You can't simply walk, you need to know the physics
When walking on ice, one should take small steps to avoid slipping. Smaller steps help avoid slipping because they result in:
A. Larger friction with the ice.
B. Smaller friction with the ice.
C. A larger normal force.
D. A smaller normal force.
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3 solutions
@Raghav Vaidyanathan I've converted your comment into a solution. If you subscribe to this thread, you will receie notifications about it.
He will want to decrease his horizontal component of force by taking smaller steps, not the friction between his feet and the ice. The reason for this is due to the fact that the maximum static frictional force to prevent him from sliding is fixed by his weight and the coefficient of friction between the ice and his foot . The maximum static frictional force does not change with the angle between his legs and the ice since the normal component is fixed by his weight. However, the horizontal component does change with the angle.
Hence, if he increases his angle by taking larger steps, the horizontal component of force is increased and eventually that will overcome the maximum static frictional force present between his foot and the ice, thus causing him to slide.
So he takes smaller steps in order to reduce the horizontal component.
That is right, I agree with that assessment.
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I would like to add something more.
"Frictional force is self adjusting."
(A) Suppose Billy is trying to move a block along a rough horizontal surface. Billy applies 2 N force, but the block doesn't move. What is the friction?
(B) Then Billy decides to apply a larger force, say 6 N to move the same block ( kept on the same horizontal surface). But the block still doesn't move. What is the friction now?
In both the experiment (A) and (B) the normal force is same. Still the value of friction in case (A) is different from that in (B).
We all agree that smaller steps ensures smaller horizontal component. For equilibrium the horizontal component has to equal the friction. Suppose the maximum static friction is 2 0 N This means if the horizontal component exceeds 2 0 N we will fall. But if the horizontal component is less than 2 0 N , say the horizontal component is 5 N then the friction is also 5 N .
Icy surface have smaller friction. A larger horizontal component is more likely to exceed the value of maximum static friction (on icy surface). To keep the horizontal component smaller than maximum static friction we need to take small steps. And if the horizontal component is smaller than the maximum static friction, whatever its value the friction will be equal to it.
And I think we should keep option "(B) smaller steps ensure smaller friction" as the correct one , without adding any more option like (E) smaller horizontal force.
What do you say?
The problem's answer actually depends on how you define "walking," "slipping," and even "friction!" (Yes, you read that right.) It is well known that there are two main categories of solid contact friction: kinetic (which might qualify as slipping in this problem) and static (much larger and more "stable" than kinetic). Let's define slipping as overcoming static friction and going into kinetic friction. Also, let's define walking: the foot touches the ground while moving forward, then pushes backwards to move the person forward. (This is our definition, but note that everybody walks differently, and this can change the answer.)
By taking small steps, you ensure that you are not moving forward with as much speed as you would with large steps. With less speed, less acceleration is required to stop the foot in motion, so the foot will much more likely experience static friction than kinetic, thus stopping the foot and preventing slipping. Static friction is stronger than kinetic friction near its maximum, and it is easily shown that the maximum static friction is small with ice; thus, the process of walking achieves a friction close to the maximum with small steps, and therefore gives more friction than large steps, and prevents slipping.
I understand that it is a long and inconcise proof, but this is considered one of the most ill-defined common problems in physics textbooks, in both high school and university physics classes. For that reason, we need to define everything ourselves. In fact, in America, people often rush by pushing their foot back before touching the ground; in that case, small steps actually reduce friction, but at the same time, would prevent slipping. The answer changes depending on your definitions. In any case, one thing is for sure: small steps prevent slipping.
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Caleb, I've reviewed the comments made about this problem, and yours was the best explanation of what's going on. It's the static friction that keeps us from slipping, and by taking bigger steps, we increase the horizontal force that could overcome this static friction. Hence, we want to minimize this horizontal force that could overcome this by taking smaller steps.
@Calvin Lin I have missed one of the option (D). Please insert option (D) among all other options
And the correct answer has been changed from (B) to (A). Which is wrong. Option (B) is correct. Please undo the mistake.
Thakns
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Math, give it up. None of the answers A) B) C) D) are even remotely correct. This problem in the textbook need to go back to the drawing board.
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Haha...
So, how can we re-phrase the problem. Any suggestion? Or should we delete it?
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@Soumo Mukherjee – I suggest that we convert this problem into a note, because, apparently, there isn't even any official consensus on the "correct" explanation. And this isn't hardly an uncommon case. On the internet, I've run across many very poorly explained "physics", which keep getting regurgitated over and over, so that misinformation continues to spread.
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@Michael Mendrin – :D yeah, lets other suffer too. >_<
Okay done . I might not be able to continue. My network is too slow. Pls moderate the discussion
Thanks
I found a related discussion here . We can look into it.
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@Soumo Mukherjee – Great link, because the answers given point out the real issues involved, including the matter of this problem being "ambiguous" Amen bro.
Can you kindly explain why it would be option B (small friction with the ice)?
Clarification: Based on the problem creator's request, the answer has been updated back to B. I am waiting on a proper explanation for this answer, otherwise I will revert it back to (A) in a few days.
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Calvin, what if none of the multiple choices are correct? If the problem asks for the sum 1+1, and the choices are A)3 B)4 C)5 D)6, what then? This is what we have here.
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I can always edit the option choices, and add in a "E". What do you (or anyone else) think should be the correct answer?
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@Calvin Lin – Okay, E) Smaller horizontal force.
Your mass plus the acceleration of gravity gives a Force vector ( F y o u ) that, when you stand straight up and down, is directly opposite the normal force. But, when your legs spread wider than your shoulders (when you get an angle in there), you can decompose F y o u into a vertical and a horizontal force. Normally, when you do the splits, the horizontal component of that vector is opposed by your own leg muscles and by the friction of the surface. When you're on a low-friction surface (or a no-friction surface), the horizontal component of F y o u is opposed only by your own muscles, which makes walking much more fatiguing.
As far as friction is concerned, I think we are supposed to take smaller steps so that friction force is lesser. But this does not mean that we cannot walk! By lesser friction, we mean that the friction must be small enough to not slip backwards.
Here is the answer from physics stack exchange that I think solves the problem once and for all:
"The reason for small steps is that the lateral forces are decreased. Imagine taking a large step on concrete. When you first put your foot down well in front of you, it will be pushing forwards on the concrete. At the end of that step when that foot is well behind you, it will be pushing backward on the concrete. The larger the step, the larger these forward and backward forces. Your ordinary shoes on ice can only sustain small forwards and backwards forces before they slip. To avoid slipping, we take smaller steps."-Olin Lathrop
The answer is right! It should be smaller friction!
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