# Two Weighted Pulleys with a Suspended Mass

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1. Apr 14, 2015

### steakums

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
ma=mg-T
I=(3/4)*(m(r^2))
a=(αr)
τ=Iα

3. 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.

2. Apr 14, 2015

### 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.

3. Apr 14, 2015

### 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.

4. Apr 14, 2015

### SammyS

Staff Emeritus
There are two different moments of inertia and two different angular accelerations as well as two different tensions.