(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Summary:

The pulley in the figure has radius (R) and a moment of inertia (I). The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is [itex]\mu[/itex]_{k}. The system is released from rest, and block B descends. Block A has mass (m_{a}) and block B has mass (m_{b}).

Question:

Use energy methods to calculate the speed of block B as a function of the distance (d) that it has descended.

Express your answer in terms of the variables m_{a}, m_{b}, R, I, [itex]\mu[/itex]_{k}, d and appropriate constants

2. Relevant equations

Conservation of Energy:

PE_{i}+ KE_{i}= PE_{f}+ KE_{f}+ frictional work

3. The attempt at a solution

(m_{a}gd) + (m_{b}gd) = m_{a}V_{a}^{2}/2 + m_{b}V_{b}^{2}/2 + I[itex]\omega[/itex]^{2}/2 + [itex]\mu[/itex]_{k}mg

0 + (m_{b}gd) = 0 + m_{b}V_{b}^{2}/2 + I[itex]\omega[/itex]^{2}/2 + [itex]\mu[/itex]_{k}mg

Is this right?

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# Pulley question / rotational kinematics

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