How do I find the coefficient of restitution COR when a sphere is hanging from a roof?

Jun 2017
Lima, Peru
The problem is as follows:

The diagram from below shows a sphere labeled $A$ and is moving with a horizontal speed of $v=4\sqrt{10}\,\frac{m}{s}$ over a frictionless table. After the collision the cable makes an angle of $53^{\circ}$ with the vertical and the sphere $A$ ends at rest. Find the $COR$ (coefficient of restitution) and the relationship between the masses.

The alternatives given are as follows:

1.&\frac{1}{2},\, \frac{1}{2}\\
2.&\frac{1}{3},\, \frac{1}{6}\\
3.&\frac{1}{2},\, \frac{1}{3}\\
4.&\frac{1}{8},\, \frac{1}{2}\\
5.&\frac{1}{2},\, \frac{1}{6}\\

When it mentions the COR for the collision I'm assuming that it is an inelastic collision. Therefore if treated as such then


$m_1 v_1=m_2 v_2$

$v_2=v_1=4\sqrt{10} \frac{m_1}{m_2}$

But that's how far I went. I'm stuck with this problem, can someone help me here?.


Math Team
May 2013
The Astral plane
Start with the definition of COR. What does that have to do with the speeds?