The two masses shown in the figure are each initially 1.80 m abovethe ground, an
ID: 2219156 • Letter: T
Question
The two masses shown in the figure are each initially 1.80 m abovethe ground, and the massless frictionless pulley is fixed 4.8 mabove the ground. (mA = 2.2 kg and mB = 3.2 kg.) What maximumheight does the lighter object reach after the system is released?[Hint: First determine the acceleration of the lighter mass andthen its velocity at the moment the heavier one hits the ground.This is its "launch" speed. Assume the mass doesn't hit the pulley.Ignore the mass of the cord.]The diagram:
Ma is on the left and Mb is on the right hanging from the same cordover a pulley. the distance from the ground to the bottom of theweights is 1.8m and the distance from the ground to the pulley is4.8m.
Explanation / Answer
1) Determine acceleration of system: Let lighter mass be m and heavier mass be M F = ma Mg - mg = (M+m) a a = g(M-m) / (M+m) 2) Determine launch speed of light mass: v^2 = 2ah v^2 = 3.6g(M-m) / (M+m) The light mass is 3.6m above the ground when the heavy mass hits the floor. 3) Determine max height: h = v^2 / 2g + 3.6 h = 1.8(M-m) / (M+m) + 3.6 h = 4.11 m
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