• Support PF! Buy your school textbooks, materials and every day products Here!

Maximum distance the car accelerates in a circle without skidding

  • #1
890
38

Homework Statement


upload_2017-7-20_20-27-10.png


Homework Equations




The Attempt at a Solution


At distance s, the speed of the car is v.
$$ v^2 = 2wτs$$
$$\frac { mv^2} R ≤ kmg$$
Let's denote the maximum distance covered without sliding is smax.
$$\frac { m2wτsmax} R = kmg$$
$$ smax = \frac {kgR} {2wτ}$$

Is this correct so far?
 

Answers and Replies

  • #2
cnh1995
Homework Helper
Gold Member
3,375
1,117
I think you have missed some syntax in your LaTex formatting.
 
  • #3
ehild
Homework Helper
15,492
1,874
Did you mean so?

Homework Statement


View attachment 207523

Homework Equations




The Attempt at a Solution


At distance s, the speed of the car is v.
$$ v^2 = 2w_τ s$$
$$\frac { mv^2} {R} ≤ kmg$$
Let's denote the maximum distance covered without sliding is ##s_{max}##.
$$\frac { m2w_τ s_{max} }{R} = kmg$$
$$ s_{max} = \frac {kgR} {2w_τ}$$

Is this correct so far?
It is correct.
 
Last edited:
  • Like
Likes scottdave
  • #4
scottdave
Science Advisor
Homework Helper
Insights Author
1,777
743
Did you mean so?
It is correct.
But should you also consider the tangential acceleration and take the vector sum of that and the centripetal acceleration, when calculating the horizontal force on the car?
 
  • Like
Likes haruspex
  • #5
272
52
I agree with @scottdave; if we assume that the tangential acceleration is due to the cars engine (and not, say, someone pushing the car) then the tangential acceleration must also be supplied by the frictional force, and so @Pushoam, your inequality is not quite right.
 
  • Like
Likes scottdave
  • #6
ehild
Homework Helper
15,492
1,874
  • #7
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,454
5,406
There is a mistake in the question. It should provide the static friction coefficient, not that of "sliding" (kinetic) friction.
 
  • Like
Likes scottdave and Chestermiller
  • #8
890
38
Did you mean so?
Yes, thanks for it.

But should you also consider the tangential acceleration and take the vector sum of that and the centripetal acceleration, when calculating the horizontal force on the car?
if we assume that the tangential acceleration is due to the cars engine (and not, say, someone pushing the car) then the tangential acceleration must also be supplied by the frictional force, and so @Pushoam, your inequality is not quite right.
Earlier, I had seen that in a uniform circular motion, when there is no force except friction acts on the body, the friction force provides the centripetal acceleration.

Here, you say that there is a component of friction in centripetal direction providing centripetal acceleration and another component in tangential direction.
But, why should one component of friction act in tangential direction?
It is not said in the question that the friction force provides tangential acceleration.

There is a mistake in the question. It should provide the static friction coefficient, not that of "sliding" (kinetic) friction.
We are going to write the eqn. of motion when the body is moving, so,the question should provide kinetic friction. Isn't it so?
 
  • #9
scottdave
Science Advisor
Homework Helper
Insights Author
1,777
743
Car tires work by maintaining static friction with the pavement for the small patch of tire in contact with the road. If there is no friction, or if you are sliding then the tires are skidding. So yes the friction is causing the car to acelerate.
 
  • #10
890
38
So yes the friction is causing the car to acelerate.
The friction is causing the car to have centripetal acceleration. This I understood.
Do you mean that the friction is causing the car to have tangential acceleration, too?
And this tangential acceleration is wτ.
 
  • #11
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,454
5,406
The friction is causing the car to have centripetal acceleration. This I understood.
Do you mean that the friction is causing the car to have tangential acceleration, too?
And this tangential acceleration is wτ.
The friction (static here) is providing the net acceleration, so both the centripetal and the tangential.
Static friction acts to oppose commencement of relative motion of the surfaces in contact; kinetic friction opposes actual relative motion.
Consequently, if the friction were kinetic it would be antiparallel to the relative velocity, so subsequent motion would be in a straight line. Kinetic friction will not get you round a bend.
 
  • Like
Likes Pushoam
  • #12
890
38
The friction (static here) is providing the net acceleration, so both the centripetal and the tangential.
How do we get to know this ?
How will I find out in which case friction provides only centripetal acceleration and in which case it provides both centripetal and tangential accelerations?
 
  • #13
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,454
5,406
How do we get to know this ?
How will I find out in which case friction provides only centripetal acceleration and in which case it provides both centripetal and tangential accelerations?
Friction is the only horizontal force acting. ##\Sigma\vec F=m\vec a##, where ##\vec a## is the acceleration of the mass, not just some component of it.
 
  • #14
890
38
Friction is the only horizontal force acting.
Car's engine couldn't provide centripetal acceleration, but, it could provide tangential acceleration. I am asking this because earlier I assumed that car's engine provides tangential acc. and friction provides centripetal acc.

So, if the question doesn't specify that it's car's engine which provides tan. acc. , then, we have to take friction providing tan. acc. Is it so?/
 
  • #15
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,454
5,406
Car's engine couldn't provide centripetal acceleration, but, it could provide tangential acceleration.
The car's engine is not in contact with the road. The car only has acceleration in consequence of external forces acting on it, and those all come via the tyre/road contact, gravity and air resistance. Without friction between tyre and road, the engine won't get you anywhere.
 
  • #16
890
38
The car only has acceleration in consequence of external forces acting on it, and those all come via the tyre/road contact, gravity and air resistance.
If all of the accelerations come from the tyre/road contact, gravity and air resistance, then why do we need an engine?
 
  • #17
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,454
5,406
  • Like
Likes Pushoam

Related Threads on Maximum distance the car accelerates in a circle without skidding

  • Last Post
Replies
15
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
3K
Replies
7
Views
851
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
8
Views
2K
Top