The launching mechanism of a toy gun consists of a spring ofunknown spring const

Question

The launching mechanism of a toy gun consists of a spring ofunknown spring constant, as shown in Figure P5.33a. If its springis compressed a distance of 0.120 m andthe gun fired vertically as shown, the gun can launch a21.0 g projectile to a maximum height of16.0 m above the starting point of theprojectile.

(a) Neglecting all resistive forces, determine the springconstant.

(b) Neglecting all resistive forces, determine the speed of theprojectile as it moves through the equilibrium position of thespring (where x = 0)

Explanation / Answer

    Given         mass of theprojectile    m = 21 g = 0.021 kg          maximumheight   H = 16 m         a) weknow that                H = u2   / 2g                       16       =u2   / 2g                   u = 2*9.8*16                        = 17.7 m/s         b) ( 1 / 2 )mu2   = ( 1 /2 ) k x2                          0.021 *17.7*17.7 = k * 0.12*0.12                   spring constant K = 456.88 N /m        

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