A particle of mass m moving with kinetic ener | vedclass

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(A) For a one-dimensional elastic collision,the final velocity $v_1$ of the first particle (mass $m_1$) colliding with a stationary particle (mass $m_

Vedclass · Accepted Answer

$\frac{E}{9}$

Vedclass · Answer

(A) For a one-dimensional elastic collision,the final velocity $v_1$ of the first particle (mass $m_1$) colliding with a stationary particle (mass $m_2$) is given by: $v_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) u_1$ Given $m_1 = m$,$m_2 = 2m$,and initial kinetic energy $E = \frac{1}{2} m u_1^2$. The final kinetic energy $E'$ of the first particle is: $E' = \frac{1}{2} m_1 v_1^2 = \frac{1}{2} m \left( \frac{m - 2m}{m + 2m} \right)^2 u_1^2$ $E' = \left( \frac{-m}{3m} \right)^2 \left( \frac{1}{2} m u_1^2 \right)$ $E' = \left( -\frac{1}{3} \right)^2 E = \frac{1}{9} E$ Thus,the kinetic energy of the first particle after the collision is $\frac{E}{9}$.

$A$ particle of mass $m$ moving with kinetic energy $E$ collides head-on elastically with another particle of mass $2m$ at rest. After the collision,the kinetic energy of the first particle is:

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