Banked Highway , Physics?A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 230 m. Traffic is moving along the highway at 35 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road? |
Free body diagram: Put in gravity, surface force (perpendicular to bank) and friction (to keep from sliding down slope). To go around a horizontal curve, net force must be directed toward the center. So make those three arrows add (in a vectory diagram) to a horizontal arrow of length mv^2/r. You know all values but the force of friction, so solve for it. All the masses cancel, so you can go straight to the coefficient of friction. If that bugs you, let m = 1 kg and solve. Then work out the coefficient of friction. (friction/surface (normal) force.)
