Question

Problem 3: Disk and stick collision A disk of mass m traveling with a velocity v1 strikes a stick of mass M and length L that is lying flat on frictionless ice as shown in the overhead view in the figure. The disk strikes at the endpoint of the stick, at a distance r from the stick's center. Assume the collision is elastic and the disk does not deviate from its original line of motion. 

Analyze the system before and after the collision. 

a) Is the system isolated? Which are the conserved quantities? 

b) For each conserved quantity write an equation that relates the variables of the problem before the collision with the ones after the collision. Make sure your expressions are in terms of the given quantities only.

Answer 1

a) The system has no interaction with any other particle, and hence the system is isolated.

In an isolated system, the energy is conserved( but not the mechanical energy, since some energy is lost as heat due to deformation during the collision), the momentum, and the angular momentum are the conserved quantities.

b) Here \(\mathrm{I}_{\text {rod }}=\mathrm{m}_{\text {rod }} \mathbf{r}^{2} / 12\)

The equation for conservation of momentum is-

\(m_{\text {disk }} v_{1}=m_{\text {disk }} v_{2}+m_{\text {rod }} v_{s}\)

The equation for the conservation of angular momentum about the dotted line is-

\(m_{\text {disk }} v_{1} r=m_{\text {disk }} v_{2} r+I \omega\)