Finding the Shortest Stopping Distance for an Automobile Using Kinetic Friction

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AI Thread Summary
The discussion revolves around calculating the shortest stopping distance for an automobile using the coefficient of kinetic friction and velocity. A user seeks guidance on the appropriate equation, noting difficulty in finding one that incorporates velocity without requiring mass. Another participant suggests using the conservation of energy principle, leading to the derived formula for distance as d = (v^2)/(2cg). The conversation highlights confusion over notation, with a clarification that the coefficient should be represented as "µ" instead of "c." The thread concludes with a resolution of the initial misunderstanding regarding the calculations.
Azytzeen
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Hello all. I am currently stuck on a problem,

"If the coefficient of kinetic friction between tires and dry pavement is 'c', what is the shortest distance in which an automobile can be stopped by locking the brakes when traveling at 'v'?
Take the free fall acceleration to be g=9.80."

Notice that 'c' and 'v' are blocked out as I am not looking for people to do the problem for me, as said on the sticky. So I was wondering, what kind of equation should I use? Because I could not find one that includes velocity or others without asking for the mass. I tried to derive some, but the answers are all wrong. So please help. Thanks in advance!
 
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Azytzeen said:
Hello all. I am currently stuck on a problem,

"If the coefficient of kinetic friction between tires and dry pavement is 'c', what is the shortest distance in which an automobile can be stopped by locking the brakes when traveling at 'v'?
Take the free fall acceleration to be g=9.80."

Notice that 'c' and 'v' are blocked out as I am not looking for people to do the problem for me, as said on the sticky. So I was wondering, what kind of equation should I use? Because I could not find one that includes velocity or others without asking for the mass. I tried to derive some, but the answers are all wrong. So please help. Thanks in advance!

Use conservation of energy. Mass "m" will cancel, then solve for distance "d":
{Delta K.E.} = {Work}
(1/2)mv^2 = c(mg)d
d = (v^2)/(2cg)


~~
 
Last edited:
Ohh, I see where my error is now. I kept on getting 88. Thanks for helping me!
 
How did you get 88 (what ?),if you didn't have the value of "c"...?Shouldn't the notation be "µ"...?

Daniel.
 

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