So Many Shoes!
There are 2 businessmen, who wear different types of shoes. Businessman A wears athletic shoes with bumpy soles, while businessman B wears dress shoes with smooth soles. Assume that both pairs of shoes are newly purchased (and standardized much like their own types).
They are both walking very quickly on a marble floor that is slightly wet as it was recently mopped. Which businessman is more prone to slip on the floor while walking?
Tip:
It might be helpful to study the structures of the shoe soles before you approach the problem.
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2 solutions
I don't think this can be considered a complete solution. You make nice claims, but you don't back them up.
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Could you please point out which claims in Michael's solution requires justification?
This solution needs to define "grip" and back up the claim that dress shoes do not grip well. Consider racing cars. When the weather is good and dry, race car drivers use bald tires. And they grip very well. In fact, they grip better than tires with grooves. The problem is that bald tires have a single flat surface, which makes friction an all-or-nothing proposition. If the track gets wet and there is any skidding, the tire will not be able to retain a grip. So in rainy conditions it's important to switch to tires with grooved treads. Sorry that this is not a complete solution - it's been decades since I properly studied friction. But I know there is more to this solution than the OP's argument.
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I think "grip" refers to traction, the amount of tangential force required to generate motion between the shoe and the ground. I agree with your reasoning, there are many factors at play in this problem. The dress shoes have no grooves, so they have a greater contact with the ground, so they would have more traction on a dry surface.
On a wet surface, a layer of water forms between the shoes and ground would significantly reduce traction, whereas the grooves on the athletic shoes would provide an escape route for water, and provide more grip.
It is not that obvious. The bumps on the soles are essentially the same as a collection of small smooth soles. On a uniformly wet road, they can all be expected to have the same coefficient of friction. As others point out, the friction force is independent of the area of contact.
The reason why bumps may be useful is twofold: it may prevent the build-up of a uniform layer of water between soles and ground, and it increases the likelihood that at least some of the bumps provide some traction. But to assess these things much more information is needed.
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The chances of slipping increases if a layer of water is formed between the shoe and the floor. Then the shoe will not be able to get traction from that water layer and slip. When we have a bumpy sole then the water will be pushed in the gaps and some part of the shoe will come in the contact with the floor and get the traction. Therefore, the bumpy sole will have less chances of slipping.
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The same reason why the water will be pushed in the gaps may be the reason why water underneath a smooth sole will be pushed outside of the shoe.
The heart of my reasoning is that bumps on shoes are just small versions of a smooth shoe. Any difference must be explained from (1) the multiplicity of bumps, (2) the difference in size, or (3) a difference between angle and/or force distribution.
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@Arjen Vreugdenhil – To my mind, the easiest way would be to use (1) and (2) rather than just one or the other.
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@Peter Byers – @Arjen Vreugdenhil I agree with your reasoning. "The reason why bumps may be useful is twofold: it may prevent the build-up of a uniform layer of water between soles and ground, and it increases the likelihood that at least some of the bumps provide some traction."
More prone is totally subjective term, and not brilliant. And so I disagree, there are several more parameters to be considered, the effect of the thin film of water on the friction coefficient, the surface area of each shoe that is on the floor. Generally with running shoes will have less area is on floor( as was stated by take a look at the shape of the sole) the so-called dress shoes (are similar to boat deck shoes) The amount of actual area for the bumpy bottom shows determines the resultant friction created. Tires has grooves to prevent hydro-planing (ie remove enough water from under tire to allow for necessary traction. Extrapolated, can anyone confidently state that a shoe with 3 points of contact each .2sqmm surface area (with rest of show being grooves have more traction that a 100sqmm surface area with ff of .2?
My answer is that problem is not mathematical nor based on strict physics formulae, but only empirical based on general principles espoused in tire design.
Finally if the "stickiness" of the dress shoe was 5 units and the running shoe was 3 can we agree that there is a possibility that the total friction (even with reduced area) for the dress shoe might far exceed the running shoe.
Again I say this is not brilliant, more like somewhat educated "Common experience"
So by studying the "Tip" I cannot get the brilliant answer...
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I think we all would agree that grooves are provided in the shoes/tires to have a better gripping in wet/rainy conditions.
I agree with Robert that we use ungrooved tires called the slick tires in racing on a dry ground as it provides a better grip by increasing the contact patch area. Although, the regular cars use groove tires as they may have to drive in rainy conditions or on wet roads.
So, grooves do help on wet floors and they would be less likely to slip.
