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 of 0.080 m and the gun fired vertically as shown, the gun can launch a 19.0-g projectile from rest to a maximum height of 22.0 m 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.

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(b) Neglecting all resistive forces, determine the spring constant.
N/m

(c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure (b).
m/s

Explanation / Answer

.potential energy of spring= 0.5 K x2 = 0.5* K * (0.080) 2 = 0.0032 K

the maximum height reached = 22 m , so potential energy = mgh = 0.019 * 0.8 * 22 = 4.096 J

a) so, potential energy of spring is converted into potential energy at height 22m

b) so,

0.5 K x2 = mgh

=>0.0032 K = 4.096

=> K = 1280.126 N-m

c) the potential energy of spring is converted into kinetic energy

0,5kx2 = 0,5mv2

=> V = 20.76 m/s

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