A ball of mass $m$ is attached to a spring that is attached to a heavy moving cart (mass of cart $M >>$ mass of ball $m$) moving at velocity $V0$. The compressed spring with known spring constant $k$ is released and the ball is fired forward. The ball then strikes a similar spring with the same spring constant attached to a wall (i.e. the spring is attached to a heavy immovable object). How far does the spring attached to the wall compress?
Is it just a matter of conservation of energy? Ek(moving ball) + E(spring potential-for the moving spring) = E(spring potential-fixed spring)
Or does the motion of the initial spring somehow affect how much energy it can transmit to the ball.
Or, in the frame of reference of the moving spring, can you simply calculate the velocity of the ball from E(spring potential) = Ek and add that to the initial velocity of the spring/ball and then use that new velocity to calculate the Ek and hence the energy transferred to the fixed spring and hence the compression of the spring.
Depending on how you approach this problem you get different answers.