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26 Nov 2019
Engineering a highway curve. If a car goes through acurvetoo fast, the car tends to slide out of the curve. For abankedcurve with friction, a frictional force acts on a fast cartooppose the tendency to slide out of the curve; the forceisdirected down the bank (in the direction water woulddrain).Consider a circular curve of radius R = 210 mandbank angle θ, where the coefficient of static frictionbetween tiresand pavement is μs. A car (withoutnegative lift) isdriven around the curve as shown in Figure 6-13.Find an expressionfor the carspeed vmax that puts the car ontheverge of sliding out, in terms of R, θ,andμs. In kilometers per hour,evaluatevmax for a bank angle ofθ = 11° andfor(a) μs = 0.47(dry pavement)and(b) μs = 0.044(wet or icy pavement).(Now you can see why accidents occur inhighway curves when icyconditions are not obvious to drivers, whotend to drive at normalspeeds.)
Engineering a highway curve. If a car goes through acurvetoo fast, the car tends to slide out of the curve. For abankedcurve with friction, a frictional force acts on a fast cartooppose the tendency to slide out of the curve; the forceisdirected down the bank (in the direction water woulddrain).Consider a circular curve of radius R = 210 mandbank angle θ, where the coefficient of static frictionbetween tiresand pavement is μs. A car (withoutnegative lift) isdriven around the curve as shown in Figure 6-13.Find an expressionfor the carspeed vmax that puts the car ontheverge of sliding out, in terms of R, θ,andμs. In kilometers per hour,evaluatevmax for a bank angle ofθ = 11° andfor(a) μs = 0.47(dry pavement)and(b) μs = 0.044(wet or icy pavement).(Now you can see why accidents occur inhighway curves when icyconditions are not obvious to drivers, whotend to drive at normalspeeds.)
