Question

A spring-loaded toy gun projects a 5.2 g nerf pellet horizontally. The spring constant is 8.5 N/m, the barrel of the gun is 12 cm long, and a constant frictional force of 0.034 N exists between the barrel and the nerf pellet. If the spring is compressed 5.6 cm for this launch, determine the speed (in m/s) of the pellet as it leaves the barrel. (Assume the pellet is in contact with the barrel for the full length of the barrel.)

Answer 1

elastic potential energy stored = 1.2 * k * x²

elastic potential energy stored = 0.5 * 8.5 * 0.056²

elastic potential energy stored = 0.013328 J

work done by friction = force * distance = 0.034 * 0.12 = 0.00408 J

This is equal to kinetic energy of pellet

0.013328 J - 0.00408 J = 0.5 * 5.2e-3 * v²

v = 1.886 m/s