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Homework Statement
In the figure the second block slides horizontally without friction while the first block falls. Use the Conservation of Energy to find the speed of the blocks after they have moved 2 meters, starting from rest. The falling block has mass 3 kg, the sliding block has mass 5 kg, and the pulley is ideal.
See Figure 1.
Homework Equations
U_{f} + K_{f }= U_{i }+ K_{i}
The Attempt at a Solution
So for the 3 kg block:
mgh_{f} = 1/2mv_{f}^{2} = mgh_{i} + 1/2mv_{i}^{2}
(3 kg)(9.8 m/s^{2})(2 m) + 1/2(3 kg)(v_{f})^{2} = 0
1/2(3 kg)(v_{f})^{2} = 58.8 J
(v_{f})^{2} = 39.2 m^{2}/s^{2}
v_{f }= 6.26 m/s
I'm not sure if I quite got the point of the conservation of energy bit. Does it mean the work done by the pulley is zero? That's what I had to assume to get v_{f} for the 3 kg block. I'm not sure what to do about the 5 kg block, though, because if I just use 2 m for the h for it, then I get the same v_{f }as the 3 kg block, which seems odd to me. But maybe I'm missing the point.
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