Problem 2: Car on the track a car circular track R A car of mass m is driving at constant speed v around a circular track with the radius of curvature R. The track surface is sloped by an angle e as depicted in the diagram with the outer edge of the track being higher than the inner edge. The coefficient of static friction between the track and the car tires is u. The acceleration due to gravity is g. Express all answers in term of some or all of the quantities listed in this note. Neglect any aerodynamic effects and any gyroscopic effects due to spinning wheel s. 111 4 (a) If the car travels at just the right speed vi, it will neither slip up or down the sloped track regardless of the value of μ. That is friction plays no role in preventing slippage at speed vi. Derive an expression for vi. O (b) For speed v> vi, friction prevents the car from slipping up the slope. What is the maximum speed v_max that the car can have before it begins slipping? (c) Choosing the angle to be 90 degree makes for an exciting track where only friction prevents the car from falling (see diagram). In this extreme situation, what is the minimum speed v_min that the car must maintain if it is not too fall? ૪. 90° m
Problem 2: Car on the track a car circular track R A car of mass m is driving at constant speed v around a circular track with the radius of curvature R. The track surface is sloped by an angle e as depicted in the diagram with the outer edge of the track being higher than the inner edge. The coefficient of static friction between the track and the car tires is u. The acceleration due to gravity is g. Express all answers in term of some or all of the quantities listed in this note. Neglect any aerodynamic effects and any gyroscopic effects due to spinning wheel s. 111 4 (a) If the car travels at just the right speed vi, it will neither slip up or down the sloped track regardless of the value of μ. That is friction plays no role in preventing slippage at speed vi. Derive an expression for vi. O (b) For speed v> vi, friction prevents the car from slipping up the slope. What is the maximum speed v_max that the car can have before it begins slipping? (c) Choosing the angle to be 90 degree makes for an exciting track where only friction prevents the car from falling (see diagram). In this extreme situation, what is the minimum speed v_min that the car must maintain if it is not too fall? ૪. 90° m
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Problem 2: Car on the track a
car
R
circular track
A car of mass m is driving at constant speed v around a circular track with the radius of
curvature R. The track surface is sloped by an angle e as depicted in the diagram with the
outer edge of the track being higher than the inner edge. The coefficient of static friction
between the track and the car tires is μ. The acceleration due to gravity is g. Express all
answers in term of some or all of the quantities listed in this note. Neglect any
aerodynamic effects and any gyroscopic effects due to spinning wheel s.
111
(a) If the car travels at just the right speed vi, it will neither slip up or down the sloped
track regardless of the value of μ. That is friction plays no role in preventing
slippage at speed vi. Derive an expression for vi.
O
(b) For speed v> vi, friction prevents the car from slipping up the slope. What is the
maximum speed v_max that the car can have before it begins slipping?
(c) Choosing the angle to be 90 degree makes for an exciting track where only friction
prevents the car from falling (see diagram). In this extreme situation, what is the
minimum speed v_min that the car must maintain if it is not too fall?
90°
m
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