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A thing ''A" directly collided with an another staitonary thing "B" and for this Collison "A" stopped. If in this Collison the original Kinetic energy made half then what is the value of coefficient of restitution?

A thing ''A" directly collided with an another staitonary thing "B" and for this Collison "A" stopped. If in this Collison the original Kinetic energy made half then what is the value of coefficient of restitution?

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

From conservation of linear momentum,

m_Av_0=m_Bv\implies v=\dfrac{m_A}{m_B}v_0

It is given that\dfrac{1}{2}m_Bv^2=\dfrac{1}{2}\implies \dfrac{1}{2}m_Bv^2=\dfrac{1}{2}\times \dfrac{1}{2}m_Av_0^2
\implies m_Bv^2=\dfrac{1}{2}m_Av_0^2

Solving the two relations gives,
\implies \dfrac{v}{v_0}=2\dfrac{v^2}{v_0^2} \implies v=\dfrac{v_0}{2}
Hence ceffcient of restitution=\dfrac{v_{sep}}{v_{app}}=\dfrac{v_0/2}{v_0}=0.5

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