1. A spring-loaded toy gun is used to shoot a ball of mass 1.5kg straight up in

Question

1. A spring-loaded toy gun is used to shoot a ball of mass 1.5kg straight up in the air, as shown in the figure. The spring has a spring constant k=677N/m. if the spring is compressed a distance of .25m from its equilibrium position (y=0) and then released, the ball reaches as 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 the movement occurs along a straight vertical line alone the y-axis.     

a. Find the muzzle velocity of the ball (that is the velocity of the ball at the spring

Explanation / Answer

If the mass is moving with speed 4.78 m/s at the equilibrium position, that means it has KE there that must be added to the additional PE that will be given it when the spring pushes it beyond the equilibrium position equal to kx^2 /2.

mgh = kx^2 /2 + (1/2)mv^2

h = (kx^2 +mv^2)/2g

h = [(667)(25x10^-2)^2 +(1.5)(4.78)^2] / (2)(9.8)

h= 3.88 meters

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