Invoke Conservation of Energy ..... Change in PE + Change in KE = 0 .... dPE = dKE d=delta or change

1. The half of the chain off the table falls a distance L/2. It's change in potential energy dPE is rho (L/2) g (L/2)

Note; [PE = mgh; rho L = mass, m]

2. The half on the table.... the part right at the edge falls a distance L/2, but a part that is at the end doesn't fall at all. The part that start's on the table and falls, will fall an average distance of L/4. Thus dPE, the potential energy change for this part is rho (L/2) g (L/4) = rho g (L)^2 / 8

dPE = dKE = 1/2mv^2

1/2 mv^2 = (rho L^2) g /4 + (rho L^2) g /8 = (3/8) rho L^2 g = (3/8) mgL [ rho L = m ]

Note; [PE = mgh; rho L = mass, m]

2. The half on the table.... the part right at the edge falls a distance L/2, but a part that is at the end doesn't fall at all. The part that start's on the table and falls, will fall an average distance of L/4. Thus dPE, the potential energy change for this part is rho (L/2) g (L/4) = rho g (L)^2 / 8

dPE = dKE = 1/2mv^2

1/2 mv^2 = (rho L^2) g /4 + (rho L^2) g /8 = (3/8) rho L^2 g = (3/8) mgL [ rho L = m ]

1/2 mv^2 = (3/8) mgL

v = sqrt(3gL/4)