Engineering a highway curve. If a car goes through a curve toofast, the car tends to slide out of the curve. For a banked curve withfriction, a frictional force acts on a fast car to oppose the tendencyto slide out of the curve; the force is directed down the bank (in thedirection water would drain). Consider a circular curve of radiusR =200 m and bank angle u, where the coefficient of static frictionbetween tires and pavement is ms. A car (without negative lift) isdriven around the curve . (a) Find an expressionfor the car speed vmax that puts the car on the verge of slidingout. (b) On the same graph, plot vmax versus angle u for the range 0to 50, first for ms =0.60 (dry pavement) and then forms =0.050 (wet or icy pavement). In kilometers per hour, evaluatevmax for a bank angle of u =10 and for (c) ms 0.60 and (d) ms 0.050. (Now you can see why accidents occur in highway curveswhen icy conditions are not obvious to drivers, who tend to drive atnormal speeds.)
Engineering a highway curve. If a car goes through a curve too
fast, the car tends to slide out of the curve. For a banked curve with
friction, a frictional force acts on a fast car to oppose the tendency
to slide out of the curve; the force is directed down the bank (in the
direction water would drain). Consider a circular curve of radius
R =200 m and bank angle u, where the coefficient of static friction
between tires and pavement is ms. A car (without negative lift) is
driven around the curve . (a) Find an expression
for the car speed vmax that puts the car on the verge of sliding
out. (b) On the same graph, plot vmax versus angle u for the range 0
to 50, first for ms =0.60 (dry pavement) and then for
ms =0.050 (wet or icy pavement). In kilometers per hour, evaluate
vmax for a bank angle of u =10 and for (c) ms 0.60 and (d) ms
0.050. (Now you can see why accidents occur in highway curves
when icy conditions are not obvious to drivers, who tend to drive at
normal speeds.)
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