Question

A rifle fires a 2.10 x 10^-2 kg pellet straight upward, because the pellet rests on a compressed spring when the trigger is is pulled. the spring has negligible mass and it is compressed by 9.10 x 10^-2 m from is unstrained length. the pellet rises to a maximum height of 6.10 m above its position on the compressed spring. ignoring air resistance determine the spring constant.

Answer 1

m = mass of pellet = 2.10 x 10⁻² kg

x = compression of spring at the time launch = 9.10 x 10⁻² m

h = height gained by the pellet above the initial position = 6.10 m

k = spring constant

using conservation of energy

spring potential energy = gravitational potential energy of pellet

(0.5) k x² = m g h

inserting the values

(0.5) k (9.10 x 10⁻²)² = (2.10 x 10⁻²) (9.8) (6.10)

k = 303.2 N/m