Question

A spring-loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in the air, as shown in (Figure 1) . The spring has spring constant k=667N/m. If the spring is compressed a distance of 25.0 centimeters 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 and down along the y axis.

Answer 1

Using the conservation of energy

Initial energy = final energy

(1/2)*k*x^2 = m*g*h

Given k = 667 N/m , x = .25 m , m = 1.5 kg

So ,

(1/2)*667*(0.25)^2 = 1.5*9.8*h

h = 0.5*667*0.25^2/1.5*9.8

h = 1.418 m

Now , to calculate hmax from equilibrium position

hmax = h - 0.25 = 1.418 - .25 = 1.168 m