A Series of Collisions

Classical Mechanics Level 2

A ball of mass $m$ and velocity $v$ collides inelastically with an identical ball, coming to rest and imparting $50$ % of its energy to the second ball. This ball then collides inelastically with a third identical ball, coming to rest and imparting $50$ % of its energy to the third ball. What is the final velocity of the third ball?

\frac{v}{3}

\frac{v}{4}

\frac{v}{2}

\frac{v}{8}

1 solution

Matt DeCross
Apr 20, 2016

The initial kinetic energy of the first ball is $\frac12 mv^2$ . After colliding twice, the remaining energy for the third ball is $\frac18 mv^2$ . Setting this equal to the kinetic energy of the third ball: $\frac18 mv^2 = \frac12 mv_f^2 \implies v_f = \frac{v}{2}.$

A Series of Collisions

1 solution

0 pending reports