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astro2525
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Homework Statement
Use the conservation of energy law to find the speed of the blocks and the angular speed of the pulley when the heavier block hits the ground. The system starts at rest. (going to include picture)
http://i.imgur.com/CjB3gzK.jpg
Homework Equations
Moment of inertia for a disk (I believe): I = (1/2)mR^2
KE = (1/2)m*v^2
KE of pulley = (1/2)I(v/R)^2
The Attempt at a Solution
R = radius .2 m
m1 = 10 kg rock
m2 = 4 kg rock
mp = mass of pulley
Tried reading some things out of my textbook but that didn't help much =(. Decided to let the PE of each block at it's initial position be 0, so the amount of GPE that is converted to KE is:
KE = (10 kg - 4 kg)(9.8 m/s^2)(2 m) = 117.6 J
calculate moment of inertia:
I = (1/2)mpR^2 = (1/2)*2*.2^2 = .04 kg*m^2
then the KE of the system:
K = (1/2)(m1 + m2)v^2 + (1/2)I(v/R)^2
K = v^2(1/2)[10 kg + 4 kg + (.04 kg*m^2 / (0.20 m)^2)] = v^2(7.5 kg)
Set v^2(7.5) equal to the available energy that was converted from PE and solve for v:
v = √(117.6 J / 7.5 kg) = 3.96 m/s
Is this stuff even right? I basically just derived it from my textbook and am having a hard time completely understanding it. Really not sure how I would get angular speed .. would it just be ω = v / R?
Rereading this gives me a headache so if anyone helps, I commend you! ;D
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