1. The problem statement, all variables and given/known data
A particle of mass ##m_1## experienced a perfectly elastic collision with a stationary particle of mass ##m_2##. What fraction of the kinetic energy does the striking particle lose, if it recoils at right angles to its original motion direction.
(Ans: ##2m_1/(m_1+m_2)## )
2. Relevant equations
3. The attempt at a solution
Let the initial velocity of ##m_1## be ##v## and let the x-axis be along the initial direction of motion. After collision, the first particle flies off at right angles and let that direction be y-axis. The vertical component of velocity of ##m_2## after collision has the direction opposite to that of ##m_1##. Conserving momentum in x direction:
$$m_1v=m_2v_{2x}$$
Conserving momentum in y direction:
$$m_1v_1=m_2v_{2y}$$
where ##v_1## is the final velocity of ##m_1##. I still need one more equation. :confused:
Any help is appreciated. Thanks!
A particle of mass ##m_1## experienced a perfectly elastic collision with a stationary particle of mass ##m_2##. What fraction of the kinetic energy does the striking particle lose, if it recoils at right angles to its original motion direction.
(Ans: ##2m_1/(m_1+m_2)## )
2. Relevant equations
3. The attempt at a solution
Let the initial velocity of ##m_1## be ##v## and let the x-axis be along the initial direction of motion. After collision, the first particle flies off at right angles and let that direction be y-axis. The vertical component of velocity of ##m_2## after collision has the direction opposite to that of ##m_1##. Conserving momentum in x direction:
$$m_1v=m_2v_{2x}$$
Conserving momentum in y direction:
$$m_1v_1=m_2v_{2y}$$
where ##v_1## is the final velocity of ##m_1##. I still need one more equation. :confused:
Any help is appreciated. Thanks!
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