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

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The minimum stopping distance for a car traveling at speed 'V' can be calculated using the formula '(v^2)/(2Mg)', where 'M' represents the coefficient of static friction. To derive this, one must apply the conservation of energy principle, equating the car's kinetic energy to the work done by the stopping force, which is influenced by static friction. It's important to note that static friction is used because the tires are not skidding; if they were, kinetic friction would apply, resulting in a longer stopping distance. The discussion emphasizes understanding the relationship between kinetic energy, stopping force, and distance to solve the problem effectively. This approach highlights the significance of energy conservation in calculating stopping distances.
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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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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).
 
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 \mu_sN = \mu_smg

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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Man, I guess I am just dumb but I couldn't figure it out...
 
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
 

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