Part A What maximum height does the lighter object reach after the system is rel

Question

Part A What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then 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 two masses shown in the figure are each initially 1.8 above the ground, and the massless frictionless pulley is 4.8 above the ground (Figure 1) . Part A What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then 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.]

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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