Question 1 A s ing-loaded toy gun is used to shoot a ball of mass m=1.50 kg stra

Question

Question 1 A s ing-loaded toy gun is used to shoot a ball of mass m=1.50 kg straight up the air, as shown in the figure. The spring has spring constant K N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y-0and then released, the ball reaches a maximum height hmax=1·17m (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. y-0 Find the constant K for the spring m:1.50 Y: D

Explanation / Answer

Given : m = 1.50 kg ; x = 25 cm = 0.25 m ; hmax = 1.17 m

Solution :

We know that , Energy of spring can be given as :

E = (1/2) Kx2 = (1/2)K(0.25)2 = 0.0325 K J

Assuming that all work is transferred as kinetic energy , then

KE = (1/2) mv2 = (1/2)(1.50)v2 = 0.75 v2

KE = 0.0325(K) = 0.75 v2

v = (0.0433K)1/2

By using equation of motion , we have

hmax = v2/2g

1.17 = 0.0433K / (2×9.81)

By solving

K = 529.78 N/m

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