A cart of mass M1 = 3 kg is attached to a block of mass M2 = 5 kg by a string th

Question

A cart of mass M1 = 3 kg is attached to a block of mass M2 = 5 kg by a string that passes over a frictionless pulley. The system is initially at rest and the table is frictionless. After the block has fallen a distance h = 1 m:

a) What is the work Wg done by gravity on the system?

b) What is the increase in kinetic energy DK of the cart-plus-block system?

c) What is the speed |v| of the cart-plus-weight system?

d) What is the work Ws done on the cart (not the block!) by the string?

e) What is the tension T in the string?

Explanation / Answer

a) Wg = F*d = m2g*d = 5*9.8*1 = 49 J b) DK = work done on the system by gravity = 49j c) 49 = 0.5(3+5)v^2 v= 3.5 m/s d) work done on cart is change in KE Ws = 0.5*3*3.5^2 = 18.375 j e) Ws =TD 18.375 = T*1 T = 18.375 N

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