Question

The massless spring of a spring gun has a force constant k = 0.04 N/cm. When the gun is aimed vertically, a 19 g projectile is shot to a height of 5.0 m above the end of the expanded spring. (See below.) How much was the spring compressed initially? (Find d, in meters.)

Answer 1

m = mass of the projectile = 19 g = 0.019 kg

h = height gained by the projectile above the end = 5.0 m

x = compression of the spring = ?

H = height of the projectile above the compressed position = h + x = 5 + x

k = spring constant = 0.04 N/cm = 0.04 N/(0.01 m) = 4 N/m

Using conservation of energy

Potential energy gained by the projectile = spring potential energy stored

mgH = (0.5) k x²

(0.019) (9.8) (5 + x) = (0.5) (4) x²

x = 0.7304 m