Question

A spring-loaded toy gun projects a 1305 g nerf pellet horizontally. The spring constant is 8.8 N/m, the barrel of the gun is 17 cm long, and a constant frictional force of 0.026 N exists between the barrel and the nerf pellet. If the spring is compressed 6.0 cm for this launch, determine the speed 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:

$v_f=2.15x10^{-4}m/s$

Explanation:

Given:

$m=1305g*\frac{1kg}{1000g}=1.305kg$

$K=8.8N/m$

$L=17cm*\frac{1m}{100cm}=0.17m$

$x_i=6.0cm*\frac{1m}{100cm}$

ΔE=Wf

$E_f-E_i=W_f$

$\frac{1}{2}*m*v^2-\frac{1}{2}*K*x_i^2=-2*F_k*L$

$m*v_f^2=-2*F*L+K*x_i^2$

Solve to vf'

$v_f=\sqrt{\frac{-2*F_k*L+K*x_i}{m}}$

$v_f=\sqrt{\frac{-2*0.026N*0.17m8.8N/m*(0.06m)^2}{1.305kg}}$

$v_f=2.15x10^{-4}m/s$