How Do You Calculate the Minimum Stopping Distance for a Car?

In summary, the conversation discusses finding the minimum stopping distance for a car traveling at a certain speed, using the equation (v^2)/(2Mg). The participants suggest using conservation of energy and the maximum value of static friction. The coefficient of static friction is used because the tires are not skidding. The conversation also touches on the concept of energy and how it relates to stopping force and distance.
  • #1
the_quack
9
0
I that nerd that does those extra problems in the back, the really hard ones, just for the heck of it.

Well, there is one that has me really stumped.

Show that the minimum stopping distance for an auto traveling at speed 'V' is equal to '(v^2)/(2Mg)'.
(I use M for the coefficient of static friction)

Maybe I'm just dumb, but I don't know where to start.

Can someone give me a little hint? It's not actually a homework problem, but I literally go CRAZY if I can't solve a problem I try...

Does it maybe have something to do with the basicx equation of 'V^2=V.^2+2ad'?
 
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  • #2
Well draw a block diagram first off.

There are going to be two energy equations and you need to apply the conservation of energy. One energy is going to be the kinetic energy as the car is moving. The other energy is going to be working in the opposite direction and it is due to kinetic friction (not static).
 
  • #3
the_quack said:
I that nerd that does those extra problems in the back, the really hard ones, just for the heck of it.

Well, there is one that has me really stumped.

Show that the minimum stopping distance for an auto traveling at speed 'V' is equal to '(v^2)/(2Mg)'.
(I use M for the coefficient of static friction)

Maybe I'm just dumb, but I don't know where to start.

Can someone give me a little hint? It's not actually a homework problem, but I literally go CRAZY if I can't solve a problem I try...

Does it maybe have something to do with the basicx equation of 'V^2=V.^2+2ad'?
Use conservation of energy. Kinetic energy lost must be due to force of friction acting over the stopping distance. To find the minimum stopping distance use the maximum value of static friction, which is [itex]\mu_sN = \mu_smg[/itex]

The coefficient of static friction is used because the tires are not skidding. If you skid, it takes longer to stop because the coefficient of kinetic friction is smaller. The question asks for the minimum stopping distance. [The force of static friction does not actually do the work in stopping the car. Rather the forces of kinetic friction on the brakes of the car do this. But those forces are limited by the force of static friction.]

AM
 
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  • #4
Man, I guess I am just dumb but I couldn't figure it out...
 
  • #5
the_quack said:
Man, I guess I am just dumb but I couldn't figure it out...
If you take my suggestion and use an energy approach, you have to understand what energy is: Work = Energy = Force x distance. What is the energy that has to be expended by application of the stopping force? (what is the kinetic energy of the car?)

Just use: kinetic energy of car = stopping force x stopping distance.

AM
 

1. What is the definition of friction?

Friction is the force that resists the relative motion or tendency of motion between two surfaces in contact.

2. How does friction affect the movement of objects?

Friction can either slow down or prevent the movement of objects. It can also cause objects to heat up and wear down over time.

3. What factors affect the amount of friction between two surfaces?

The amount of friction between two surfaces is affected by the roughness of the surfaces, the weight of the objects, and the type of material the surfaces are made of.

4. Can friction ever be beneficial?

Yes, friction can be beneficial in many ways. It allows us to walk without slipping, helps vehicles move on roads, and helps us grip objects.

5. How is friction involved in proof or mathematical equations?

In mathematical equations, friction is often used to calculate the force needed to move an object or the force that is resisting its motion. It is also used to determine the work done by friction in a system.

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