Explore BrainMass

Explore BrainMass

    A sphere rolls down a track onto inside circular track

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    In a vertical plane, a uniform sphere, mass m, radius r, released from rest at a point h meters above ground level, rolls without slipping down a straight section of track then around the inside of a circular track of radius R. Given R>>r.
    Find the minimum initial height h, such that the sphere barely maintains contact at the highest point of the circular track. SEE ATTACHMENT for a diagram.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:53 pm ad1c9bdddf
    https://brainmass.com/physics/energy/sphere-rolls-down-track-onto-inside-circular-track-16462

    Attachments

    Solution Preview

    Preliminary physics:
    Note 1. As the sphere rolls downward, it gains translational kinetic energy,
    (1) KEtrans= .5 m v^2
    and also gains rotational kinetic energy,
    (2) KErot= .5 I w^2 in which I is the moment of inertia of a sphere, and w is the angular velocity in rad/sec. Recall that for the sphere,
    (3) I= .4 m r^2, and from motion equations,
    (4) w= v/r
    Note 2. While descending to ...

    Solution Summary

    A sphere rolls down a track onto inside circular tracks are analyzed. The minimum initial heights to maintain contacts are given.

    $2.49

    ADVERTISEMENT