An engineer wants to design a circular racetrack of radius r such that cars of mass m can go around the track at speed V without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle θ of the track, measured from the horizontal. Express the answer in terms of m, r, V, and g. Suppose the race cars actually round the track at a speed w>V. What additional radial force Fr is required to keep the cars on the track at this speed? Express the answer in terms of m, r, V, w, and g.

An engineer wants to design a circular racetrack of radius r such that cars of mass m can go around the track at speed V without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle θ of the track, measured from the horizontal. Express the answer in terms of m, r, V, and g. Suppose the race cars actually round the track at a speed w>V. What additional radial force Fr is required to keep the cars on the track at this speed? Express the answer in terms of m, r, V, w, and g.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 92P: (a) Calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m...

See similar textbooks

Similar questions

In the figure, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 284 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?
A Wall of Death is a carnival show featuring a motorcyclist rides along the vertical wall of the cylinder and performs various stunts while doing so. Given that the radius of the cylinder is 7 m and the static coefficient of friction is 0.8, what is the minimum speed in m/s2 that the motorcyclist must do to prevent the motorcycle to slip from the wall?
A roller-coaster car of mass 309 kg (including passengers) travels around a horizontal curve of radius 35.2 m. Its speed is 21.3 m/s. a. What is the magnitude of the total force exerted on the car by the track? answer in N b. What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. answer in degrees c. If the track is frictionless, then what banking angle would ensure that the car does not slide off of the track? (The banking angle is the angle between the direction normal to the track and the vertical.) answer in degrees
A car travels at a constant speed of 25.5 mi/h (11.4 m/s) on a level circular turn of radius 43.0 m, as shown in the bird's-eye view in figure a. What minimum coefficient of static friction, ?s, between the tires and the roadway will allow the car to make the circular turn without sliding?
A car weighing 10.7 kN and traveling at 13.4 m/s without negative lift attempts to round an unbanked curve with a radius of 61.0 m. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires and the road is 0.350, is the attempt at taking the curve successful?
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 roller-coaster car of mass 330 kg (including passengers) travels around a horizontal curve of radius 44.7 m. Its speed is 10.0 m/s. A) What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. in degrees B) If the track is frictionless, then what banking angle would ensure that the car does not slide off of the track? (The banking angle is the angle between the direction normal to the track and the vertical.) in degrees
A body of masss 3 kg moves in a counterclockwise circular path of radius 9 meters, making one revolution every 8 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component. A. Compute the cetripetal force acting on the body. (_,_) B. Compute the magnitude of that force.
A car is traveling on a curved road with a radius of R=150m. The car is traveling at speed v=22 m/s and has mass m=1450kg. a) What is the net force exerted on the car in Newtons? b) The force on the car is provided by friction. What should the coefficient of friction be between the tires and the road to give the net force found in part a?
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).
A bob of mass m is suspended from a fixed point with a massless string of length L (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle θ. a. What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always making an angle θ from the vertical? b. How long does it take the bob to make one full revolution (one complete trip around the circle)? Express your answer in terms of some or all of the variables m, L, and θ, as well as the free-fall acceleration g.
A pickup truck has a box sitting loose in its bed. The box has a mass of 2.5 kg and the coefficient of static friction between the box and the pickup bed is 0.8. The mass of the truck is 3150 kg and its tires have a coefficient of static friction with the road of 0.9. The truck is currently going through a roundabout with a radius of 30m. How fast can the truck go and not have the box slide on the truck bed? Please answer in m/s.