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 0.080 m and the gun fired vertically as shown, the gun can launch a 21.0 g projectile to a maximum height of 22.0 m above the starting point of the projectile.
(a) Neglecting all resistive forces, determine the spring constant.
1. 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).
2. m/s

Explanation / Answer

(a) According to conservation of energy, 1/2kx^2 = mgh k = 2mgh/x^2     = 2*21.0*10^-3*9.8*22.0/(0.08)^2     = 1414.87 N/m According to equations of motion, V^2 = 2gh         = 2*9.8*22.0 ==> V = 20.76 m/s

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