Problem: On a frictionless horizontal air table, puck A (with mass 0.249 kg ) is moving toward puck B (with mass 0.371 kg ), which is initially at rest. After the collision, puck A has velocity 0.123 m/s to the left, and puck B has velocity 0.646 m/s to the right. A) What was the speed Vai of puck A before the collision? B) Calculate the change in the total kinetic energy of the system that occurs during the collision.

FREE Expert Solution

A) Momentum is conserved:

$\boxed{\begin{array}{rcl}{\mathbf{m}}_{\mathbf{a}}{\mathbf{v}}_{\mathbf{ia}}\mathbf{+}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{ib}}& \mathbf{=}& {\mathbf{m}}_{\mathbf{a}}{\mathbf{v}}_{\mathbf{f}\mathbf{a}}\mathbf{+}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{f}\mathbf{b}}\end{array}}$

$\begin{array}{rcl}{\mathbf{m}}_{\mathbf{a}}{\mathbf{v}}_{\mathbf{ia}}& \mathbf{=}& {\mathbf{m}}_{\mathbf{a}}{\mathbf{v}}_{\mathbf{fa}}\mathbf{+}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{fb}}\mathbf{-}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{ib}}\\ {\mathbf{v}}_{\mathbf{ia}}& \mathbf{=}& \frac{{\mathbf{m}}_{\mathbf{a}}{\mathbf{v}}_{\mathbf{fa}}\mathbf{+}{\mathbf{m}}_{\mathbf{b}}\mathbf{(}{\mathbf{v}}_{\mathbf{fb}}\mathbf{-}{\mathbf{v}}_{\mathbf{ib}}\mathbf{)}}{{\mathbf{m}}_{\mathbf{a}}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{249}\mathbf{)}\mathbf{(}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{123}\mathbf{)}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{371}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{646}\mathbf{-}\mathbf{0}\mathbf{)}}{\mathbf{0}\mathbf{.}\mathbf{249}}\end{array}$