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 Figure P5.33a. If its spring is compressed a distance of 0.100 m and the gun fired vertically as shown, the gun can launch a 18.0 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.

(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 5.33b

Explanation / Answer

x = 0.1m
m = 0.018kg
h = 22m
All energy from the spring must be converted to purely gravitational potential energy at the top of the balls motion so
1/2 kx 2 = mgh k = 2mgh/x2 = 2*0.018kg * 9.8m/s2 * 22m/0.12 = 776N/m Now all spring's potential energy is converted to kinetic energy. 1/2 kx 2 = 1/2mv2 v = vkx2/m = v776 * .12/0.018 = 20.76m/s Hope that helps v = vkx2/m = v776 * .12/0.018 = 20.76m/s Hope that helps

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