How Fast Does a Ball Shoot from a Toy Cannon with Friction?

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The discussion centers on calculating the speed of a soft rubber ball projected from a toy cannon, considering the effects of friction. The ball, weighing 5.30 g, is propelled by a spring compressed by 5.00 cm with a force constant of 9.00 N/m. As the ball travels 16.0 cm through the barrel, a constant frictional force of 0.0320 N is present. An initial calculation of the speed yielded an incorrect result, prompting suggestions to adjust the distance friction acts upon from 0.11 m to the full 0.16 m. The conversation emphasizes the importance of accurately accounting for friction in the calculations to determine the correct exit speed of the projectile.
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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 9.00 N/m. When it is fired, the ball moves 16.0 cm through the horizontal barrel of the cannon, and a constant frictional force of 0.0320 N exists between barrel and ball.

(a) With what speed does the projectile leave the barrel of the cannon?

Wnet = \DeltaKE
Ws - Wfk = .5mv2 - 0
.5kx2 - fkd = .5mv2
.5(9)(.052) - (.032)(.11) = .5(.0053)v2
v = 1.7079

Final answer is incorrect. Any ideas?
 
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Have you tried replacing .11 with .16? Friction acts over full length of barrel. What is the answer?
 

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