launching mechanism of a toy gun consists of a spring of unknown spring constant

Question

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 0.100 m and the gun fired vertically as shown, the gun can launch a 24.0-g projectile from rest to a maximum height of 24.0 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.
(b) Neglecting all resistive forces, determine the spring constant.

(c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0)

Explanation / Answer

a) The elastic (or spring potential) energy in the spring is transformed to kinetic energy when it’s released. Then, this kinetic energy changes entirely to gravitational potential energy when the projectile comes to a stop momentarily at the top of its flight path. b) k = 2mgh/y² = 2*.024*9.8*24/.1² = 11289.6 N/m c) v = sqrt(2gh) = sqrt(2*9.8*24) = 21.68 m/s

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