The two blocks shown in the figure are moving with an initial speed v . (a) If t

Question

The two blocks shown in the figure are moving with an initial speed v.

(a) If the system is frictionless, find the distance d the blocks travel before coming to rest. (Let U = 0 at the initial position of block 2. Use the following as necessary: m1, m2, v, and g for the acceleration due to gravity.)

d =

(b) Is the work done on the block 2 by the rope positive, negative, or zero?

Explain.

(c) Calculate the work done on block 2 by the rope. (Use the following as necessary: m1, m2, v, and g for the acceleration due to gravity.)

W =

*I was confused on C because I thought you would use Wc = Ui - Uf and didn't understand where the v came from.

Explanation / Answer

part a )

The blocks initially have KE = 1/2*(m1 + m2)v^2

They stop when this energy gets converted into PE in m2:

1/2(m1 + m2)v^2 = m2*g*d

d = (m1 + m2)v² / (2*m2*g)

part b )

work on block 2 is negative because here we are doing work againg gravity and there is no acceleration in upward direction .

part c )

W = change in kinetic energy

initial kinetic energy = 1/2(m1+m2)v^2

they stop when kinetic energy = 0

W = Kf-ki

W = 0 - 1/2(m1+m2)v^2

W = -1/2*(m1+m2)v^2

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