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I am a high school student and I am very confused in a topic which involves "WALKING" and it is majorly related to friction,

THIS IMAGE INVOLVES A QUESTION ON WALKING OVER ICE

This is a question from a very famous book called "Concepts of Physics" and all the questions given in this book are very conceptual without any wrong answer and the answer to this question{ which you are seeing in the image} is that if we take small steps it will ensure us to manage with the smaller friction, I searched it everywhere to find a satisfactory explanation that how it ensure smaller friction but I didn't find any correct explanation,

I think because when I just starts walking and take larger steps, my front foot experiences a larger forward force(I just feel it but I don't know why it is) so to balance it larger friction will be required, but if I take small steps my front leg experiences less forward force from my muscles so in order to balance i.e to prevent it from slipping less frictional force is required, I seriously don't know why it is? if My explanation is correct, I want to know how it is happening that my muscles push more forward to my front leg when I take larger steps? If my explanation is wrong, then what is the correct explanation? And then why do we feel this?

Most people finds a critical angle for this and says that if the angle increase beyond it then the person would slip, but trust me it is not that easy to find it mathematically, they all are doing it wrongly, as it involves our muscles too. By the way I don't want any mathematically proven answer because I think they all are wrong. I just need a theoretical explanation for the questions that I asked.

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Anytime you push off the ground to take a step forward, it's the frictional force on your rear foot that allows you to do so. The contact between your foot and the ground will determine how hard you can push - based on the coefficient of friction and the normal force, there is some upper limit of force which friction can provide. If you try to push off harder, friction can't fully oppose the force of your foot pushing backwards, so your foot will slip.

When you take small steps, you push off lightly, lowering the amount of force exerted through your back foot, as well as the opposing force of friction that pushes back. If you took large steps, your rear foot would exert a large force, and friction might not be able to provide a force that large, which would result in your foot slipping. In this sense, taking small steps decreases the frictional force exerted, keeping it under the limit where slipping would occur.

I'll also note the difference between static and dynamic friction. When your foot starts to slip, it is governed by dynamic friction rather than static friction, which is always less than static friction. In this senes, taking small steps without slipping can provide more friction than you'd get by slipping while taking large steps.

Overall, the question seems very poorly worded to me. Taking smaller or larger steps certainly does not affect the normal force. I'd also interpret "larger friction" and "smaller friction" to refer to the coefficient of friction, which is also unchanged by the step size. If we take it to mean "larger frictional force" or "smaller frictional force", the question is still unclear. Smaller steps will reduce the amount of force supplied by friction, if both step sizes are non-slipping. But if the large step size does slip, smaller steps can result in a larger frictional force, due to the difference between dynamic and static friction. So, the answer will depend on if the large step slips or not - if it does, the small step may provide a larger frictional force; if it does not, the small step provides a smaller frictional force.

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  • $\begingroup$ Yes, the main problem here is that the question is very poorly worded! That "famous book" is full of poorly-worded questions. $\endgroup$
    – Bill N
    Oct 27 '20 at 15:17
  • $\begingroup$ The question would be fine if choices a and c added in the word "required". i.e. "larger required friction" and ,"smaller required friction". Then choice c would be correct, as smaller steps would require a smaller friction force to be accomplished. $\endgroup$ Oct 27 '20 at 15:19
  • $\begingroup$ @BioPhysicist But compared to what? Suppose we take a small step that's right on the cusp of slipping, pushing off with the limit of static friction. Compare that to a big step that does slip, which provides a frictional force equal to the limit of dynamic friction. The big step requires a smaller frictional force than the small step. A small step does not necessarily require a smaller frictional force than a big one, if the big one slips. A small step may have a larger or smaller frictional force, depending on exactly what it's compared to. $\endgroup$ Oct 27 '20 at 15:24
  • $\begingroup$ @NuclearHoagie I think we are both not in agreement to what we mean by a the size of a step. To me a "big step" is one that requires a large acceleration. If you are trying to achieve a larger acceleration, then you will require a larger frictional force to achieve that acceleration. Of course one can perform large steps slowly and small steps quickly, so my interpretation isn't perfect. But with this a large step (larger acceleration) would require a larger frictional force than a smaller one. So we would want to take smaller steps so as to not exceed the maximum limit and slip. $\endgroup$ Oct 27 '20 at 15:34
  • $\begingroup$ @BioPhysicist Completely agree that "step size" is ill-defined here, and I think we're both right under different interpretations. There's a lot that could be improved in both the question and the answers. $\endgroup$ Oct 27 '20 at 15:55
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(Because smaller steps mean more weight acting directly above the foot causing higher normal and larger friction.? depending on walking motion?) Also larger steps means higher component of force acting parrallel to direction of movement (pushing motion) meaning more chance friction reaches mu* reaction causing u too slip

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