Stop to know how to stop
In order to stop a car in shortest distance on a horizontal road, one should
(A) apply the brakes very hard so that the wheels stop rotating
(B) apply the brakes hard enough to just prevent slipping
(C) pump the brakes (press and release)
(D) shut the engine off and not apply brakes
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4 solutions
But in the second case won't rolling friction come into play?
This is a comparison between sliding (a) and rolling(b) friction. Rolling friction has less force than sliding. So (a) should be the correct answer. The reason you do not want this to happen (anti-lock brakes) is because you can easily lose control of the vehicle while sliding, not because you stop quicker.
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If you lose control of the car is you swerve side ways,just turn into the skid.The tradeoff is ,fast enough and the car rolls sideways.A quick judgement of risk is needed. Good example are gokarts ,cools examples are gokarts braking on wood decking.
Hi Math Philic , can you please explain the answer , I answered based on my experience from playing NFS Most Wanted !!
How did you get the correct answer?
@Calvin Lin I have placed the wrong option as the answer. In stead of option (C) option (B) is the correct answer. Please change the answers.
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It depends on whether or not the car is ABS-equipped. If it is, then you should depress the brake quickly but not instantly, so that the ABS system can maintain the fine line between static and sliding friction. If the car is not ABS-equipped, then you have to gauge this fine line by feel, which may involve some pumping of the brakes but preferably you would keep your foot down on the brake with just enough pressure through the entire braking process. So I would consider (B) to be the best answer and not (C).
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The solution involves the subtle difference in the value of coefficient of kinetic friction and coefficient of static friction.
If we examine option (A) then the car would slide and kinetic friction would come into play. While in option (B), i.e. if we prevent the tires to slip then static friction would come into play. Since μ k is less than μ s , therefore kinetic friction is less then static friction. And the deceleration in case (A) will be less than in case (B).
I don't know about the other two option. Why are they not correct?
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@Soumo Mukherjee – Yes, you don't want to slide since μ k < μ s . Pumping the brakes means that the brakes are not being utilized fully through the process compared to keeping the brake pressed down just enough to avoid skidding. As for turning the engine off, most braking systems are power assisted, so cutting power will diminish their performance greatly. I'm not certain what would happen with older cars that don't have power-assisted brakes, but hopefully there aren't too many of those on the road anyway. :)
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@Brian Charlesworth – :D yes there aren't any. I was reading about ABS.
Thanks
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@Soumo Mukherjee – Hahahahaha That looks like a valid experiment. :) Normally dogs love the water; I don't what's going on with these two, (although they look adorable, nevertheless).
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@Brian Charlesworth – Got them in my search result. May be the sea is what they are afraid of. Might have seen water all around for the first time. And then are are waves.
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@Soumo Mukherjee – Good point. Dogs are often scared of breaking waves, and for these little guys any wave must look imposing.
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@Brian Charlesworth – It seems you like dogs. Generalizing that, may be you like all the animals. With help of analogy, you probably also like cats. See this is what math does to you :D
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@Soumo Mukherjee – Haha Yes, in this case the generalization is quite appropriate. :)
P.S.. I've done an analysis of the question you asked in your "Discussing Doubts" post. I hope it's helpful; it was fun to work on.
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@Brian Charlesworth – Thanks. On mercy of my broadband service. I am hoping to spend time discussing math with you. :)
@Soumo Mukherjee – This is indeed nice :) +1
I have updated the answer to B. Can you add an explanation? Thanks!
Yeah , I thought so too !!
How can gaming experience be compared to real one ??? But it seems strange too if you compare it to the fact that the wrong answer does indeed work out fine in NFS Mostwanted , if you pump the brakes , the car takes a sudden halt .
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Well while racing if I have gained high speed and I need to take a turn without losing much speed as well as control I tap the arrows instead of pressing any one constantly. I don't play with gaming console. I use my keyboard. It turns out that that's the way I win most of the races. If NFS did take into account the physics then I would say tapping or pumping helps to control the car. I can't comment about stopping. Moreover In NFS why would anyone need to stop :D
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@Soumo Mukherjee – I just realized my mistake . Just verified my view by playing NFSMW .Pumping the brakes only works when you are making sharp turn but also works if you are already driving at a high speed .
@Soumo Mukherjee – well apart from NFS experience ; I also saw on discovery that pumping break stops the car faster :\ :(
In the show "what happened next ?" I hope that anyone else must also have seen it..
good one...same here
Depends....
If the car is going very fast, (B) would be better. If it is going very slowly, (A) would be better.
With ABS, one should always slam on the brakes.
when it is slipping,it means uk.(miu kinetik) you need to have biggest friction force when it has us.(miu static)
Try using latex ;)
Let's compare cases A , B , C , and D .
A vs. B : If the wheels of the car stop turning, then the force stopping the car is the kinetic friction between the tires and the road. If there is no slipping, then we are maximizing static friction. μ s > μ k , so the static friction case wins: case B .
B vs. C : Pumping the brakes can result in slipping, but even if it doesn't, it still isn't as effective as braking just hard enough to prevent slipping. Therefore B wins again.
B vs. D : Okay, many cars don't even let you turn the engine off in motion. But if it did, the car would continue rolling until you braked (without power brakes, I should add) or it eventually came to a stop (plenty more time than maximum static friction makes). Since B is faster in every case, that is our answer.