Calculating Initial Velocity in a Simple Car Braking Problem

In summary, the problem is to find the initial velocity of a car after locking up the wheels while braking. To solve this, the braking distance is given as 20 feet, the final velocity is 50m/s, the mass of the vehicle is 2000kg, and the coefficient of friction is 0.6. The solution involves calculating the force of friction and using it to find the deceleration rate, which is then used to find the initial velocity. It is also clarified that during braking, the frictional force applied by the road to the car is nearly equal to the static or sliding friction, and not rolling friction.
  • #1
Xeonicus
4
0
The problem is simple, its a matter of finding a car's initial velocity after locking up the wheels while braking. Here is what I know:

The braking distance (skid marks) go for 20 feet, the final velocity is 50m/s, the mass of the vehicle is 2000kg, and the coefficient of friction of the tire and asphalt is 0.6. What is the initial velocity?

Here is how I did it first:
1) force friction = 0.6 * 2000 * 9.8 = 11760N
2) m * a = 2000 * a = -force friction + ( 2000 * -8.5 )
2000 * a = -11760 - 17000
a = 14.38 m/s^2
3) Then I go on to solve for the intial velocity after getting the deceleration.

In step 2, I used -8.5 for a typical deceleration rate of a vehicle when it slams on the brakes. What I'm told though, is that I don't need to add this force for braking and I only need to put in the friction force (0.6 * normal). So I'd just have "m * a = -force friction" and the deceleration would be -5.88 m/s^2. It seems to me though, that a vehicle would deceleration more quickly if the brakes were applied, more so than just slowed down by the force of rolling friction the road applies.

So can anyone clear this up for me? Something to do with internal/external forces?
 
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  • #2
1.) Lock up wheels with brakes = coefficient of sliding friction

2.) Brake as hard as possible without skidding = coefficient of static friction

In an emergency-if you like your car, use #2.
 
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  • #3
"In step 2, I used -8.5 for a typical deceleration rate of a vehicle when it slams on the brakes. What I'm told though, is that I don't need to add this force for braking and I only need to put in the friction force (0.6 * normal). "

I was wondering where that "8.5" came from! The only force causing the car to decelerate IS the friction of the tires sliding on the road.

As long as the wheels are rolling, the road does not supply ANY "rolling friction".
 
  • #4
HallsofIvy said: "As long as the wheels are rolling, the road does not supply ANY "rolling friction"."

If it doesn't when the wheels are rolling, then when does it?

Don't you really mean that since rolling friction is much less than static friction, that during breaking, if the wheels are rolling, the frictional force applied by the road to the car is nearly equal to the static friction?
 
  • #5
jdavel said:
HallsofIvy said: "As long as the wheels are rolling, the road does not supply ANY "rolling friction"."

If it doesn't when the wheels are rolling, then when does it?

Don't you really mean that since rolling friction is much less than static friction, that during breaking, if the wheels are rolling, the frictional force applied by the road to the car is nearly equal to the static friction?

Sorry, this is my fault, my original post said "rolling friction". I should not have
mentioned rolling friction at all. The rolling friction is not a factor in this problem, only the static friction or the sliding friction. I edited it so as not to cause confusion for anyone else. I must have been on crack when I wrote that! -Mike
 
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FAQ: Calculating Initial Velocity in a Simple Car Braking Problem

What is a simple car braking problem?

A simple car braking problem refers to the issue of a car not being able to brake properly or efficiently. This can be caused by various factors such as worn brake pads, low brake fluid, or faulty brake lines.

How do you know if your car has a braking problem?

Some signs of a car braking problem include squealing or grinding noises when braking, a vibrating brake pedal, or a longer stopping distance. If you notice any of these issues, it is important to get your car checked by a mechanic.

What are the common causes of a simple car braking problem?

The most common causes of a simple car braking problem include worn brake pads, low brake fluid, air in the brake lines, and faulty brake calipers or rotors. These issues can be caused by regular wear and tear or lack of proper maintenance.

How can a simple car braking problem be fixed?

The solution to a simple car braking problem depends on the specific issue. In most cases, replacing worn brake pads or adding more brake fluid can fix the problem. However, if the issue is more severe, such as faulty brake lines, it may require professional repair or replacement.

How can a simple car braking problem be prevented?

To prevent a simple car braking problem, it is important to have regular maintenance checks on your vehicle. This includes checking and replacing brake pads, topping off brake fluid, and inspecting brake lines for any damage. It is also recommended to avoid harsh braking and to drive with caution to prolong the life of your brakes.

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