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bologna121121
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Homework Statement
Two masses, one of [tex]m_{1}= 3kg[/tex], the other of [tex] m_{2}=4kg[/tex], hang from opposite sides of a pulley of radius .15m. When released from rest, the heavier mass falls .34m in 4s. What is the rotational inertia of the pulley?
Homework Equations
Newton's second law and [tex]\tau = I\alpha[/tex]
The Attempt at a Solution
I tried using Newton's 2nd law on each of the masses:
[tex]T_{1} - m_{1}g = m_{1}a[/tex]
[tex]m_{2}g - T_{2} = m_{1}a[/tex]
where [tex]T_{1}[/tex] and [tex]T_{2}[/tex] are the tensions of the rope on each mass.
solving for these tensions yields
[tex]T_{1} = m_{1}(g+a)[/tex]
[tex]T_{2} = m_{2}(g-a)[/tex]
I originally planned to plug these into [tex]\tau = I\alpha[/tex] and use linear kinematics equations to solve for the acceleration and therefore the angular acceleration, but it is clear that [tex]T_{1}[/tex] is greater than [tex]T_{2}[/tex] something seems to have gone wrong, because wouldn't this imply that, through Newton's third law, the net torque would be causing [tex]m_{1}[/tex], the lighter block, to fall? Thanks for the help.