4. Question Details SerCP8 5.P.039. My Notes Ask Your Teacher The launching mech

Question

4. Question Details SerCP8 5.P.039. My Notes Ask Your Teacher 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 0.100 m and the gun fired vertically as shown, the gun can launch a 17.0 g projectile to a maximum height of 24.0 m above the starting point of the projectile. s0 (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 Need Help? aTak to a Tuter Show My Work (optional)

Explanation / Answer

here,

x= 0.1 m

mass , m = 0.017 kg

height , h = 24 m

a)

let the spring constant be K

using conservation of energy

0.5 * k * x^2 = m * g * h

0.5 * k * 0.1^2 = 0.017 * 9.81 * 24

solving for k

k = 800.5 N/m

b)

let the speed at equilibrium position be v

using conservation of energy

0.5 * k * x^2 = 0.5 * m * v^2 + m * g * x

0.5 * 800.5 * 0.1^2 = 0.5 * 0.017 * v^2 + 0.017 * 9.81 * 0.1

solving for v

v = 21.7 m/s

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