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 0.160 m and the gun fired vertically as shown, the gun can launch a 17.0 g projectile to a maximum height of 16.0 m above the starting point of the projectile. Figure P5.33 (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 5.33b. m/s

Explanation / Answer

a)spring potential energy=kinetic energy of the bullet

b)kinetic energy of the bullet = gravitaional potential energy of the bullet

0.5mv^2=mgh

v=2gh=2*9.8*16=17.07m/s

a)0.5kx^2=0.5mv^2

k=17*10^-3*313.6/0.16*0.16

=208.25N/m

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