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Ice - smaller steps vs longer steps


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A question in a very famous physics book in my region is as follows:

While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure:

a) larger friction

b) smaller friction

c) larger normal force

d) smaller normal force

This is a single correct multiple choice question.

Contrary to common idea, which is that smaller steps would give you more friction, the book states the opposite, smaller steps would give smaller friction!?

So as per my reasoning, in both the cases, the normal force would be the same, equal to mg, where m is the mass of the person, to maintain vertical equilibrium, so options 3 & 4 are incorrect.

Now while taking smaller steps, the impending motion of either of the person's feet relative to the ice is very low, as compared to the impending motion of the feet relative to ice in the case of larger steps, which should be more, so that gives lesser friction in smaller steps( less than the limiting friction), giving the 2nd option as correct.

Is my reasoning correct?

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The normal force is going to average mg in either case, but I would expect fluctuate more with large steps, so be lowest at some points with larger steps.

Lateral forces would generally peak with larger steps.

So smaller steps should allow you to maintain grip, effects of walking technique, including timing maximum normal force with maximum lateral force, notwithstanding.

Edited by J.C.MacSwell
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