Stopping Distance: Car F, G, and H

In summary, three cars (F, G, and H) with the same velocity and identical tires slam on the brakes. Car F, the most massive, travels the longest distance to skid to a stop, followed by car G and then car H. This is because the force of friction and energy dissipated are directly proportional to the mass of the car. To find the distance traveled, we can use the equation d = E/F, where E is the energy dissipated and F is the force of friction, which is equal to the coefficient of friction (u or \mu) multiplied by the mass and acceleration due to gravity (mg).
  • #1
Soaring Crane
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Three cars (cars F, G, and H) are moving with the same velocity, and slam on the brakes. The most massive car is F, and the least massive is H. Assuming all 3 cars have identical tires, which car travels the longest distance to skid to a stop?

Will they all travel the same distance in stopping?
If mgh = mv^2/2 for each car:

F – (3mv^2)/2 = 3*mgh h = v^2/2g
G – (2mv^2)/2 = 2mgh h = v^2/2g
H – mv^2 = mgh h = v^2/2g

Thanks.
 
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  • #2
The same tires implies the same coefficient of friction, u or [itex]\mu[/itex].

The force of friction applies, Ffriction = [itex]\mu[/itex]mg, and the energy dissipated is Efriction = Ffriction*d, where d is the distance traveled.

Find dF = dG = dH.
 
  • #3
How do I find the energy of friction to find each car's d?

To find d, it would be E/F?

Thanks again.
 

1. What is stopping distance?

Stopping distance is the distance that a car travels after the brakes are applied until it comes to a complete stop. It includes the distance covered during the driver's reaction time and the braking distance.

2. How is stopping distance calculated?

Stopping distance is calculated by adding the thinking distance (distance covered during the driver's reaction time) and the braking distance (distance covered while the brakes are applied).

3. What factors affect stopping distance?

The factors that affect stopping distance include the speed of the car, the condition of the tires and brakes, the road surface, and the driver's reaction time.

4. How do cars F, G, and H differ in their stopping distance?

Cars F, G, and H may differ in their stopping distance due to various factors such as their weight, tire size and type, braking system efficiency, and overall design and engineering. It is important to note that different models of the same car brand may also have varying stopping distances.

5. How can a driver reduce the stopping distance of their car?

A driver can reduce the stopping distance of their car by maintaining a safe speed, ensuring that their tires and brakes are in good condition, and keeping a safe following distance from other vehicles. It is also important to have quick reaction times and to properly use the brakes when needed.

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