It's an MCQ from the book : Concepts of Physics- by HC Verma

Choose the correct alternative

Q. In order to stop a car in shortest distance on a horizontal road, one should:

a) apply the brakes very hard so that the wheel stops 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.

One can easily rule out the possibility of c) and d), but I am actually confused in parts a) and b). I want to compare cases a) and b) in detail.. Could anyone possibly help!??

Note that answer given in the solutions is option a).

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## Comments

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TopNewestBeautiful problem!!

When you want the car to stop in the shortest possible distance, then it should have the highest possible deceleration. One can notice that both situations a and b result in deceleration of the car. But,in case b, the force of friction on the wheel is much lesser than that in case a.

Now, the above statement is the most important and beautiful to understand..

In case a, the wheels do not rotate. The friction is kinetic in nature, and has a constant value.

In case b, the wheels rotate about that point of the wheel that is in contact with the ground. Notice that this point (which previously had circular motion) is now not moving due the friction force exerted by the ground. This friction force is static, and adjusts its magnitude according to the requirement of stopping the moving point which comes in contact with it. This very frictional force can take any value less than the limiting static frictional force.

So, the force of friction on the wheels is lesser in case of pure rolling (case b) than in case of only translation without rolling(case a)..

You might also say that the static friction may reach the limiting value to give the wheel only rotational motion. But that again reduces to kinetic friction..

To conclude, the friction force on the wheels in case a is generally greater than that is case b.

I hope that my answer is accurate and convincing.. I appreciate that you use Dr. Verma's book which is excellent..

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Thanks dude! I did think a lot away from this. Made a weird explanation for this answer. It may sound awkward. I thought that when we stop rotation of tyres the will start skidding and small rubber particles will wear off (the so called special 'stunt marks' in case of biker performing a stunt). As these partices are circular therefore the tyres would effectively move on them (hard to understand!!). and hence friction will be lesser. But I was stunned after such a clear and simple explanation. Thanks Samarth!!

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Thank you and I must tell you that a lot can be learnt and understood from each problem in H.C.Verma's "Concepts of Physics", and this problem is an illustration to the same.

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Why would you say that c) can be easily ruled out? I believe that's what most modern cars use.

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Your belief is not true! I also used to believe the same thing, but then I googled and found this: Anti Lock Braking System - ABS and how it works. Also as explained in Samarth's comment, the only stopping force is friction so we need to maximize friction. Hence it can be easily seen that in case c) when one pumps and releases the brakes, the wheels stop to rotate suddenly and torque of friction causes them to rotate again and friction oscillates from its maximum value(kinetic friction) to 0 (when tyre comes back in rotation again) and is not the maximum every time. Hence the stopping distance in this case would be even less than case a). But as perfectly stopping the rotation of tyre could result in skidding, Hence case c) is preffered over a) although giving more stopping distance. Hope it explains ur query and sorry for bad english ! typed in a hurry....

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No problem, it makes perfect sense :)

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