Question 4 Question 4.For a car travelling at a certain speed, it is possible to bank a curve at just the right angle so that no frictionis necessary to maintain the car's turning radius.R(a) At what angle B should the curve be banked for a car travelling with speed v? Express your answeras 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 M, what is themaximum speed that will allow the car to complete the turn without sliding?

Answered: For a car travelling at a certain…

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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Question 4

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The car's weight, mg, acts vertically downwards. The road surface applies an upward normal reaction N to the car. The vertical component of the reaction is required to balance the downward weight of the car, so

$N \cos β = m g$

The horizontal component of the reaction is $N \sin β$ which acts towards the center of curvature of the road. This force is equivalent to $\frac{m v^{2}}{R}$

$∴ N \sin β = \frac{m v^{2}}{R}$

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