Coefficient of friction of any CONTACT area with wet stone is the same. Less area, more pressure. So that's not the issue. The issue is that there is a layer of water between the shoe and the wet stone. If the sole area is uninterrupted over a sufficiently large area, it will take some time (on the order of 1/10 second) for the lower pressure to push that layer all the way out to the perimeter. During that time, the sole is in contact only with water - and the water is moving. 1/10 second is long enough to move a shoe far enough to lose balance. All the analogies with tires are only partially correct. The purpose of the tire grooves is to provide a path for the liquid water to move far enough out of the way so that the contact patches can establish contact. Obviously, the faster the tire is going and the deeper the water, the more challenging this is.
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While the friction does not depend on the contact area, the traction (the amount of tangential force required to generate motion between the shoe and the ground) does depend on the contact area. Greater contact area --> Greater traction.
I agree, if the sole is smooth, then more water accumulates between the ground and the sole, resulting in smooth soled shoe being more slippery.
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Tangential friction = traction.
The traction per unit of area depends on the pressure between soles and ground: τ = μ p. The total traction (= friction force) is equal to F = A τ = μ A p = μ Fn = μ m g. This is independent of the area of contact!
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@Arjen Vreugdenhil – That is true... when there is contact. Consider a boat floating free vs. a boat grounded. The coefficient of friction with the ground is not the issue, as the floating boat is not in contact with the ground.
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@Ray Williamson – If some of the shoe is subject to a buoyant force, then the normal force Fn is less, resulting in proportionally less traction. This is true for either type of sole.
On a "slightly wet" flour, it is unlikely, however, that buoyant force comes into play. Walking in a puddle, that might be different.
@Arjen Vreugdenhil – I understand that the maximum friction is μ N , so the amount of force required to slip does not depend on area of contact. I think this is true only if the object is rigid and the normal force applied is uniform.
I came across a discussion on a ELI5 Reddit page where they explain that traction depends on the surface area. What I understand from it is that the distribution of force across the sole can be uneven, and if the force in a small area exceeds the slipping force, then the sole will slip. If we increase the total contact area, then the chance of force exceeding the required force in a small area decreases, and the sole would be less likely to slip.
There is too much ambiguity in this problem. For example, what does slightly wet mean? Is there a uniform layer of water on the floor, or just a few damp spots? Do the soles of the shoes have the same coefficient of static friction? Suppose that the dress shoe has a higher coefficient of friction and the wetness of the floor is spotty. Which one then has the greater likelihood of slipping?
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I agree with you, it should be mentioned in the question that there is a uniform layer of water instead of the floor being recently mopped.
This depends on more factors that are considered here. There is bound to be friction with the marble floor. This means that the more contact with the floor, the more friction, i.e. B is better. The rest will be down to the design of the shoe. Some shoes are designed to grip earth, gravel or an uneven surface. Some indoor shoes are designed to bend and squeeze and grip on harder surfaces. Since this just defines the shoes as athletic shoes, I would disagree with the solution.
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I would have agreed with you if we were comparing shoes only on the dry surface. However, grooves are cut on purpose to avoid slipping when the floor has a uniform layer of water. The grooves do it by pushing the water in the gaps and removing the layer of water underneath. On the same reasoning, we have grooves in tires even though they will provide less traction on dry surface.
It's been many years since I studied friction as well, but one thing I remember is the calculation to determine the degree of horizontal force necessary to overcome the static force of friction between two surfaces depend solely upon the vertical force applied by each surface to the other and the coefficient of friction between the two materials. There is no component of surface area of contact in the calculation. In fact, the grooves in tires do not exist to decrease the surface area between the tire and the road, but instead are essential to channel water away from the point of contact thus preventing hydroplaning.
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Traction if different than friction and it do depend on the contact surface area. Here is a Reference .
I do agree with you on the hydroplaning.
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Rohit, the reference you give indicates that traction = coefficient of traction times normal force. This is precisely what has been said about friction. You will have to be more specific in your argument.
Another thing to consider is the difference between static and kinetic friction. If a smooth sole has started sliding, the entire sole is sliding, and receives a smaller amount of friction (kinetic) than it could when not sliding (static).
The use of multiple bumps has the advantage than, while one bump is slightly sliding, another bump may be placed on the ground stationary, and receive the higher amount of static friction.
OK, reality check. I moved to Malaysia a few years ago. We get a lot of rain and most of the rooms have no carpet. We have hard tile floors in one of the rooms in our school. Whenever a student comes in wearing blades (I think Americans call them "cleats", they are bound to slip. I always have to tell them to take them off. When they wear their school shoes (which are usually fairly flat because boys drag their feet). Of course, when I wear my walking trainers, they have a much better grip. As I already stated, this really depends on the type of athletic shoe and how they are designed. Indoor athletic shoes are designed to squeeze and grip on hard surfaces; shoes designed for soft grass are designed to be harder and dig into the ground and will slip much more easily.
