Question
Use the method of Problem $1.6$ to predict the final velocities if two bodies of masses $m$ and $M$, with $m \ll M$, approach one another both traveling at speed $v_{0}$ (relative to the lab) and undergo a head on, elastic collision.
Step 1
Step 1: From the conservation of momentum and energy, we have the following two equations: \begin{align*} m v_{01} + M v_{02} &= m v_1 + M v_2 \quad \text{(momentum conservation)} \\ \frac{1}{2} m v_{01}^2 + \frac{1}{2} M v_{02}^2 &= \frac{1}{2} m v_1^2 + Show more…
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Consider a head-on, elastic collision between two bodies whose masses are $m$ and $M$, with $m<<M .$ It is well known that if $m$ has speed $v_{0}$ and $M$ is initially at rest, $m$ will bounce straight back with its speed unchanged, while $M$ will remain at rest (to an excellent approximation). Use this fact to predict the final velocities if $M$ approaches with speed $v_{0}$ and $m$ is initially at rest.
The Space and Time of Relativity
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Masses $m$ and $3 m$ approach at the same speed $v$ and undergo a head-on elastic collision. Show that mass $3 m$ stops, while mass $m$ rebounds at speed $2 v$
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