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Mechanics Banked Track Question

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1. a car moves in a horizontal circular path of radius 6m around a bend that is banked at an angle arctan(0.5) to the horizontal.
Without slipping the maximum speed the car can travel is 28 m/s

find the coefficient of friction between the tyres of the car and the road surface.

So i've set up the picture and the forces, but no matter what I do there are too many unknowns for me to solve or it just becomes horrible.

I've tried to see if I could find just F and R first but I cannot.
2. (Original post by tavtavtav)
a car moves in a horizontal circular path of radius 6m around a bend that is banked at an angle arctan(0.5) to the horizontal.
Without slipping the maximum speed the car can travel is 28 m/s

find the coefficient of friction between the tyres of the car and the road surface.

So i've set up the picture and the forces, but no matter what I do there are too many unknowns for me to solve or it just becomes horrible.

I've tried to see if I could find just F and R first but I cannot.
Don't have time to explain, but watch this: https://www.youtube.com/watch?v=iwNVksd-0L8 - it explains it very clearly.
3. (Original post by Zacken)
Don't have time to explain, but watch this: https://www.youtube.com/watch?v=iwNVksd-0L8 - it explains it very clearly.
Thanks, I'll keep the link for future reference.
I feel really bad every time I post a question in here as I actually solved in myself just now.

It's not for lack as effort too, as I actually got stuck during the morning, got bogged down for well over an hour trying different ways for the that single question, came back to it now, still couldn't solve it and posted here.

In the meantime I managed to solve a similar question where the theta was the unknown rather than mu, then used similarly working.

Next time I'll be sure to make so to work at it even longer first.
4. (Original post by tavtavtav)
Thanks, I'll keep the link for future reference.
I feel really bad every time I post a question in here as I actually solved in myself just now.

It's not for lack as effort too, as I actually got stuck during the morning, got bogged down for well over an hour trying different ways for the that single question, came back to it now, still couldn't solve it and posted here.

In the meantime I managed to solve a similar question where the theta was the unknown rather than mu, then used similarly working.

Next time I'll be sure to make so to work at it even longer first.
You feel bad? Don't be silly! It's great that you can solve it for yourself. Also, nobody minds how many questions you put on on here, I've answered hundreds of the same users questions on here, honestly, don't worry about it; feel free to use the site as you see fit.

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