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:

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

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

Problem Details

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.

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Conservation of Momentum concept. You can view video lessons to learn Intro to Conservation of Momentum. Or if you need more Intro to Conservation of Momentum practice, you can also practice Intro to Conservation of Momentum practice problems.