Question

A spring-loaded toy gun projects a 6.1 g nerf pellet horizontally. The spring constant is 8.5 N/m, the barrel of the gun is 13 cm long, and a constant frictional force of 0.039 N exists between the barrel and the nerf pellet. If the spring is compressed 6.6 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

Answer:

0.664 m/s

Explanation:

Conversion to metric unit:

6.1 g = 0.0061 kg

13 cm = 0.13 m

6.6 cm = 0.066 m

As the spring is released from its compression stage, its elastics energy is converted into the pellet's kinetic energy, which is also affected by the work of friction force:

$E_e = E_k + W_f$

$kx^2/2 = mv^2/2 + Fs$

where k = 8.5 N/m is the spring constant, x = 0.066m is the compression length, m = 0.0061 kg is the pellet mass, v is the velocity of the pellet as it leaves the barrel, F = 0.039 N is the constant frictional force, s = 0.13 m is the distance that the friction force applies on the pellet.

$8.5*0.066^2/2 = 0.0061*v^2/2 + 0.039*0.13$

$0.0185 = 0.00305v^2 + 0.00507$

$v^2 = 0.44$

$v = \sqrt{0.44} = 0.664 m/s$