Question

2. A nerf gun is loaded with a spring. The spring has a spring constant of 400 N/m and the “ammunition” is a foam dart with a mass of 0.2kg. When loaded, the spring is compressed 0.05m. (Ignore any air resistance.)

a) How much elastic potential energy does the foam dart have when the spring is compressed and the nerf gun is fully loaded?

b) How much kinetic energy does the foam dart have when the spring is compressed and the nerf gun is fully loaded?

c) How much elastic potential energy does the foam dart have just after the foam dart is shot and the spring is decompressed?

d) How much kinetic energy does the foam dart have just after the foam dart is shot and the spring is decompressed?

e) Calculate the speed of the dart as it leaves the nerf gun when the spring is decompressed.

Answer 1

a)

Initial elastic potential energy is

b)

Since there is no initial velocity Vi=0 ,the initial kinetic energy is

c)

final elastic potential energy is

d)

By Conservation of energy

e)

Since