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    Conservation of Momentum

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    If a metal ball strikes a pendulum and sticks to it. It will have a relationship for conservation of momentum of m*v = (m + M) *V (m and v are the mass and initial velocity of the projectile, M is the mass of the pendulum with no initial velocity and big V is the combined velocity of the pendulum and projectile).

    The conservation of energy after the collision is :
    1/2 (m + M) * V^2 = (m + M)gh

    The vertical rise of the pendulum is represented by h and the horizontal distance swung through is d. The quantities are related by:
    R^2 = (R-h)^2 + d^2

    Based on these equations, I need to derive a relationship for little v (on quantities m,M, g, R, d) and for d (in terms of m, M, g, R, and v)but am having some difficulty getting this to work out nicely. Any guidance?

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    Solution Preview

    m*v = (m + M) *V
    or v= (m + M) *V/ m --------------------(1)

    ½ (m + M) * V^2 = (m + M) g h
    Canceling (m + M) from both sides and rearranging

    V^2 = 2 g h or V= (2 g h) ^ ½ --------------------(2)

    R^2 = (R-h)^2 + d^2

    R^2 = ...

    Solution Summary

    The solution derives an equation for a metal ball striking a pendulum and sticking to it.