What is the relationship between initial velocity and tire marks after braking?

In summary, the formula relates the initial velocity of a car in a street with the length of the mark on ground left by the tires when the brakes are set at maximum force, stopping the wheel. A is somewhere between 0 (on ice) and 1 g (ideal conditions, really good rubber), and v=\sqrt{2*.75*32*100}=69\,\mbox{ft/s} or 47 mph.
  • #1
DaTario
1,029
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Does anybody know the empirical formula that relates the initial velocity of a car in a street with the length of the mark on ground left by the tires when the brakes are set at maximum force, stopping the wheel ?
 
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  • #2
[tex]v=\sqrt{2ad}[/tex]
a is somewhere between 0 (on ice) and 1 g (ideal conditions, really good rubber). A g is 32 ft/s/s. So for example if a is .75 g (sorta typical), d = 100 ft,
[tex]v=\sqrt{2*.75*32*100}=69\,\mbox{ft/s}[/tex]
or 47 mph.
 
  • #3
Now I realized that dimensional analysis could have helped...

But is there any simple way to derive this expression ?
 
  • #4
It's just an example of uniformly accelerated motion. Are you familiar with the kinematics of uniform acceleration?
 
  • #5
Ok, I got it now. But the reason it seems to me as a little more envolved problem was the presence of gravity acceleration in the explanation and formula of Mr. Krab. Was it because the friction coeficient can reach some sort of "maximum value" in ideal situations? It still doesn't make sense to me.

But the mention to Torricelli equation has cleared the way a lot.
 
  • #6
DaTario said:
But the reason it seems to me as a little more envolved problem was the presence of gravity acceleration in the explanation and formula of Mr. Krab.
The force of friction depends on the coefficient of friction and the normal force. The normal force is just the weight = mg. Thus the acceleration [itex]a = F/m = ( \mu m g)/ m = \mu g[/itex].
 
  • #7
Ok. I am satisfied with the answer.
Just another complemetary question regarding something Mr. Krab has said:

[tex] v = \sqrt{2 a g} [/tex]

a is somewhere between 0 (on ice) and 1 g (ideal conditions, really good rubber). A g is 32 ft/s/s.

Is it true that [itex] \mu [/itex] is 1 in the friction between tires' rubber and the asphalt ?
 
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  • #8
DaTario said:
Is it true that [tex] \mu [\itex] is 1 in the friction between tires' rubber and the asphalt ?

Yes, it is about 1-1.2 for good tires on hot asphalt. It's quite a bit less (~0.6) if the wheels are locked.
 
  • #9
Thank you so much...
But friction coeficient can be much larger than that for other pairs of materials isn't it?
 
  • #10
Well, racing tires can generate quite a bit more friction (as can regular tires on special surfaces), but [tex]\mu[/tex] still won't go much over 2 or 3. For most pairs of materials, it is less than 1.

Also note that there are different types of friction, and the one being discussed here (Coulomb friction) is pretty limited. I'm only talking about cases where [tex]F_{\rm{max}}= \mu N[/tex] is a reasonable approximation. It's pushing it for street car tires, and not very good at all for certain types of racing tires.
 

What causes tires to leave marks after braking?

When you apply the brakes on your vehicle, the friction between the tires and the road surface causes the tires to grip and slow down. This friction also causes the tires to heat up and create a thin layer of melted rubber on the surface of the tire, which is what leaves the marks.

Are tire marks after braking dangerous?

In most cases, no. The marks left by tires after braking are usually just a normal result of the friction between the tires and the road. However, if you notice excessive or prolonged tire marks, it could indicate a problem with your tires or brakes and should be checked by a professional.

Do tire marks after braking affect tire lifespan?

Tire marks after braking do not significantly affect the lifespan of your tires. However, if you frequently engage in aggressive or sudden braking, it can cause excessive wear and tear on your tires, leading to a shorter lifespan.

How can I prevent tire marks after braking?

Tire marks after braking are a natural result of driving and cannot be completely prevented. However, you can minimize them by avoiding sudden or aggressive braking and maintaining your tires properly. Good tire maintenance includes regular rotation, balancing, and checking for proper tire pressure.

Do different types of tires leave different marks after braking?

Yes, different types of tires can leave different marks after braking. For example, performance tires with a softer rubber compound may leave more noticeable marks compared to all-season tires with a harder rubber compound. Additionally, the tread pattern on the tires can also affect the appearance of the marks.

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