The launching mechanism of a toy gun consists of a spring of unknown spring cons

Question

The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure below. If the spring is compressed a distance of0.200m and the gun fired vertically as shown, the gun can launch a19.0-g projectile from rest to a maximum height of18.0m above the starting point of the projectile.

The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure below. If the spring is compressed a distance of0.200m and the gun fired vertically as shown, the gun can launch a19.0-g projectile from rest to a maximum height of18.0m above the starting point of the projectile. (a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height. (b) Neglecting all resistive forces, determine the spring constant. 171 The given projectile height is measured from the starting point of its motion. You appear to have assumed it is measured from the rest point of the spring.N/m (c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (wherex= 0), as shown in Figure (b). 18.97 m/s

Explanation / Answer

a) potential energy(P.E) of spring to kinetic energy(K.E) of bullet(when the bullet is fired)
kinetic energy of bullet to potential energy (when the bullet reaches the maximum height)

b) By conservation of energy

P.E of spring = P.E of bullet at its max height

which means 1/2 k x2 = mgh

where m= mass of bullet = 23 g = .023 kg
g = acceleration due to gravity = 9.81 m/s2
h= max height = 19 m
x = max compression of spring = 0.110 m

k = spring constant

Sovle for k.

k = 2x .023 x9.81 x 19 / .1102

= 708.59 N/m

c)By conservation of energy
P.E of spring = K.E of bullet when it is fired.

which means 1/2 k x2 = 1/2 m v2

where

m= mass of bullet = 23 g = .023 kg
x = max compression of spring = 0.110 m

k = spring constant = 708.59 N/m (from (b))

V= velocity of the bullet( to be calculated)

v2 =  k x2 /m = 372.78

v = 372.78= 19.31 m/s

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