Helps.