Center-of-mass work stopping distance

In summary, the question is asking for the distance traveled by a 1000kg car moving at 90km/h when the driver applies maximum force to the brakes, causing the car to skid to a stop. The coefficient of kinetic friction between the tires and the road is 0.80. The solution to this problem involves setting up a vector equation where the net force is equal to the force of kinetic friction. The normal force and the force of gravity cancel each other out, leaving only the friction force. The specific setup is explained in the book, and the question only requires an explanation for this setup.
  • #1
epicbattle
10
0

Homework Statement



To avoid an accident, the driver of a 1000kg car moving 90km/h on a straight horizontal road steps o the brakes with maximum force. The car skids to a stop. The coefficient of kinetic friction between tires and road is 0.80. How far does the car travel during the skid?

Homework Equations



Integral of F(net)*dL from 1 to 2 = delta K (transfered)

This is actually solved in my book, but I don't understand how they set it up.
They set it up like:
F(net) = F(n) +mg + F(k) = F(k)

where n is normal force and F(k) is force of kinetic friction.

Why do they set it up so the forces are equal to F(k)?

It is unnecessary to solve. Just an explanation for the setup is what I am looking for. Thank you very much.
 
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  • #2
epicbattle said:
F(net) = F(n) +mg + F(k) = F(k)
I assume that this is a vector equation. F(n) acts upward and is equal and opposite to mg which acts downward. Those two forces cancel, leaving only the friction force.
 
  • #3
...I feel silly. Thank you very much.
 

1. What is center-of-mass work stopping distance?

Center-of-mass work stopping distance is the distance required for an object to come to a complete stop after applying a braking force. It takes into account the mass and velocity of the object, as well as the force applied to stop it.

2. How is center-of-mass work stopping distance calculated?

The formula for calculating center-of-mass work stopping distance is: d = (mv^2)/(2μF), where d is the stopping distance, m is the mass of the object, v is the initial velocity, μ is the coefficient of friction, and F is the braking force.

3. What factors affect the center-of-mass work stopping distance?

The center-of-mass work stopping distance is affected by the mass and velocity of the object, the coefficient of friction between the object and the surface it is traveling on, and the amount of braking force applied.

4. How does the center-of-mass work stopping distance relate to road safety?

The center-of-mass work stopping distance is an important factor to consider in road safety as it helps determine the distance required for a vehicle to come to a complete stop. It is influenced by various factors such as the condition of the road, the vehicle's speed, and the brakes' effectiveness. Understanding and calculating the center-of-mass work stopping distance can help drivers make informed decisions and prevent accidents.

5. Can center-of-mass work stopping distance be reduced?

Yes, center-of-mass work stopping distance can be reduced by decreasing the mass or velocity of the object, increasing the coefficient of friction, and applying a greater braking force. This is why it is important to regularly maintain and check your vehicle's brakes, as well as follow speed limits and road safety regulations.

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