A toy gun

A toy gun uses a spring with a spring constant of 10 N/m to shoot a ping-pong ball of mass 5 g. The spring is compressed to 10 cm shorter than its equilibrium length when the gun is loaded. At what speed is the ball released?

The equilibrium point is the natural choice for a reference point. Using the equation found previously for the work, we have

The spring loses contact with the ball at the equilibrium point, so the final potential energy is

PE_f = 0 .

The initial potential energy is

The loss in potential energy of 0.05 J means an increase in kinetic energy of the same amount. The velocity of the ball is found by solving the equation KE = (1/2)mv² for v,