Spring-loaded toy gun projects a 5.9 g nerf pellet horizontally. the spring constant is 8.5 n/m, the barrel of the gun is 17 cm long, and a constant frictional force of 0.037 n exists between the barrel and the nerf pellet. if the spring is compressed 6.8 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.) m/s

Solution:

As per the question:

Mass of the pellet, m = 5.9 g = 0.059 kg

Spring constant, k = 8.5 N/m

Length of the barrel, l = 17 cm = 0.17 m

Frictional force, F = 0.037 N

Compression in spring,

Now,

To calculate the speed of the pellet:

Using the principle of conservation of energy:

Change in spring potential energy is used in doing work against the friction force and provides the required kinetic energy:

v = 0.5289 m/s

Explanation:

Given:

Spring force on the pellet:(inside the barrel)

Net force on the pellet:(INSIDE THE BARREL)

Acceleration of the pellet:(inside the barrel)

Using the equation of motion:

where, v & u are the final and initial velocities respectively

is the velocity at the exit of the barrel