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Mechanics: Kinetic & Potential Energy

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A small circular object with mass m and radius r has a moment of inertia given by I=Bmr^2. The object rolls without sliping down a track. The track ends with a ramp with height R=2.5m that launches the object vertically. The object begins at a height H=6.0 m. To what maximum height will it rise after leaving the ramp if B=.40?

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Solution Summary

The kinetic and potential energy is examined for a small circular object. A step by step solution provided.

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Initial height of the object = H = 6m

Initial potential energy of the object = mgH = 6mg .......(1)

As the object rolls down the track, its PE is gradually converted into kinetic energy (translational and rotational).

Translational KE at the end of the track = 1/2 mv^2 .......(2)

Rotational KE at the end of the track = 1/2 Iw^2 = 1/2 Iv^2/r^2 .......(3) where w = angular speed and w = ...

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