Question

A spring-loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in the air. The spring has spring constant k=667 N/m. If the spring is compressed a distance of 19.0 cm from its equilibrium position y=0 and then released, the ball reaches a maximum height hmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up along the y axis.

Find vm the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y=0).

Find the maximum height h max of the ball.

Answer 1

A) Apply conservation of energy

initial elastic potential energy = final kinetic energy + gravitational poitential energy

(1/2)*k*y^2 = (1/2)*m*v^2 + m*g*y

(1/2)*667*0.19^2 = (1/2)*1.5*v^2 + 1.5*9.8*0.19

==> v = 3.51 m/s <<<<<<<<<<-------------Answer

B) now Apply conservation of energy after the ball leaves the spring.

initial kinetic energy = final gravitational potential energy

(1/2)*m*v^2 = m*g*h

==> h = v^2/(2*g)

= 3.51^2/(2*9.8)

= 0.629 m <<<<<<<<<<-------------Answer