Electric fan
Paul has two identical ceiling fans, Fan A and Fan B , in separate but otherwise identical rooms. Fan A is switched on the entire time, while Fan B remains switched off.
After some months of use, which fan's blades will be dustier?
Assumptions:
Upon sticking to the blade, dust is held by a strong electromagnetic force.
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7 solutions
This question is riddled with WAY too many assumptions. Skoteh90 mentioned many already. More starting assumptions need to be specified, such as: If both fans start with zero dust on them, if the dust is in suspension to start (if so, how much space is above the fan blades, etc), if the room is completely undisturbed, if the blades are statically conductive...the list goes on and on.
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Hi Andrew, You're absolutely right that you could make a pages-long list of assumptions that we might have included on this question, but how many assumptions are needed to make a reasoned argument? What is important here is picking (for yourself) a set of assumptions that simplify the problem sufficiently that you can construct an argument for (or against) dust accumulating on Fan A.
Too often, the questions we select for Problem of the Week are tied to assumptions that basically prescribe the method of solution. This week, we've asked a different kind of question. We believe we have the correct answer for all but the most specialized conditions in the room. We would love to see solid evidence that contradicts our answer under general conditions, but you will have to provide your own assumptions.
Agreed, one for Mythbusters ... I think some dust would be blown off this spinning fan, assuming...
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I don't think it would make for the most exciting episode of Mythbusters, to be honest. Plus, if you've ever owned a fan you'll have seen it confirmed for yourself.
We could also argue that the rotating fan will send the dust toward the ground, thereby creating a concentration gradient in room A that does not exist in room B....
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Many people involved in this discussion have already noted that no simple formula can answer this question, so we are left to identify for ourselves the physical effects that would (or wouldn't) lead to excess dust on Fan A. Can we provide a convincing reason (given what little we know about the rooms containing each fan, except that they are identical) that a concentration gradient would be a dominant factor in answering the question? I would imagine that rotation rate and dust particle size should weigh more heavily in our determinations.
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@Daniel Lalonde Can you elaborate how does this concentration gradient will affect the dust collection the fans?
i also must say that this question seems stupid, as I think that any dust that would have landed on the fan would be blown off. That is why I clicked answer B. Even though I was adjudged wrong I think that the question is flawed. Regards, David
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Note that when you want to take dust off a blade, you can't just blow it off. You have to wipe it with a cloth as there are forces at play — the dust doesn't simply sit there. When you get down to the surface, more interesting things happen like the relative velocity between the surface and the fluid coming to zero. Check out this video of: dye molecules settling in a flowing liquid .
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Please clarify in more detail to me why air can not blow dust off of a surface. I see it happen every time I clean my computer with compressed air or vacuum a surface.
https://j.gifs.com/l52gjr.gif
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@Skoteh90 . – I should have been more clear, by "blow" I mean flow along the surface like in the case of the fan blades.
There's a difference between an air duster and the movement of air past a fan blade — the blade cuts through a volume of air so the air flows along the surface while the duster shoots a stream that's purely perpendicular to the surface. If you try to clean your computer by dragging it through air or flowing air past it in a wind tunnel, you'll get a different result.
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@Josh Silverman – When there are multiple layers of dust particles collected on a surface for years like an old car then moving the car for the first time may cause some of the dust to slip off. That is mainly because of inertia of the dust. Also, if the car is standing in a stationary parking and a strong wind is blowing then again it may cause some of the dust to slip off the car.
However, if the car is traveling on a calm day, air will be dragged with the surface of the car and won't really push the dust particles off the car. Moreover, due to this drag friction, the surface of the car will get charged and attract and accumulate more dust.
There's no way the dust on top of A would stick to the fan as easily as the dust on fan B simply because it's moving.
There are a few things working against this, one is that static forces are strong while the mass of dust particles is very small, another is that fluid slows down near a surface.
