"A spring with a spring constant "k" is compressed 10 cm from equilibrium. A ball of mass 100 g is at rest next to it. The spring then decompresses quickly back to its equilibrium position causing the ball to shoot forward. If the spring constant is 500 N/m, what is the ball's kinetic energy? And what is the ball's momentum after it is struck by the spring?"
KE = 1/2mv^2
PEspring = 1/2kx^2
The Attempt at a Solution
I have attempted to solve this by using the conservation of mechanical energy to surmise that the kinetic energy of the ball after it is released would be equivalent to the potential energy of the spring before the ball is released. However, what is confusing me is that, after the ball is released from the spring, wouldn't its velocity be higher at first, and then gradually peter off? Thus, since kinetic energy equals 1/2mv^2, and momentum equals mv, wouldn't the kinetic energy and the momentum of the ball taper off over time, as well? So I'm not sure which moment of time they want me to find the kinetic energy and momentum for. Should I just assume it's the maximum amount of kinetic energy and momentum, right at the moment when the ball is released from the spring and starts moving?