Given the compression of a spring, the mass of the ball bearing, the ellapsed time for the launch and the velocity of the ball bearing shot by the spring, we calculate the potential energy stored in the spring before the launch, the spring constant and the average power output of the spring during the ball bearing launch.
We start by computing the initial potential energy in the spring, and we do this by computing the kinetic energy in the ball bearing (all the initial spring potential energy converts to the kinetic energy of the ball during the launch).
Once we have the initial spring potential energy, we find the spring constant by using the spring potential energy formula: PE=1/2*kx^2 and solving for the spring constant k.
Finally, given the launch time for the spring gun, we compute the average power output of the spring by dividing the energy transferred by the time it takes for the launch. P=delta-E/delta-t, and we have the average power output for the shot.
