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

#### Chemist116

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:

$\begin{array}{ll} 1.&\frac{1}{2},\, \frac{1}{2}\\ 2.&\frac{1}{3},\, \frac{1}{6}\\ 3.&\frac{1}{2},\, \frac{1}{3}\\ 4.&\frac{1}{8},\, \frac{1}{2}\\ 5.&\frac{1}{2},\, \frac{1}{6}\\ \end{array}$

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

$p_1=p_2$

$m_1 v_1=m_2 v_2$

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

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

#### topsquark

Math Team
Start with the definition of COR. What does that have to do with the speeds?

-Dan