Question

The launching mechanism of a popgun consists of a trigger released spring. The spring is compressed to a position yA and the trigger is fired. The projectile of mass m rises to a position yC above the position at which it leaves the spring. Consider a firing of the gun for which m = 30.0 g, yA = -0.140 m, and yC = 10.0 m.

Neglecting all resistive forces, determine the spring constant _____

a. 302 N/m

b. 84.6 N/m

c. 300 N/m

d. 304 N/m

Find the speed of the projectile as it moves through the equilibrium position B of the spring ______

a. 14.0 m/s

b. 15.0 m/s

c. 16.0 m/s

d. 17.0 m/s

Answer 1

Neglecting all resistive forces, determine the spring constant

just use conservation of energy

mgy_c - mgy_A = 1/2kx²

k = 2 ( mgy_c - mgy_A ) / x²

k = 2 * 30e-3 * 9.8 ( 10 + 0.14) / 0.14²

k = 304.2 N/m

option (d) is the closest

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Find the speed of the projectile as it moves through the equilibrium position B of the spring

I assume point B is just at the launch point ( muzzle velocity)

so,u

using conservation of energy

1/2mv²  = 1/2kx² + mgy_A

v = sqrt (( 302.4 * 0.14² 30e-3 ) - ( 2 * 9.8 * 0.14))

v = 13.95 m/s

option (a) seems fine