Question

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 = 270 m and bank angle $ heta$, where the coefficient of static friction between tires and pavement is $mu_s$. A car (without negative lift) is driven around the curve as shown in Figure (a). Find an expression for the car speed $v_{max}$ that puts the car on the verge of sliding out, in terms of R, $ heta$, and $mu_s$. Evaluate $v_{max}$ for a bank angle of $ heta = 12^circ$ and for (a) $mu_s = 0.50$ (dry pavement) and (b) $mu_s = 0.053$ (wet or icy pavement). (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.)

          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 = 270 m and bank angle $	heta$, where the coefficient of static friction between tires and pavement is $mu_s$. A car (without negative lift) is driven around the curve as shown in Figure (a). Find an expression for the car speed $v_{max}$ that puts the car on the verge of sliding out, in terms of R, $	heta$, and $mu_s$. Evaluate $v_{max}$ for a bank angle of $	heta = 12^circ$ and for (a) $mu_s = 0.50$ (dry pavement) and (b) $mu_s = 0.053$ (wet or icy pavement). (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.)

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 = 270 m and bank angle heta, where the coefficient of static friction between tires and pavement is mus. A car (without negative lift) is driven around the curve as shown in Figure (a). Find an expression for the car speed vmax that puts the car on the verge of sliding out, in terms of R, heta, and mus. Evaluate vmax for a bank angle of heta = 12^circ and for (a) mus = 0.50 (dry pavement) and (b) mus = 0.053 (wet or icy pavement). (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.)

Added by Kyle G.

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