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Two objects with masses 5Kg and 2Kg hang 0.6m above the floor from the ends of a cord 6m long passing over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the 2.00Kg object.

Diagram of the pulley

Discussion:

Set up : After the $5Kg$ object reaches the floor, the $2Kg$ object is in free fall, with downward acceleration $g$.

Execution: The $2Kg$ will accelerate upward at$$\frac{5-2}{5+2}g=3g/7$$ and the $5Kg$ object will accelerate downward at $3g/7$.

Let the initial height above the ground be $h_0$.

When the large object hits the ground, the small object will be at a height $2h_0$ and moving upward with a speed given by $$v_0^2=2ah_0=6gh_0/7$$. The small object will rise to a distance $v_0^2/2g=3h_0/g$ and so the maximum height reached will be $$2h_0+3h_0/7=17h_0/7=1.46m$$ above the floor, which is $0.860m$ above its initial height.