PHysics-Changes in mechanical energy for nonconservative forces?

Question

A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and there is a constant friction force of 0.032 N b/t the barrel and the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the ball have max speed? (c) What is this max speed?

I figured out part a, need help w/ b & c....

Answer 1

Using conservation of energy from the elastic potential energy to the kinetic energy of the launch and then factoring in the work done by the frictional force in the barrel on the ball, the velocity when it leaves the barrel is 1.4 m/s. The maximum velocity of the ball is at the point that the spring releases the ball. At that point, according conservation of energy, the velocity of the ball will be 1.94 m/s.

This all assumes that there is only friction acting on the ball after it is released from the spring. If this is not the case, then you have to account for the constantly changing force supplied by the spring as its length changes due to decompression. This changing force up against a constant frictional force will cause a constantly changing acceleration in the launch phase requiring much more involved math to determine the velocity of the ball.

Answer 2

The spring has an energy Es = 1/2 kx^2 before the cannon shoots.

The force of friction does work Wf = Ff*d where d = 15 cm and Ff is the constant friction force.

So at the end of the barrel, the energy remaining is Es - Ws = 1/2mv^2.

Now, does the 15 cm include the 5 cm that the spring is compressed? If no then max speed => 1/2kx^2 = 1/2mv^2 so

vmax = sqrt(k/m)*x where x = 5 cm.

If yes, then the calculation is more complicated so I suspect the above answer is what is being sought.