Three identical, solid, uniform density cylinders, each of mass 17 kg and radius

Question

Three identical, solid, uniform density cylinders, each of mass 17 kg and radius 1 m, are mounted on frictionless axles that are attached to brackets of negligible mass. A string connects the brackets of cylinders #1 and #3 and passes without slipping over cylinder #2, whose bracket is attached to the ledge. Cylinder #1 rolls without slipping across the rough ledge as cylinder #3 falls downward.

This system is released from rest from the position shown -- with cylinder #3 at a height of 4 m above the ground.

a) How fast is cylinder #3 moving just before it hits the ground?
v = m/s
8.85 NO

HELP: Use conservation of energy.
HELP: Don't forget, there is linear and rotational kinetic energy. Which cylinder has only linear kinetic energy, which one has only rotational kinetic energy, and which one has both?

b) What is the rotational speed of cylinder #2 at the time in (a)?
w = rad/s

c) Cylinder #3 is now replaced by a sphere of the same mass. How fast is it moving just before it hits the ground?
v' = m/s

d) Finally, cylinder #1 is replaced by a sphere of the same mass and radius. How fast is cylinder #3 moving just before it hits the ground?
v'' = m/s

Explanation / Answer

Answer: (16)(9.81)(4.4) = 2/5(16)v^2 and 10.388 = v''

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