The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is 16.0 N when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.

Let the mass of the lighter block be m

Mass of heavier block = 2m


Tension in the string, T = 16 N


Consider the following diagram:


asa4.png


If acceleration produced in the system = a


And acceleration due to gravity, g = 10m/s2


When the system is set into motion,


For the heavier block, 2mg = T + 2ma


For the lighter block, T = mg +ma



After the system is released from rest, change in height of the heavier block in the first second, h = 1/2 at2 (where t=1sec)


⇒ h = 0.5 × g/3 × 12


⇒ h = g/6 m


Decrease in gravitational potential energy corresponding to this =(2m-m) ×g×h




= 19.6 J


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