Question

110 points] A concrete highway curve of radíus R s banked at an angle . A rubber-tired car of mass m can take the curve with some maximum speed Umar without sliding he coefficient of static friction between the tires and the road is ue and the coefficient of kinetic friction between the tires and the road is the (a) Sketch the free body diagram of the car in the space below. Label all forces accord- ingly, including the correct form of friction (kinetic or static) and include an appropriate Ule coordinate system. Be aware of the relative length of your vectors. na Ancoso frosoft nsino Fr . Is F FG = f sing (b) Assuming that m R, 0,Ms, and we are all known values, derive an expression for Umar the maximum speed with which the car can take the curve without slipping. Your final answer will be some combination of these known variables and possibly g. Hint: start by writing out the equations of motion, SF = ma for each coordinate axis you defined in your free body diagram.

Answer 1

f = us N m net r = radius of curvature of curve. 10 N mg Force equations at maximum speed v, at threshold of sliding up incline. Efx=m2 = N sin € + usN cos e 2F, = 0 = N cos 0 - us N sin 0 - mg Solving this pair of equations for the maximum speed v gives: Vmax = V rg(sin e + Mscos e) cos 6 - ussin e The limiting cases are: Vmax = Vrg tan e Frictionless case Vmax = Vrgus Flat roadway