(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A race-car driver is driving her car at a record-breaking speed of 225kh/h. The first turn on the course is banked at 15 degrees, and the car's mass is 1450kg.

a) Calculate the radius of the curvature for this turn

b) Calculate the centripetal acceleration of the car.

c) If the car maintains a circular track around the curve (does not move up or down the bank), what is the magnitude of the force of static friction?

d) What is the coefficient of static friction necessary to ensure the safety of this turn?

2. Relevant equations

vector v^2 = (vector gravity)(radius)(tan incline of bank)

centripetal acceleration = vector v ^2 / radius

3. The attempt at a solution

First of all, I don't really understand centrifugal force. Centripetal force is for when an object has uniform circular motion, right? How is it affected by centrifugal force?

So my basic understanding of this question is, when a car makes a turn it doesn't slide off laterally because of the friction between tires and the road, and if the curve has a bank it would increase force of friction when a car goes on it.

Given:

V = 225km/h = 225000m/h = 62.5m/s

Incline of bank = 15 degrees

M = 1450kg

vector v^2 = (vector gravity)(radius)(tan incline of bank)

So

(radius) = (vector v)^2 / (vector gravity)(tank incline of bank)

(radius) = (62.5m/s)^2 / (9.8m/s^2)(tan15)

(radius) = (3906.25m^2/s^2) / (2.625902086m/s^2)

(radius) = 1487.58m

This is strange because if I divide (62.5m/s)^2 / (9.8m/s^2) first and then multiply it with (tan15) I get 106.80m

So I'm not sure which answer is correct.

I think all the other questions need a correct radius value so I can't go further :/

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# Centrifugal and centripetal force question: race-car and banked curve question

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