Banked Turn with Friction - Physics of Speed Limits on Banked Curves

We take a look at the general case of finding the maximum speed at which a car can drive around a banked curve without skidding out. 0:00 We set up the problem using F = ma (Newton's 2nd Law) in the vertical (a = 0) and horizontal (a = mv^2 / R) directions to 4:17 relate the maximum speed to the ramp angle, radius of curvature of the road, and the coefficient of friction. Finding the speed limit on a banked curve is a very standard problem in mechanics in undergraduate physics, AP Physics, and IB Physics, and is useful for those who design banked roads. 7:48 Finally, we show the specific results for maximum speed vs. ramp angle for the specific case of an exit ramp radius of curvature of 100 m, acceleration due to gravity of 10 m/s^2, and a coefficient of friction of 0.9, which is reasonable for a dry day for rubber on asphalt. In addition, we explore what would happen if the road were unbanked and if the road were banked (tilted) the wrong way.

[@jaybirdyz2220]

you just saved my physics grade. 100% soooonnnnnnnn

[@samuels.8951]

why isnt the value of N equal to cos(theta)*mg? isnt it usually the case when objects are on a curb?

[@JJgetshit]

Thanks. I'm in a horribly run physics course at the moment, and this really helped me to understand the problem.

[@rubenlee6123]

Brilliant video. What equation did you use to get that graph? I don't know if I'm being completely stupid but I gave a graphing calculator the equation shown with the numbers given (R = 100, etc.) and got a totally different tan graph, and now I'm confused. Also, I used this process to find the max speed with different dimensions (R = 15, theta = 75, and COF = 0.32). Putting this in my calculator gives me a math error, as the denominator ends up negative. What does that mean in the context of turning? Are those just unfeasible dimensions? Hope you can help clear this up.

[@AddisShimelis]

I am confused, what is the difference between v²=R.g.tan theta and the above equation?

[@pennywise5283]

what about mg sin theta when adding the sum of forces in the x direction (the car is on an incline isn't it?).

[@haaarison]

just want to say you're a lifesaver - really appreciate how visual your diagrams are, finally got my head around it :)

[@plushyimpala1456]

thank you so much, i literally couldnt find anyone else doing this type of problem

[@gerakore8948]

thanks a lot. finally makes sense. i guess my way of doing FBD where gravity is off to the side and everything else on the axis's doesn't work for this kind of problem although makes other problems a lot more convenient.

[@UntoldTalesRealm]

Better explained🎉🎉🎉

[@748813592415]

Great video. I have always found banked curves on roads and highways to be aesthetically pleasing.

[@natashakesarwani2879]

😢😢😢