A spring-loaded pellet gun is designed to fi re 3.00-g projectiles horizontally at a speed of 45.0 m/s. (a) If the spring is compressed to its maximum design difference of 8.00 cm, what spring constant is required?

The spring constant required = 949.2 N/m

Explanation:

The energy stored in the spring is converted to kinetic energy of the projectiles fired.

Energy stored in spring's = kx²/2

Kinetic energy of bullets = mv²/2

k = spring constant = ?

x = maximum compression of the spring = 8 cm = 0.08 m

m = mass of projectiles fired = 3.0 g = 0.003 kg

v = velocity of projectiles fired = 45.0 m/s

kx² = mv²

k (0.08²) = 0.003 (45²) = 6.075

k = 949.2 N/m

The spring constant required = 949.2 N/m