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charan1
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Homework Statement
http://session.masteringphysics.com/problemAsset/1070551/3/12.P70.jpg
The two blocks in the figure are connected by a massless rope that passes over a pulley. The pulley is 15 cm in diameter and has a mass of 2.6 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.46 N-m.
If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?
Homework Equations
Tnet=I[tex]\alpha[/tex]
T=FD
F=ma
[tex]\alpha[/tex]=a/r
Moment of inertia of a disc:
I=.5mr2
g is gravity!
The Attempt at a Solution
T1 is tension of the left mass, T2 is tension of the right mass
m1 is mass of left mass, m2 is mass of right mass
T1=-m1a+m1g
T2=m2a+m2g
[tex]\Sigma[/tex]T= TT1 - TPully friction - TT2
I[tex]\alpha[/tex]=TT1 - TPully friction - TT2
Ia/r=(-m1a+m1g)r - .46 - (m2a+m2g)r
Ia/r= -m1ar + m1gr - .46 -m2ar -m2gr
Ia = -m1ar2 + m1gr2 - .46r -m2ar2 -m2gr2
Ia + m1ar2 + m2ar2 = m1gr2 - .46r -m2gr2
a(I + m1r2 + m2r2) = m1gr2 - .46r -m2gr2
a = (m1gr2 - .46r -m2gr2) / (I + m1r2 + m2r2)
I=.5mr2
I = (.5)(2.6)(.075)2
I = .0073125
m1 = 4kg
m2 = 2kg
r = .075m
g=9.8
a = ((4)(9.8)(.0752) - .46(.075) -(2)(9.8)(.075)2) / (.0073125) + (4)(.075)2 + (2)(.075)2
a = (.2205 - .0345 - .11025) / (.0073125 + .0225 + .01125)
a = .07575/.0410625
a = 1.8447
yf=yi+vit+.5at^2
0=1 + 0 + .92235t^2
t=1.04124 seconds
is this correct?