Consevative and non-conservative forces

[Tmtamrak]

A toy cannon uses a spring to project a 5.39 g soft rubber ball. The spring is originally compressed by 4.99 cm and has a force constant of 8.04 N/m. When the cannon is fired, the ball moves 15.8 cm through the horizontal barrel of the cannon, and there is a constant frictional force of 0.0328 N between the barrel and the ball.



At what point does the ball have maximum speed?


I do not know where to start... If I set F=fx and F=ma, then I get speed at 4.99cm which is incorrect. Can someone please help?

 

[ideasrule]

Imagine the process. At first, the spring is stronger than friction and accelerates the ball. At some point, friction overcomes the spring force and the ball starts slowing down. So the point of maximum speed is the point where these two forces are equal.

 

[Tmtamrak]

Thank you so much for responding.
If that is the case, my answer still does not make sense. If Kx=friction, then 8.04x=0.0328 which causes x to be 0.4079cm.

 

[ideasrule]

That's the distance from equilibrium. Remember that the spring is originally 4.99 cm from equilibrium.

 

[Tmtamrak]

thank you, thank you, thank you! :-)