Two Weighted Pulleys with a Suspended Mass

AI Thread Summary
The discussion revolves around solving a physics problem involving a uniform circular disk and a non-uniform pulley with a suspended mass. The user is struggling to find the acceleration of the hanging mass, which requires first determining the tension in the cord. They note that the tension is uniform throughout but are unsure how to relate the forces and torques to find the acceleration. Suggestions include drawing free-body diagrams and considering the effects of the pulley's moment of inertia on the forces involved. The conversation emphasizes the need to use force balance and torque rather than energy conservation for this problem.
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Homework Statement


Consider a uniform 10-kg circular disk with diameter .4m. The disk is free to rotate about a horizontal axis through its center. A (massless) cord wrapped around the disk passes over a 2-kg pulley, P, with diameter .2m and is attached to a 25-kg mass. The pulley's mass distribution is non-uniform, so its moment of inertia may be estimated as I=(3/4)*(m(r^2)). When the hanging mass is released from rest, it descends 1.2 m to the ground. Find
A) The acceleration of the hanging mass.
B)The tension in the cord
C)The angular velocity of the pulley when the mass reaches the ground.

Homework Equations


ma=mg-T
I=(3/4)*(m(r^2))
a=(αr)
τ=Iα

The Attempt at a Solution


I am having trouble with part A. I know that to find the acceleration I obviously have to solve for the tension in the cord but solving for the tension is part B. I also know that the tension in the rope will be uniform throughout, so I should be able to substitute in terms I know to be able to solve for acceleration. However, I cannot figure out how I am supposed to solve for acceleration in this case. Any help is appreciated.
 
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Have you thought about using conservation of energy to solve this problem? Draw the free-body diagrams, and label what forces are acting where, keep in mind that the moment of inertia of the pulley will affect the force.
 
I would use conservation of energy, but this class has not even touched energy at all. We are expected to use force balance and torque only.
 
steakums said:

Homework Statement


Consider a uniform 10-kg circular disk with diameter .4m. The disk is free to rotate about a horizontal axis through its center. A (massless) cord wrapped around the disk passes over a 2-kg pulley, P, with diameter .2m and is attached to a 25-kg mass. The pulley's mass distribution is non-uniform, so its moment of inertia may be estimated as I=(3/4)*(m(r^2)). When the hanging mass is released from rest, it descends 1.2 m to the ground. Find
A) The acceleration of the hanging mass.
B)The tension in the cord
C)The angular velocity of the pulley when the mass reaches the ground.

Homework Equations


ma=mg-T
I=(3/4)*(m(r^2))
a=(αr)
τ=Iα

The Attempt at a Solution


I am having trouble with part A. I know that to find the acceleration I obviously have to solve for the tension in the cord but solving for the tension is part B. I also know that the tension in the rope will be uniform throughout, so I should be able to substitute in terms I know to be able to solve for acceleration. However, I cannot figure out how I am supposed to solve for acceleration in this case. Any help is appreciated.
There are two different moments of inertia and two different angular accelerations as well as two different tensions.
 
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