physics

A 100g golf ball moving with a velocity of 20 m/s, collides with an 8 kg steel ball at rest,if the collision is elastic,compute the velocities of both balls after the collision.

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  1. Both kinetic energy and momentum are conserved. Assume a head-on collision with motion along the x axis only.

    There is an easy way to do this without aq lot of algebra.

    The center-of mass velocity is
    Vcm = 0.1*20/8.1 = 0.2469 m/s

    In a coordinate system travelling at Vcm, both balls reverse direction and keep the same speed.

    Golf ball initial velocity in CM system = 20 - 0.2469 = 19.753 m/s
    Golf ball final velocity in CM system = -19.753 m/s
    Golf ball final velocity in lab coordinates = -19.753 +.2469 = -19.506 m/s

    Steel ball initial velocity in CM coordinates = -0.2469 m/s
    Steel ball final velocity in CM coordinates = +0.2469 m/s
    Steel ball final velocity in lab coordinates = +0.4938 m/s

    Check: Final KE = 0.98 + 19.02 = 20.00 J = Initial KE

    Final momentum = 3.9504 - 1.9506 = 2.00 kg m/s = Initial momentum

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