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I\'m having trouble setting up part (b) of this question. The problem reads: A t

ID: 1751033 • Letter: I

Question

I'm having trouble setting up part (b) of this question. The problem reads:
A toy cannon uses a spring to project a 5.30 g soft rubberball. The spring is originally compressed by 5.00 cm and hasa force constant of 8.00 N/m. When the cannon is fired, theball moves 15.0 cm through the horizontal barrel of the cannon andthe barrel exerts a constant friction force of 0.0320 N on theball. (a) With what speed does the projectile leave the barrel ofthe cannon? (b) At what point does the ball have maximunspeed? I was able to solve part (a): vf =1.4 m/s The answer in the back of the book says that part (b)is 4.6 cm, but I have no idea how to find this answer. I'm having trouble setting up part (b) of this question. The problem reads:
A toy cannon uses a spring to project a 5.30 g soft rubberball. The spring is originally compressed by 5.00 cm and hasa force constant of 8.00 N/m. When the cannon is fired, theball moves 15.0 cm through the horizontal barrel of the cannon andthe barrel exerts a constant friction force of 0.0320 N on theball. (a) With what speed does the projectile leave the barrel ofthe cannon? (b) At what point does the ball have maximunspeed? I was able to solve part (a): vf =1.4 m/s The answer in the back of the book says that part (b)is 4.6 cm, but I have no idea how to find this answer.

Explanation / Answer

b) when it has a maximum speed, the acceleration = 0, net force =0 net force = elastic force - friction force = k(a - x) - F = 0 plug k = 8.00 N/m, a = 5.00 cm, F = 0.0320 N and get x = 4.6 cm

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