Roller coaster friction calculations

[thestudent101]

I have a physics assignment. Part of it is to calculate the speed throughout the rollercoaster and to not exceed 4.5g's of force. Anyway, I'm calculating the speed of the rollercoaster using the formula
0=g(h2-h1)+0.5(v2^2-v1^2)+μNd
(I have already simplified to not include the mass (excluding the reaction force which will be takne out later)
the first two parts of the equation are fine, and μ is 0.01 and the rollercoaster has traveled a distance of 13.8m. To calculate the reaction force I have been using trig ratios, estimating the angle off the diagram, and using -mg as the adjacent side. I am now stuck because I'm on a 90 degree inclince. The angle between the adjacent side (-mg) and the reaction force is 90degrees so I can't use trig ratios as the angle is 90 degrees and if i swap the sides around the hypotenuse is no longer the longest side.

I was thinking that maybe friction would simply be zero
eg. assume a force of 10N if the cart is facing up on a horizontal plane, -10N if the cart is facing down on a horizontal plane. Theoretically wouldn't it be 0N halfway? But then you can't have zero friction can you?


Please help! :)

 

[CWatters]

I would assume zero for this part of the problem. On a vertical surface there is no friction because no force N pushing the surfaces together.

Aside: In reality roller coasters aren't simple blocks of wood sliding on a surface anyway. They have rollers to stop it lifting off the track, friction in bearings, air resistance etc but can ignore all these because they are not specified in the problem Anyway they result in a slower speed and the problem says "not exceed 4.5g". Ignoring friction helps err on the side of safety.

 

[CWatters]

I suspect that thenext part of the problem has the coaster go around a curved part of the track. If the curve is in the vertical plane what must you remember to avoid a 1g error in the answer?

 

[thestudent101]

The coaster is already on a curve, it is just at one of the sides of it so the reaction force is 90 degrees. (I said vertical plane because it was easier to describe). We are doing instantaneous calculations so that would still mean friction is virtually zero right? And what must I do to avoid the 1g error? I've heard about it in physics, but forgot about it until now.

 

[thestudent101]

Now I'm calculating for the top of the loop. How do I do the friction there? Do you have g as -9.8? So you take away friction instead of adding it?