I thought along similar lines to Gabriel. I also know that boots made for yachting have very smooth soles to grip the wet deck. On the other hand these yachting boots have razor thin grooving. Does anyone have a link to any experiments to resolve the issue?
Nice explanation, I really liked how you linked the concepts of shoes and tires. The grooves give the space for the water to move away and water does not form a layer between the shoes and the floor. This prevents them from slipping.
This is wrong, For every unit of sole that touches the floor adds a small amount of friction, not touching the ground adds no friction. Friction is how a business man would stop themselves from falling. A speed racing car is tread less but a normal car has treads to protect the tires from pieces of debris laying on the ground; It is cheaper rather than making the whole tire thicker. A shoe has tread because it sinks into the ground and pushes of the sides of holes that it created a marble floor is not soft and cannot allow tread to sink in. Treads = grabbing puncture able materials and safety from damage. Thesis: Contact = Friction = Stability = Your wrong.
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I think opposite as the amount of friction does not depend on the area of contact. Two blocks of same material and of equal masses but a different base area would suffer an equal amount of friction when moved on the same rough floor.
The main culprit here is the water layer. If a layer of water created between the two contacts then they will slip more. That is why we put lubricants in the machines.
The bumpy sole does not allow the water layer to be formed between the shoes and the floor and hence it provides more grip.
While friction does not depend on the area of contact, traction does depend on the area of contact. While walking on wet mud, the shoes sinks in, so it has a greater contact area than a smooth shoe and therefore can provide greater traction. In this case the shoe "sinks" into the layer of water and displaces the water. The smooth shoe does not come in contact with the ground because of the layer of water in between. As a result, the grooved show has greater grip compared to the smooth shoe.
This is simple:
a smooth sole is more likely to slide than a bumpy sole
Can you explain how you arrived at this result? (This will allow others who cannot solve the problem to understand your solution fully).
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Can you explain that logic? I hope you are not misinterpreting the smooth sole as a frictionless sole. To clarify, a smooth sole means the sole without grooves.
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Actually, I did misunderstand
since at school, we are taught 'smooth' as 'frictionless'.
I'm not sure what this question is trying to do. It seems to be using a real world example with unrealistic examples while asking you to figure it out realistically. I know that grooves and texture on an object is bound to give it more friction, but it also means less of the shoe is to make contact with the floor, and the rounded, rubbery sole is going to have a hard time touching down. A flat sole however: all of it makes contact at the same time, and remains in contact; even if force is put in a direction other than up or down, it is all still on the floor and will find it hard to move. It also depends how much water there is and what material the soles are made of. I've worn both of these types of shoes before and I would never dream of going in sports shoes on wet marble floor!
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The 'unrealistic example' is that I think it is trying to make you assume that all of the shoe in example A makes contact with the floor at once just like example B? Despite them both being different shapes and it explicitly asking you to examine the structures of the soles. If the case is that all of shoe A hits the floor at once, why not have both shoes be the same design but have it states that one has texture on its soles and the other doesn't? Semantics just confuses people. Not really a brain-teaser, just "guess how the writer interpreted the question".
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Also, how much pressure is exerted can change the circumstances.
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@Aidan Eaglesfield – I meant force exerted on the shoes, oops. Low force on both pairs has different results, as does high force on both. And also how a person walks, really there's so many variables that change depending on how you define walking alone, let alone semantics of if the diagrams are actually accurate representations of the hypothetical and what material they're both made of.
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@Aidan Eaglesfield – According to you, what is the purpose of having grooves in the shoe soles?
@Aidan Eaglesfield – I am just a 13 year old kid
@Aidan Eaglesfield – Yes. But the main factor is friction.
@Aidan Eaglesfield – I am just a 13 year old kid
I do not know. OK I am just a 13 year old kid
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@Syed Hamza Khalid – But you are right, friction is the main factor, given no other circumstances
No, No, No. You silly gooses down here. Its distribution of weight and Psi. Think, if I have 200 lbs pushing down on 1 square foot, or if I have 200 lbs pushing down on 1/2 of a square foot, which one is going to have the most pressure/grip applied between the surface of the shoe and the ground? The one with the least amount to surface area.
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Yep. Pretty much. It's called friction.
Consider the tyre problem originally asked by Pranshu Gaba.
Imagine a vehicle tire without grooves. If there are no grooves, then a tire is in contact with the wet road, which shows that dress shoes do not grip well. A tire without grooves can be compared to a shoe that is very smooth. In this case, if the shoes' soles are smooth, then walking on a wet ground with these shoes on is dangerous.
Since the soles of the athletic shoes reduce the area of contact between the wet ground and the shoe, the chance of slipping is less. It is not surprising that if athletes run on track with these shoes, then they don't slip, which boost their running performance in the Olympics. Otherwise, it would not be possible for the runners to run smoothly.