For a car travelling at a certain speed, it is possible to bank a curve at just the right angle so that no friction is necessary to maintain the car's turning radius. B (a) At what angle B should the curve be banked for a car travelling with speed v? Express your answer as a function of v, R, and g (not the normal force). (b) Using your answer from the previous part and assuming a coefficient of friction of µ, what is the maximum speed that will allow the car to complete the turn without sliding?

For a car travelling at a certain speed, it is possible to bank a curve at just the right angle so that no friction is necessary to maintain the car's turning radius. B (a) At what angle B should the curve be banked for a car travelling with speed v? Express your answer as a function of v, R, and g (not the normal force). (b) Using your answer from the previous part and assuming a coefficient of friction of µ, what is the maximum speed that will allow the car to complete the turn without sliding?

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 59P: A single bead can slide with negligible friction on a stiff wire that has been bent into a circular...

See similar textbooks

Similar questions

A turn has a radius of R and is banked at an angle theta so that on a perfectly icy (frictionless) day a car with a speed v will not slip. What is v in terms of R and theta?
If a curve with a radius of 95 m is properly banked for a car traveling 65 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95 km/h ?
A car rounds an unbanked curve of radius 65 m. If the coefficient of static friction between the road and car is 0.70, what is the maximum speed at which the car can traverse the curve without slipping?
A given highway turn has a 105 km/h speed limit and a radius of curvature of 1.4 km a. What banking angle in degrees will prevent cars from sliding off the road, assuming everyone travels at the speed limit and there is no friction present?
A car with a mass of 1000kg travels around a banked curve of radius 40m with a speed of 27m/s. In the absence of friction, what are the values of the horizontal and vertical components of the normal force?
Engineers who design roads typically “bank” (incline) curves in such a way that a car traveling at the recommended speed does not have to rely on friction between its tires and the road in order to round the curve. Suppose the radius of curvature of a road segment is 55 m, and the recommended speed is 45 km/hr. At what angle should the curve be banked?
A car is rounding a flat, unbanked curve with radius R = 200m, a.) If the coefficient of static friction between tires and road is 0.89, what is the maximum speed at which the driver can take the curve without sliding? b.) If the curve is to be banked at 12 degrees, how fast could the car go safely if friction is to be neglected?
A curve in a stretch of highway has radius 512 m. The road is unbanked. The coefficient of static friction between the tires and road is 0.600. a. What is the maximum safe speed that a car can travel around the curve without skidding? answer in m/s b. Which of the following is the correct free-body diagram of the car when it enters the curve at a speed greater than the maximum safe speed? (OPTIONS ATTACHED) c. When the car enters the curve at a speed greater than the maximum safe speed (speed at which the car won’t skid), which of the following statements are correct? The static frictional force is not large enough to keep the car in a circular path. The car skids toward the outside of the curve. The car skids toward the inside of the curve. The static frictional force is large enough to keep the car in a circular path.
A car weighing 10260 N and traveling at 10.6 m/s without negative lift attempts to round an unbanked curve with a radius of 75 m. What is the mass of the car? What magnitude of the frictional force on the tires is required to keep the car on its circular path? If the coefficient of static friction between the tires and the road is 0.5, is the attempt at taking the curve successful? Answer either "yes" or "no" (but without the quotes).?
A point moves with deceleration along the circle of radius R so that at any moment of time its tangential and normal accelerations are equal in moduli. At the initial moment, t =0 the velocity of the point equals . Find: the velocity of the point as a function of time and as a function of the distance covered s.
A car travels around an unbanked curve at 17 m/s. If the static friction coefficient between the tires and the road is 0.45, what is the minimum radius curve that the car can take at this speed without slipping?
A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle.A. Compute the centripetal force acting on the body at time t.⟨, ⟩B. Compute the magnitude of that force. HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation).Then find the position vector r→(t) of the body at time t.Then find its acceleration vector a→(t) at time t.Then use Newton's 2nd law to find the centripetal force F→(t).