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 0.180 m and the gun fired vertically as shown, the gun can launch a 19.0 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

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 0.180 m and the gun fired vertically as shown, the gun can launch a 19.0 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

1/2)kx^2 = mgh
a)
k = 2mgh/x^2
k ? (2)(0.019)(9.8)(26.0) / 0.18^2
k ? 298.83 N/m
b)
(1/2)mv^2 = mgh
v^2 = 2gh
v ? ?((2)(9.8)(26.0)
v ? 22.57 m/s

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