Spring is stretched by l

Feb 2017
please, give me a tip

Two objects with mass M and m are on a flat horizontal table. A horizontal spring with spring constant K is attached to the two objects as show in Fig If the system is released from rest when the spring is stretched by l, find the maximum velocity of the object with mass m.

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Aug 2008

max speed will occur when the spring relaxes to its uncompressed length ...

(1) energy conserved

$\dfrac{1}{2}kL^2 = \dfrac{1}{2}Mv_1^2 + \dfrac{1}{2}mv_2^2$

(2) momentum is conserved

$Mv_1 = mv_2$

solve for $v_1$ in terms of $v_2$ and sub into the energy equation, then solve for $v_2$