# Breaking force over set distance.

1. Oct 19, 2011

### fwFAWFSERG

Hey guys, I have been having trouble trying to reason out in relation to real life application.

Problem:
Two vehicles (1,2) are travelling at 60mph approaching a red light 300 meters ahead. First let us state that both vehicles have the same starting & ending points, as well as the same final & initial velocities.

Vehicle A braked to 45mph relatively early (300m-250m) and coasted a majority of the way, braking @ the final stretch (100m-0m).

Vehicle B coasted relatively early (300m-150m) and braked in one application to a stop (150m-0m).

Question?
-Does the wear on the brakes differ, since both applied a braking force to decelerate from 60mph-0mph.
-Is the difference in friction negligible between 60mph vs. 40mph? (Car B and car A have the same friction/stopping power exerted upon them because they travel the same distance, at speeds relatively similar?)
-This may boil down to is the rate of deceleration/distance proportional to velocity ?

Thanks!

Last edited: Oct 19, 2011
2. Oct 19, 2011

### dacruick

Intuition tells me that the wear and tear on the breaks must differ. I don't know what units wear and tear are measured in so it will be hard for me to quantify anything.

An analogous situation is speeding up in a car. Lets say two cars have identical final velocities and initial velocities. But one car speeds up at 'x' mphs while the other one speeds up at '3x' mph. One of the cars will have used more gas than the other right? There is no way to tell which car used more gas until you can find out the acceleration that yields optimal power output per unit volume of fuel. So basically unless you can find the variable "wear and tear per unit torque per second" for breaks then you wont be able to tell.

3. Oct 19, 2011

### fwFAWFSERG

What about simply from a energy perspective, does friction/deceleration differ in aiding the braking of the vehicle depending on which speed the vehicle is coasting at (longer distance coasting @ higher speed vs shorter distance @ slower speed).

4. Oct 19, 2011

### Naty1

The flaw in this "real life" logic is that "coasting" most of the distance disippates energy (speed) via rolling friction and air resistance before the brakes are applied.

It is always more 'efficient' to coast, slow down, for as long a distance as possible to utilize
the momentum of the car instead of the gas pedal...and use friction to slow the vehicle instead of the brakes.

5. Oct 19, 2011

### fwFAWFSERG

"The flaw in this "real life" logic is that "coasting" most of the distance disippates energy (speed) via rolling friction and air resistance before the brakes are applied. "

Since you are travelling the same total distance, is there a difference between coasting at a lower speed vs a higher speed. Will you generally endure the same rolling friction and air resistance?

6. Oct 19, 2011

### dacruick

Why analyse coasting friction at all? The OP's question is about breaking. The wear and tear on breaks due to rolling is either 0 or negligible in comparison to breaking.

7. Oct 19, 2011

### dacruick

This doesn't have anything to do with the question.
The internal friction should be negligible between 40mph and 60mph, but the wind resistance will not be.

8. Oct 20, 2011

### Lsos

If you apply the brakes in one go, then they will heat up more than if you spread it out over two times. That might have an impact on wear and tear and how much friction they can supply...whether positive or negative. Besides that, the brakes in both instances dissipate the same energy except for rolling and air resistance.

Air resistance rises with speed squared, so the car that braked in one go will have less braking to do. The rolling resistance I think is more or less the same no matter how fast you go.

Last edited: Oct 20, 2011