Two Weighted Pulleys with a Suspended Mass

[steakums]

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.

 

[RaulTheUCSCSlug]

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.

 

[steakums]

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.

 

[SammyS]

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.