A flat (unbanked) curve on a highway has a radius of 220 m. A car successfully rounds the curve at a speed of but is on the verge of skidding out. (a) find the coefficient of friction necessary to keep the car on the road (b) If the coefficient of static friction between the car’s tires and the road surface were reduced by a factor of 2, with what maximum speed could the car round the curve? (b) Suppose the coefficient of friction were increased by a factor of 2; what would be the maximum speed?

A flat (unbanked) curve on a highway has a radius of 220 m. A car successfully rounds the curve at a speed of but is on the verge of skidding out. (a) find the coefficient of friction necessary to keep the car on the road (b) If the coefficient of static friction between the car’s tires and the road surface were reduced by a factor of 2, with what maximum speed could the car round the curve? (b) Suppose the coefficient of friction were increased by a factor of 2; what would be the maximum speed?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 40P

See similar textbooks

Similar questions

Problem 5: A car negotiates an unbanked 85.2 m radius curve at 19.9 m/s. Calculate the minimum coeficient of friction needed to negotiate the curve. Hg = || sin() cotan() atan() cosh() cos() asin() acotan() tanh() O Degrees tan() ♫ acos() E sinh() cotanh() Radians 7 ^^^ 4 1 1 + 0 VO BACKSPACE * ∞02 - 8 9 5 63 DEL HOME END CLEAR
A bank curve on a highway is designed for traffic to move at 60km/hr. The radius of thecurve is 200m. If traffic was moving slower than the designed speed due to rain, at 40km/hr,what must be the minimum coefficient of friction between the tires and the road that would allow the car to stay on the road without sliding? Is this static of kinetic friction?
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 = 180 m and bank angle 8, where the coefficient of static friction between tires and pavement is µs. 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, 0, and us. Evaluate Vmax for a bank angle of = 10° and for (a) μ = 0.51 (dry pavement) and (b) µs = 0.050 (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.) (a) Number i 36.5 (a) Units R m/s^2 EN FN 8 FNr Car
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 = 190 m and bank angle θ, where the coefficient of static friction between tires and pavement is μs. 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, θ, and μs. Evaluate vmax for a bank angle of θ = 12° and for (a) μs = 0.58 (dry pavement) and (b) μs = 0.044 (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.)
An automobile moves on a level horizontal road in a circle of radius 50 m. The coefficient of static friction between tires and road is 0.50. (a) Calculate the maximum speed with which this car can round this curve. Now, suppose the road is covered with ice, there is no friction. Instead, the road is banked. (b) Calculate the angle the road must be banked at in order to make the car round the curve with the same maximum speed.
In a grand prix race of mass m= 600 kg as it travels on a fast track on a circular arc of radius r = 100 m because of the shape of the car and the wings on it. The passing air exerts a negative lift FL downward on the car. If the coefficient of static friction between the tire and the track is 0.75 and if the car is on the verge of sliding out of the turn when its speed is 28.6 m/s, what is the magnitude of the negative lift acting downward on the car?
If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). Part (a) Calculate the minimum speed, in meters per second, required to take a 88 m radius curve banked at 11° so that you don't slide inwards, assuming there is no friction. Part (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 18 km/h?
(a) If the coefficient of kinetic friction between tires and dry pavement is 0.80, what is the shortest distance in which you can stop a car by locking the brakes when the car is traveling at 28.7 m/s (about 65 mi/h)? (b) On wet pavement the coefficient of kinetic friction may be only 0.25. How fast should you drive on wet pavement to be able to stop in the same distance as in part (a)? (Note: Locking the brakes is not the safest way to stop.)
A vehicle drives around a flat circular corner with a radius of 105m. If the maximum coefficient of static friction between the wheels and pavement is 0.90, then what is the maximum speed that the car can maintain without skidding?
A freeway off-ramp is a quarter-circle of roadway of radius R = 50 m, as shown in the two figures below. (a) What is the ideal banking angle μ of a section of this road, if the speed of the cars on it is v = 15m/s? At this ideal angle no friction is required for the cars to keep from slipping off the road. (b) What minimum coefficient of friction ?s is necessary so that a car at rest on this section will not slip sideways? (c) For the ?s found in part (b), what is the maximum speed a car can drive on this section without slipping sideways?
Is it safe to drive your 1600-kg car at speed 27 m/s around a level highway curve of radius 150 m if the effective coefficient of static friction between the car and the road is 0.40?
How large must the coefficient of static friction be between the tires and the road , if a car is to round a level curve of radius 130 m at a speed of 114 km /h ?