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 50 m, and the recommended speed is 40 km/hr. At what angle should the curve be banked?

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 50 m, and the recommended speed is 40 km/hr. At what angle should the curve be banked?

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 7OQ: A door in a hospital has a pneumatic closer that pulls the door shut such that the doorknob moves...

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A door in a hospital has a pneumatic closer that pulls the door shut such that the doorknob moves with constant speed over most of its path. In this part of its motion, (a) does the doorknob experience a centripetal acceleration? (b) Does it experience a tangential acceleration?
A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown in Figure P5.59. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle θ that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (b) What If ? Repeat the problem, this time taking the period of the circle’s rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem. Figure P5.59
Engineers are designing a curved section of a highway to fit into a specific area. The curve has radius 121 m and is banked at an angle such that a car can travel around the curve at 28.7 m/s and stay on the road without the aid of a frictional force. Calculate the required banking angle (as measured above the horizontal). 0 =
An engineer wants to design an oval racetrack such that 3.20 x 10° lb racecars can round the exactly 1000 ft radius turns at 105 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h. Find the banking angle 0 necessary for the race cars to navigate the turns at 105 mi/h without the aid of friction. This banking and radius are very close to the actual turn data at Daytona International Speedway, where 3.20 × 10³ lb stock cars travel around the turns at about 175 mi/h. What additional radial force is necessary to prevent a race car from drifting on the curve at 175 mi/h? radial force: N
An engineer wants to design an oval racetrack such that 3.20 x 10° lb racecars can round the exactly 1000 ft radius turns at 105 mi/h without the aid of friction. She estimates that the cars will round the turns at a maximum of 175 mi/h. Find the banking angle 0 necessary for the race cars to navigate the turns at 105 mi/h without the aid of friction. This banking and radius are very close to the actual turn data at Daytona International Speedway, where 3.20 x 10 lb stock cars travel around the turns at about 175 mi/h. What additional radial force is necessary to prevent a race car from drifting on the curve at 175 mi/h? radial force:
A highway curve has a radius of 300m. At what angle (in degrees) should it be banked for a traffic speed of 100km/hr?
When a fighter pilot makes a very quick turn, he experiences a centripetal acceleration. When this acceleration is greater than about 4 × g the pilot will usually lose consciousness (“black out”). Consider a pilot flying at a speed of 950 m/s who wants to make a very sharp turn. What is the minimum radius of curvature that he can take without blacking out?
What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the ms between tires and track is 0.32?
A 10.7 kN car travelling at 13.4 m/s attempts to round an unbanked curve with a radius of 70 m. What force of friction is required to keep the car on its circular path?
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?
Medical testing has established that the maximum acceleration a pilot can be subjected to without losing consciousness is approximately 5.00g. A pilot can avoid “blackout” at accelerations up to approximately 9.00g by wearing special “g-suits” that help keep blood pressure in the brain at a sufficient level. What is the minimum safe radius of curvature for an unprotected pilot flying an F-15 in a horizontal circular loop at 658 km/h?
Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway.When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding.When the highway is wet, however, the frictional force may be negligible, and banking is then essential. a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R = 190 m. (It is a normal car, rather than a race car, which means that any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle u prevents sliding?