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Draggu
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Homework Statement
15. A solid sphere of mass 6.0 kg is mounted on a vertical axis and can rotate freely without friction. A massless cord is wrapped around the middle of the sphere and passes over a 1.0 kg pulley and is attached to block of mass 4.0 kg, as shown. What is the speed of the block after it has fallen 80 cm? Treat the pulley as solid cylinder.
Homework Equations
E initial = E after
ωp = angular velocity of pulley
ωs = angular velocity of sphere
rp = radius of pulley
rs = radius of sphere
Forces
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Pulley: Iα = Rp(T2-T1)
(rp^2/2)(a/rp) = Rp(T2-T1)
=(a)/2 = T2-T1
Block: mg-T2 = ma
=39.2 - T2 = 4a
Sphere: Iα = Rs(T1)
T1 = (2/5)(6)(rs)^2
T1= 2a/5
a = 8m/s^2
T2=7.2N
T1=3.2N
v^2-v0^2 = 2ad
v0 = 0
v^2 = 2(8)(.8)
v=3.57m/s
So initially I thought energy would be used in this situation, but now I'm trying to think if it's even necessary.
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