What is the speed of a BB fired from a spring-compressed BB gun?

[pinkyjoshi65]

A BB gun fires a 8.24-g projectile by using a compressed spring (k = 2.88 × 103 N/m) and a 15.1 cm long barrel. As the disc travels through the barrel, it experiences a constant frictional force of 0.125 N. If the spring is compressed 16 mm, what is the speed of the BB as it leaves the gun?


So now we know that the Force is kx= 2.88*103*0.016= 4.74N

so..we use F=ma and find a.

then i got stuck..

 

[cyprusad]

Gain in kinetic energy during the course of the motion of the disc, from the instant it was fired till the point when it leaves the barrel; is the sum of the potential energy of the compressed spring and the work done by the barrel(which is negative) If v is required, use:

$$\frac{1}{2} mv^{2} = \frac{1}{2} kx^{2} - Fs$$

F is the constant retarding force applied by the barrel, and s is the length of the barrel.
The above equation is just the work energy theorem.