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

In summary, a race-car driver is attempting to navigate a turn at a record-breaking speed of 225km/h. The turn has a 15 degree incline and the car has a mass of 1450kg. The problem is flawed as it does not provide enough information to solve it accurately. The given solution provided in the conversation uses the equations v=sqrt(grtan(angle)) and ac=v^2/r, but these assume that the track is banked for the given speed and angle with zero friction. A possible solution given in the conversation is to ask the instructor to explain how they solved part a and to recommend a book on classical physics for further understanding.
  • #1
zeion
466
1

Homework Statement


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?


Homework Equations



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

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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  • #2
zeion said:
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?
All you need is centripetal force. (Centrifugal force is a "fictitious" force used when analyzing things from an accelerating frame--no need for that here.)

As far as this problem goes, you are not given enough information to solve it. Can you please tell me the textbook this is from and the problem number. (In case I have the textbook.)
 
  • #3
Doc Al said:
As far as this problem goes, you are not given enough information to solve it. Can you please tell me the textbook this is from and the problem number. (In case I have the textbook.)

This is from an independent learning course from the Independent Learning Center in Ontario. It's in Lesson 4 of Unit 1.

What other information do I need to solve it?
 
  • #4
zeion said:
This is from an independent learning course from the Independent Learning Center in Ontario. It's in Lesson 4 of Unit 1.
I don't have that one. This exact problem has cropped up before. The problem is flawed.

What other information do I need to solve it?
Generally a road is banked for a given speed so that a car can make the turn without needing any friction. You are not given any information about the speed for which the curve is designed.
 
  • #5
Can i sue them for giving flawed questions?
 
  • #6
you better read the contents before you go to this question.
firstly, you have to draw a FBD.
a)Fn=Fg/cos15
Fn=14711N
Fc=sin15
Fc=14711*sin15
Fc=3807N
r=Fc/mv^2
r=6.72*10^4m
b) a=Fc/m
a=2.626m/s^2
 
  • #7
wmhcan said:
you better read the contents before you go to this question.
firstly, you have to draw a FBD.
a)Fn=Fg/cos15
Fn=14711N
Fc=sin15
Fc=14711*sin15
Fc=3807N
r=Fc/mv^2
r=6.72*10^4m
On what basis did you calculate r? You don't know the speed for which the track is banked. (You cannot assume that it's banked for the given speed of 225 km/h.)

(And your equation for r is upside down.)
 
  • #8
ok so i just did that 2 weeks ago, got full marks for it XD.so for a) u use v= sqrt ( g r tan(angle))

v= velocity
g= Earth's gravitational force

v= 225km/h = 62.5 m/s
angle= 15
m= 1450kg

so I'm not going to draw a FBD, you do that yourself, now continueing with a)

v^2= g r tan(angle)
62.5^2=9.8 r tan 15
r=3906.25 / 2.63
r=1485.3m

b) ac = centripetal acceleration

ac= v^2 / r , meh I'm not going to write the rest of the problem to this because i believe you can finish this.
solution = 2.63 m/s^2

c) Fs max = m g sin(angle)

Fs max= magnitude of the force of static friction

solution = 3677.8N

d) (can't make the mu symbol for coefficient of friction >< )

mu s = tan (angle)
mu s = tan 15
mu s = 0.268
you're very welcome, please send me a fruit basket for x-mas =D
 
  • #9
the_morbidus said:
so for a) u use v= sqrt ( g r tan(angle))

v= velocity
g= Earth's gravitational force

v= 225km/h = 62.5 m/s
angle= 15
m= 1450kg

so I'm not going to draw a FBD, you do that yourself, now continueing with a)

v^2= g r tan(angle)
62.5^2=9.8 r tan 15
r=3906.25 / 2.63
r=1485.3m
That equation assumes that the track is banked for the given speed and angle and zero friction.

Sorry, no fruit basket.
 
  • #10
darn it i really wanted that fruit basket XD .

well i say we should complain to the teachers, after all I am only the poor little student that is using the equations that are given in the book >.> .

but i did get 3/3 marks for that question, therefore i assume it was meant to be a flawed example for the simple purpose of teaching the student?
 
  • #11
the_morbidus said:
but i did get 3/3 marks for that question, therefore i assume it was meant to be a flawed example for the simple purpose of teaching the student?
Ask your instructor to explain how he did part a. (Do you understand how the equation you used is derived?)
 
  • #12
yes i understand how the equation was obtained, but I'm in the process of learning so i might think i know but i might not know at all.

anyways what books on classical physics for around grade 12 and perhaps beyond would you recommend that explain it well and are reasonable to understand??
 
  • #13
the_morbidus said:
yes i understand how the equation was obtained, but I'm in the process of learning so i might think i know but i might not know at all.
How would you derive it? Start with a free body diagram.

anyways what books on classical physics for around grade 12 and perhaps beyond would you recommend that explain it well and are reasonable to understand??
This should be in just about every textbook, so perhaps poking around your library will turn up one to your liking.

Here are some web resources: http://www.batesville.k12.in.us/physics/phynet/mechanics/Circular%20Motion/banked_no_friction.htm" [Broken]
 
Last edited by a moderator:

1. What is the difference between centrifugal and centripetal force?

Centrifugal force is the outward force experienced by an object in a rotating frame of reference, while centripetal force is the inward force that keeps an object moving in a circular path.

2. How do centrifugal and centripetal forces apply to a race car on a banked curve?

Centrifugal force acts on the race car, pushing it away from the center of the curve, while centripetal force (provided by the friction between the tires and the road) keeps the car moving along the curved path.

3. What factors affect the magnitude of centrifugal and centripetal forces in a banked curve?

The speed of the car, the radius of the curve, and the angle of the bank all affect the magnitude of centrifugal and centripetal forces experienced by the car.

4. Can centrifugal and centripetal forces be balanced in a banked curve?

Yes, if the angle of the bank and the speed of the car are properly matched, the two forces can be balanced and the car can maintain a constant speed along the curved path.

5. How do centrifugal and centripetal forces affect the stability of a race car on a banked curve?

Centrifugal force can potentially cause a race car to lose traction and slide off the track, while centripetal force helps to keep the car stable and on the desired path. Proper balance between the two forces is crucial for a race car to maintain stability on a banked curve.

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