Question

A toy gun uses a spring to project a 5.5-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 14 cm long, and a constant frictional force of 0.033 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 6.0 cm for this launch? (Assume the projectile is in contact with the barrel for the full 14 cm.)

_____m/s

Answer 1

Mass of the soft rubber sphere = m = 5.5 g = 5.5 x 10^-3 kg

Force constant of the spring = k = 8 N/m

Amount the spring is compressed = X = 6 cm = 0.06 m

Length of the barrel of the gun = L = 14 cm = 0.14 m

Friction force on the sphere = f = 0.033 N

Speed the projectile leaves the barrel = V

The initial potential energy of the spring is converted into the kinetic energy of the projectile plus the work done against friction.

kX²/2 = mV²/2 + fL

(8)(0.06)²/2 = (5.5x10^-3)V²/2 + (0.033)(0.14)

V = 1.89 m/s

Speed the projectile leaves the barrel at = 1.89 m/s