Difficult energy conservation/rotational energy problem

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The discussion revolves around a physics problem involving a hanging mass, a sliding block, and a hollow cylindrical pulley. Key points include the need to calculate the moment of inertia for the pulley, which has both inner and outer radii, and the impact of friction on the system's energy conservation. The participant expresses confusion about how to incorporate the two radii into the moment of inertia calculation, suggesting a possible application of the parallel axis theorem. Additionally, the problem setup lacks a clear statement of the specific question being addressed. Understanding the relationship between kinetic energy, potential energy, and work done by friction is crucial for solving the problem.
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Homework Statement


In the figure below, the hanging object has a mass of m1 = 0.405 kg; the sliding block has a mass of m2 = 0.825 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface isμk = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table.
10-p-049.gif


Homework Equations


KE = 1/2Iw^2
KE = 1/2mv^2
PE = mgh
Non-conservative work = (delta)KE + (delta)PE

The Attempt at a Solution


The left side has negative work because of friction. On the right side, I put the KE of each as well as the potential energy (ONLY on m1, I believe?)

I think my only problem is the moment of inertia for the two pulleys. I don't understand how to implement the two radii. The answer shows that there is a combination of both. I have no idea why. Parallel axis theorem maybe?
 
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doneky said:
I think my only problem is the moment of inertia for the two pulleys.
There is only one pulley. It has a hollow cylinder with inner radius ##R_1## and outer radius ##R_2##. You need to compute its moment of inertia ##I##.

You also have not stated the actual problem, i.e., what you are asked to find, only the setup.
 
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