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 its 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 to a maximum height of 26.0 m above the starting point of the projectile.

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

(b) Neglecting all resistive forces, determine 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

a) 1/2*k*x^2 = mgh k = 2*0.022*9.81*24 / (0.1)^2 = 1035.94 N/m b) 1/2*k*x^2 = 1/2*m*v^2 + mgx v^2 = 2g(h-x) v = 21.65 m/s

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