Question 339: Work, Energy and Power & Circular Motion

Question

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s
2
, find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

Accepted Answer

We have,
$$a = \left( {{{{m_1} - {m_2}} \over {{m_1} + {m_2}}}} ight)g = \left( {{{0.72 - 0.36} \over {0.72 - 0.36}}} ight) 	imes 10 = {g \over 3} = {{10} \over 3}$$
$$T = {{2{m_1}{m_2}g} \over {{m_1} + {m_2}}} = {{2 	imes 0.72 	imes 0.36 	imes 10} \over {0.72 + 0.36}} = 4.8$$ N
$$s = {1 \over 2}a{t^2} = {1 \over 2} 	imes {{10} \over 3} 	imes {1^2} = {5 \over 3}$$ m
The work done by the rope on 0.36 kg is
$$W = Ts\cos 0^\circ  = 4.8 	imes {5 \over 3} =  + 8$$ J

Work, Energy and Power & Circular Motion

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s 2 , find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

Integer / Numeric Answer Type