spring-loaded toy gun is used to shoot a ball of mass \\(m= 1.50\\; \ m{kg}\\) s

Question

spring-loaded toy gun is used to shoot a ball of mass (m= 1.50; m{kg}) straight up in the air, as shown in The figure shows a toy gun consisting of a vertical tube, whose bottom is attached to a horizontal block, and a vertical spring placed inside the tube. The bottom end of the spring is attached to the block. Two positions of a ball are shown. In the first position, the ball rests on a plate on top of the spring inside the tube and in the second position, the ball is at distance h max above the top of the tube. An arrow is directed upward from the first position of the ball to its second position. The top of the tube has zero y-coordinate.. The spring has spring constant (k = 667; m{N/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 ( exttip{h_{ m max}}{h_max}) (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

Explanation / Answer

using equation

E = 1/2 k y2 + m g y

E1 = 1/2 k y12 + m g y1

E1 = 1/2 X 667 X ( -0.25 )2 + 1.5 X 9.8 X ( - 0.25 )

E1 = 20.84 - 3.675

E1 = 17.165 J

and

E2 = 0

next

E3 = m g hmax

m g hmax = 17.165

hmax = 17.165 / 1.5 X 9.8

hmax = 1.167 m

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