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 the figure below. If itsspring is compressed a distance of 0.100 m and the gun fired vertically as shown,the gun can launch a 25.0 gprojectile to a maximum height of 24.0 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), as shown infigure
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), as shown infigure

Explanation / Answer

Compression x = 0.1 m

Mass m = 25 g = 0.025 kg

Height h = 24 m

We know from law of conservation of energy ,

Potential energy at maximum height = Maximum compressionalpotential energy of the spring

mgh = ( 1/ 2) kx ^ 2

From this spring constant k = 2mgh / x ^ 2

                                             = 1176 N / m

(b). Maximu speed V = A w

Where A = amplitude = maximum compression = 0.1 m

             w = angular frequency = [ k / m]

                 = 216.88 rad / s

So, V = 21.688 m / s

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