Ʃ1. The problem statement, all variables and given/known data A car of mass 2,000 kg is moving round a curve on a banked track (see diagram-We were actually only given the top picture "a" and not the bottom one, but both are relevant) at a constant speed. The coefficient of static friction between the car's tires and the track is μs = 0.140. The radius of curvature of the car's path is r = 200m, and the angle of bank of the track is θ = 10.0o . Showing all your work, find the speed that the car must travel such that the force of static friction parallel to the slope is zero. 2. Relevant equations Ʃ Fx= Fnx= Fnsin10=Fc = mv^2/r (No Ffrictionx because it should =0) Equation #1 Ʃ Fy= Fny -Ffrictiony-mg=0 Ffrictiony= 0.140 sin 10 Fny= Fncos10 ƩFy= Fncos10-0.140Fnsin10=mg Equation #2 3. The attempt at a solution Divide equation 1 by equation 2: (mv^2/r =Fnsin10)/(mg=Fn(cos10-0.140sin10): m's cancel and Fn's cancel then solve for v: v=√(rg(sin10/cos10-0.140sin10) v=18.8 m/s My question is this: I understand that the so-called design speed is the speed a car can get around the track without friction and that this is expressed as v=√(rgtan theta) because there is no element of friction to use. For the problem above, I initially solved it using this simpler "design speed" formula and got an answer very close to my answer above. However, close is not necessarily right! I looked at the question again and figured that since the coefficient of static friction was given that I needed to include the Ffriction in the y direction. Am I right on this? I am finding banked curve free body diagrams with friction to be confusing. There seem to be so many elements and it's hard to keep track. I also have some difficulty understanding the X and Y directions of friction as for what they really mean. I get that the x direction in this problem involves the Fnx as the only force acting as the centripetal force only because the problem states that the x direction static friction is zero. If it didn't and was perhaps asking for the min speed it could go around curve w/o slipping then I would have Fstaticfriction in the opposite direction as Fnx (ie: static friction away from center)? I am having a hard time wrapping my brain around these banked tracks problems. Am I at least on the correct path with how I worked the problem above? Thanks!