Two blocks are connected by a massless string which hangs over a massless pulley

Question

Two blocks are connected by a massless string which

hangs over a massless pulley as shown. The blocks

are released from rest, and the hanging block falls a

distance d (it does not hit the floor). Block M rests on

a table 1.0 m above the floor.

a clear explanation of how to get them

Two blocks are connected by a massless string which hangs over a massless pulley as shown. The blocks are released from rest, and the hanging block falls a distance d (it does not hit the floor). Block M rests on a table 1.0 m above the floor. The system is moving at a speed of Vf when the blocks have fallen through a distance d. Answer the following questions about the system, in terms of m, M, g, h, and vf. The acceleration of the system is: a >g a =g a

Explanation / Answer

1) a = (m-M)*g/(M+m)
a < g

2) Ki = 0

b) H = (h+d) m
Ui = (m+M)*g*H = (m+M)*g*(h+d)

3)Ei = (m+M)*g*(h+d)

4) Uf = M*g*(h+d) + m*g*h

5) Kf = 0.5*M*Vf^2 + 0.5*m*Vf^2 = 0.5*(M+m)*Vf^2

6) Ef = Uf+Kf = M*g*(h+d) + m*g*h + 0.5*(M+m)*Vf^2

7)Ei = Ef

(m+M)*g*(h+d) = M*g*(h+d) + m*g*h + 0.5*(M+m)*Vf^2

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