A car is traveling on a banked curve as shown in the figure below. The radius of curvature of the road is R, the banking angle is 0, and the coefficient of static friction is μs.nxRAny(a) Determine the range of speeds the car can have without slipping up or down the road. (Use any variable or symbol stated above along with the following as necessary: g. Note that the subscript ofVmin=Vmax=(b) Find the minimum value for μ such that the minimum speed is zero. (Use the following as necessary: R, 0, and g.)μs =μsis lowercase.)

Answered: A car is traveling on a banked curve as…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section: Chapter Questions

Problem 62A

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Modem roller coasters have vertical loops like the one shown here. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. (a) What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g ? (b) How high above the top of the loop must the roller coaster start from rest, assuming negligible friction? (c) If it actually starts 5.00 m higher than your answer to (b), how much energy did it lose to friction? Its mass is 1.50103kg .
A banked highway is designed for traffic moving at 90.0 km/h. The radius of the curve is 310 m. What is the angle of banking of the highway?
A space station, in the form of a wheel 120 m in diameter, rotates to provide an artificial gravity of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of the wheels rotation in revolutions per minute that will produce this effect.
(a) What is the radius of a bobsled turn banked at 75.0and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?
What is the ideal speed to take a 100.0-m-radius curve banked at a 20.0angle?
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) A 22.0-kg child is riding a playground merry-go-round that is rotating at 40.0 rev/mm. What centripetal force is exerted if he is 1.25 m from its center? (b) What centripetal force is exerted if the merry-go-round rotates at 3.00 rev/min and he Is 8.00 m from its center? (c) Compare each force with his weight.
In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is an inertial force sensed and used by the riders to explain events in the rotating frame of reference of the barrel. Explain in an inertial frame of reference (Earth is nearly one) what pins the riders to the wall, and identify all forces acting on them.
If a car takes a banked curve at less than the ideal speed, friction is needed to keep It from sliding toward the inside of the curve (a problem on icy mountain roads). (a) Calculate the ideal speed to take a 100.0 m radius curve banked at 15.0. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
A 30.O-g ball at the end of a stung is swung in a vertical circle with a radius of 25.0 m. The rotational velocity Is 200.0 cm/s. Find the tension in the string: (a) at the top of the circle, (b) at the bottom of the circle, and (c) at a distance of 12.5 cm from the center of the circle (r=12.5cm).
An office door is given a sharp push and swings open against a pneumatic device that slows the door down and then reverses its motion. At the moment the door is open the widest, (a) does the doorknob have a centripetal acceleration? (b) Does it have a tangential acceleration?
Suppose a mass is moving in a circular path on a frictionless table as shown below. In Earth’s frame of reference, there is no centrifugal force pulling the mass away from the center of rotation, yet there is a force stretching the siring attaching the mass to the nail. Using concepts related to centripetal force and Newton’s third law; explain that force stretches the string, identifying its physical origin.

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