mecànica de colisió de una partícula amb un extrem de una barra

txoc de una partícula en un extrem de una barra a velocitat constant V:
m_{1} = k·m_{2}


m_{1}·d_{t}[x(t_{0})] = m_{1}·d_{t}[x(t_{1})] + m_{2}·d_{t}[s(t_{2})]·R


m_{1}·V = m_{1}·d_{t}[x(t_{1})] + m_{2}·d_{t}[s(t_{2})]·R


txoc inelástic:
si d_{t}[x(t_{1})] = d_{t}[s(t_{2})]·R ==>


d_{t}[x(t_{1})] = V·( m_{1}/(m_{1}+m_{2}) )


d_{t}[x(t_{1})] = V·( k/(k+1) )
d_{t}[s(t_{2})] = (V/R)·(k/(k+1) )


txoc elástic


m_{1}·V = m_{1}·(-V) + m_{2}·d_{t}[s(t_{2})]·R


d_{t}[s(t_{2})] =  (V/R)·(m_{1}/m_{2})
d_{t}[s(t_{2})] =  (V/R)·k