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physics

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If a hollow metal cylinder of radius r is rolling towards a circular bump of height h.
calculate the minimum speed needed to progress over a circular bump.

  • physics - ,

    at the top of the bump it stops rolling and stops going forward (teeters motionless)
    Thus at the top the kinetic energy is zero and the potential energy is m g (r+h)
    At the bottom the potential energy is m g r
    so it gained potential energy of m g h
    That is how much kinetic energy it lost
    Ke = .5 m v^2 + .5 I w^2
    I = m r^2
    w = v/r
    so in terms of v
    Ke = .5 m v^2 + .5 m r^2 (v^2/r^2)
    Ke = m v^2 total (half translational and half rotational)
    so
    m v^2 = m g h
    v = sqrt (g h)

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