Q)The two blocks in an atwood machine have masses 2kg and 3 kg . find the work done by gravity during the fourth second after the system is released from rest?

Let T be tension in rope

and a be accln of blocks

since 3kg is heavier one, it will tend to fall due to gravity

so, on balancing eqns, we have a= (m₁-m₂).g/(m₁+m₂)

    T = 2m₁.m_2.g/(m₁+m₂)

so T = 24 N and a = 2 m/sec²

at 4th second, after free fall , it falls a distance S = 1/2*2*16 = 16 m

work done by gravity = mgh = 3*10*16 = 480 J

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IIT Kgp - 2005 batch