Physics - W.E.P. Question with Solution | TestHub

The work done by gravity on the chain can be calculated from the change in its potential energy. The initial potential energy (relative to the table edge as zero) is due to the hanging $2\text{ m}$ length. The mass of this part is $m_h=(2/4)\cdot 2\text{ kg}=1\text{ kg}$, and its center of mass is $1\text{ m}$ below the edge. So, $P{E}_i=-m_{h}g(1)=-1\cdot 10\cdot 1=-10\text{ J}$. When the entire chain leaves the table, its center of mass is $L/2=4/2=2\text{ m}$ below the edge. The final potential energy is $P{E}_f=-Mg(L/2)=-2\cdot 10\cdot 2=-40\text{ J}$. The work done by gravity is $W_g=-(P{E}_f-P{E}_i)=-(-40-(-10))=-(-30)=30\text{ J}$. Since the chain is released from rest, its initial kinetic energy $K_i=0$. By the Work-Kinetic Energy Theorem, $W_{net}=\Delta K=K_f-K_i$. Thus, $K_f=30\text{ J}$.