A question on work, power and energy

[ritik.dutta3]

Homework Statement

The two blocks in an Atwood machine have masses 2 kg and 3 kg. Find the work done by gravity during the fourth second after the system is released from rest.

Homework Equations

Work done by gravity= mgh

The Attempt at a Solution

Both the masses will have the same acceleration 'a'. Let T be the tension in the string.
m1= 2 kg, m2= 3 kg, g= 10 m/s^2

T-m1g=m1a
therefore, T- 20= 2a

m2g- T= m2a
therefore, 30 - T= 3a
on solving both the equations, a= 2 m/s^2

distance traveled by the blocks would be 1/2(at^2). So, the heavier block would travel 16 m downwards and the lighter block 16 m upwards.
Net mass= 3-2= 1 kg
hence, the work done should be
W= mgh= 1 x 10 x 16 = 160J

but the answer is 67J.
where am I going wrong?

 

[Tanya Sharma]

distance traveled by the blocks would be 1/2(at^2). So, the heavier block would travel 16 m downwards and the lighter block 16 m upwards.

You have used distance traveled in 4 seconds .Whereas you need distance traveled during the 4th second i.e between 3rd and 4th sec.

 

[ritik.dutta3]

Got it! Thanks! :D