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

The picture shows a rotating platform that serves as a playground

merry go round. The platform rotates on low-friction bearings about its center

axis. It has a radius of 2.0 meters, and its moment of inertia about the center

axis is 200 kg m2.

Suppose that the platform is given an initial rotation rate of 1.0 radians per

second. A small dense brick having a mass of 50 kg, initially at rest, is then

placed on the platform at a distance of 0.5 meters from the rotation axis. The

brick initially slides, but eventually stops sliding at a distance 1.0 m from the

axis. How many Joules of mechanical energy are converted to heat?

2. Relevant equations

[itex]I_{brick}=mr^{2}[/itex]

[itex]L_{i}=L_{f}=>I_{i}\omega_{i}=I_{f}\omega_{f}[/itex] (cons. of angular momentum)

[itex]ΔK=-fx +W_{ext}[/itex] (work-energy theorem)

3. The attempt at a solution

[itex]I_{brick i}=(50kg)(0.25m^{2})=12.5kg.m^{2}[/itex]

[itex]I_{brick f}=(50kg)(1m^{2})=50kg.m^{2}[/itex]

[itex]I_{i}=I_{disk i}+I_{brick i}=212.5kg.m^{2}[/itex]

[itex]I_{f}=I_{disk f}+I_{brick f}=250kg.m^{2}[/itex]

[itex]\omega_{f}=\frac{I_{i}}{I_{f}}\omega_{i}=0.85\frac{rad}{s}[/itex]

[itex]ΔK=-fx[/itex] (no external work, just friction)

[itex]\frac{1}{2}I_{i}\omega_{i}^{2}-\frac{1}{2}I_{f}\omega_{f}^{2}=15.94 J[/itex]

Just wondering if my solution method is looking ok. Thanks for the help!

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# Homework Help: Merry-go-round with brick and sliding friction.

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