# A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'.

1. Jan 6, 2013

### SAUMYA B

Should the driver apply brakes or turn the car in a circle of radius 'r' to avoid hitting the wall?
This question is in the excercise of circular motion chapter.
In this question I don't uderstand from where to start. Some help would be greatly appreciated.

2. Jan 6, 2013

### PiersNewberry

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

Assume that you can apply the breaks to just before a skidding state and can also turn the car in such a way to maintain the wheels in a just before skidding state, then look at the force vectors working on the car and deduce the one which on average is bigger away from the wall throughout each manoever.

But as car tyres stop much better when going sideways the question doesn't really give a real world answer... you really need a lot more data to give a proper answer

3. Jan 10, 2013

### Andrew Mason

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

You have to determine how the turning distance relates to the stopping distance.

1. What is the force that static friction must apply to the car in order for the car to turn in a circle of radius r? That will give you the maximum value of r (rmax) in terms of friction force and speed.

2. What is the maximum braking force? (assume the car has anti-skid brakes).

3. Calculate the stopping distance, s, if the car brakes. This will be a function of friction force and speed.

4. Compare r with s to see which is the better choice.

[note: You have to assume that the car will not roll if it turns but will either turn or slide depending on the speed and coefficient of static friction].

AM

4. Jan 10, 2013

### Containment

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

It's a trick question the answer is both! Joking of course but unless it's icey doing both would probably actually make the most sense if the driver is really in danger of hitting the wall :)

I would start by trying to figure out how large of a circle the driver would make at their current speed because it seems pretty simple and you'll have 1/2 of the problem understood :)

5. Jan 10, 2013

### Andrew Mason

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

I think the answer will show that it is better not to turn more than a turn of radius 2r.

AM

6. Jan 10, 2013

### jbriggs444

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

Is the car approaching the wall dead-on or is it approaching at an angle?

Are you free to make the assumption that the total force of the tires on the pavement is limited to a fixed maximum (e.g. mg times the coefficient of friction for rubber on road)?

The optimum strategy would seem obvious given that assumption.

7. Jan 11, 2013

### CWatters

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

Write an equation of motion for stopping in a straight line. Rearrange to give equation for the stopping distance r . Substitute to replace the acceleration term with a term based on coefficient of friction eg

Newton says..
f=ma
a=f/m

the definition of coefficient says..
k (coefficient of friction) = ratio of force to normal force = f/mg
rearrange
f/m = k*g
so finally the acceleration term is..

a= k*g

or k = a/g

which shouldn't be too surprising.

Write equation for centripetal force. Make similar substitution to the above. Rearrange to give equation for the radius r

Which r is larger.

8. Jan 12, 2013

### Andrew Mason

Re: A car driver going at some speed 'v' suddenly finds a wide wall at a distance 'r'

Just to add to this point, if the driver does not know whether the distance r is large enough to complete a turn of radius r to avoid the collision, he is better off braking and not turning at all.

AM

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