1. The problem statement, all variables and given/known data If the coefficient of static friction is 0.38 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.] 2. Relevant equations I am trying to figure out the Vmax 3. The attempt at a solution I was able to find the Vmin in doing: ΣFx = ma = mv^2/r Fnsinθ = mv^2/r (1) Designed for 100km/h ~ 27.78m/s so theres no friction involved for now. Fn is the normal force. Fnsinθ/Fncosθ = mv^2/mgr tanθ = v^2/gr θ = arctan(v^2/gr) = arctan((27.78)^2/(9.8*76)) = 46.02° When you go very slow, the car's tendency is to slide down, so the friction acts up the ramp: ΣFx = mv^2/r Fnsinθ - fcosθ = mv^2/r (1) ΣFy = 0 Fncosθ + fsinθ - mg = 0 Fncosθ + fsinθ = mg (2) To eliminate Fn , f and m, i used the definition of friction: f = μ*Fn Fn = f/μ And replaced Fn by f/μ in both equations: fsinθ/μ - fcosθ = mv^2/r (1)* fcosθ/μ + fsinθ = mg (2)* I divided (1)* by (2)* to eliminate some values: (fsinθ/μ - fcosθ)/(fcosθ/μ + fsinθ) = mv^2/mgr (Factor f out and cancel it) (sinθ/μ - cosθ)/(cosθ/μ + sinθ) = v^2/gr Plugging in θ = 46.02° I found the min speed: v = 18.73m/s = 67.43km/h I have to find the max speed now but this time friction acts down the ramp to prevent car from shooting up. I just can't figure out how?