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utkarshakash
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Homework Statement
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.
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Homework Equations
Conservation of Momentum
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 Xaxis
[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 Xaxis
[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???
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