(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two equal balls are in contact on a table. A third equal ball strikes them simultaneously and remains at rest after the impact. Show that the coefficient of restitution is 2/3.

I have attached an image for clarity of problem. Please open it.

2. Relevant equations

Conservation of Momentum

3. The attempt at a solution

Let the mass of balls be m and coefficient of restitution be e.

[itex]\frac{v_{2}}{vcosθ_{2}} = e[/itex]

Also,

[itex]\frac{v_{1}}{vcosθ_{1}} = e[/itex]

Applying Conservation of Momentum along X-axis

[itex]v=v_{1}cosθ_{1}+v_{2}cosθ_{2}[/itex]

Along Y- axis

[itex]v_{1}sinθ_{1}=v_{2}sinθ_{2}[/itex]

Substituting the value of v1 and v2 in the above equation

[itex]evcosθ_{1}sinθ_{1}=evcosθ_{2}sinθ_{2}[/itex]

[itex]cosθ_{1}sinθ_{1}=cosθ_{2}sinθ_{2}[/itex]

Multiplying 2 on both sides

[itex]sin2θ_{1}=sin2θ_{2}[/itex]

Rearranging and simplifying

[itex]2cos(θ_{1}+θ_{2})sin(θ_{1}-θ_{2})=0[/itex]

[itex]θ_{1}+θ_{2}=\frac{∏}{2}[/itex]

[itex]θ_{1}-θ_{2}=0[/itex]

[itex]θ_{1}=θ_{2} and θ_{1} = \frac{∏}{4}[/itex]

Now substituting the value of θ1 in equation of momentum along X-axis

[itex]1=e(cos^{2}θ_{1}+cos^{2}θ_{2})[/itex]

[itex]e=\frac{1}{cos^{2}θ_{1}+cos^{2}θ_{2}}[/itex]

[itex]e=\frac{1}{2cos^{2}θ_{1}}[/itex]

[itex]e=1[/itex]

What's wrong here???

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find the coefficient of restitution

**Physics Forums | Science Articles, Homework Help, Discussion**