The dust hitting the top of each fan is much more significant because of the larger surface area. Fan A reduces that larger amount of dust from sticking by moving air against its surface
I don't understand what your point is here. Are you saying that the effective surface area of Fan A's blades is smaller?
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"I don't understand what your point is here."
The top surface of each blade is about 10x larger than the side surface of each blade. So a force that reduces dust from the top of each blade is 10x more significant than a force that reduces dust from the side of each blade because there's 10x more dust. So I ignore the sides in my argument. The top of each blade is also affected most by air particle collisions because the impact is parallel to the surface. Where if you applied a force perpendicular to the surface the surface would absorb the force from behind the dust particle. So the side of the fan again is ignored.
"There are a few things working against this"
Yes, and those are valid points but they do not stop the dust particles from breaking their static friction when introduced to air particles moving fast enough. Why I mentioned the Example of a blade moving at 1000RPM or 16RPS in my mind is so fast that no amount of static friction would hold the majority of dust particles against that amount of work. As well "fluid"/gas does slow down near a static surface because of communal friction but that friction again can be broken when enough of a force is applied. The speed of the fan was never stated therefore I can assume any speed and therefore any force. While the friction is static the force I can apply is variable and I can assume a force large enough to break any static friction.
Then we can add the angular momentum pushing against this static friction as well.
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The top of each blade is also affected most by air particle collisions because the impact is parallel to the surface.
What I'm saying is that the air flowing past the fan actually flows slowly near the surface, and when it's exactly at the surface it comes to zero (it's dragged along with it). For instance check out what happens with dye settling in a moving fluid . It just isn't the case that the surface is experiencing a wind equivalent to the speed of the rotation.
Then we can add the angular momentum pushing against this static friction as well.
Do you mean centripetal acceleration? How large do you think that could be? Keep in mind that the mass of a dust particle is small. Given that dust does manage to accumulate on fans, does that tell us anything about how it compares with the electromagnetic forces keeping the dust stuck?
Why I mentioned the Example of a blade moving at 1000RPM or 16RPS in my mind is so fast that no amount of static friction would hold the majority of dust particles against that amount of work.
Let's say the ceiling fan blade is
1
m
long. Then the speed at the outer edge would be roughly
2
π
×
1
m
×
1
6
Hz
≈
1
0
0
m
/
s
≈
2
2
0
m
p
h
which is just slightly higher than the top speed of a NASCAR vehicle. As it happens, racecars do get dusty. In any case, ceiling fans spin significantly more slowly than racecars, and they accumulate dust
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@Josh Silverman – "It just isn't the case that the surface is experiencing a wind equivalent to the speed of the rotation." Some air can get trapped against the surface in small pockets held in place by kinetic friction as well as slowed by friction with the surface, Your video demonstrates this behavior well. Although it also demonstrates how adding a stronger flow force can break this surface. Notice how the brush does not come in contact with all of the die. It touches the right most section then after accelerating the liquid to the left fast enough the entire span of die breaks free from the surface. So again if the friction against the surface that is slowing the dust/air particles isn’t greater than the force of the airflow collisions, it will break free.
Yeah, I meant centripetal acceleration. The redirection of the dust while the blade moves from angle to angle around the circle paired with conservation of their momentum causing them to move towards the outer edge, it's been awhile since I've brushed up on my terms. Yes the dust is probably light so in turn, this force is less significant, but again this is weight is another assumption we are allowed to make.
No, real ceiling fans are not as fast as racecars, they’re about ⅓ to ½ the speed. Up to 500RPM. Again not a given in the problem, therefore assumption may be made. Nothing with a smooth surface traveling over 200MPH will collect significant dust in my opinion. Maybe a couple particles here and there, but nothing compared to something traveling at 30MPH or 130RPM in our fan’s case. Maybe if it was wet, oily or had a very jagged surface.
Although debate can be fun, my main point was to bring to light that this "Basic" "Level 1" Classical Mechanics problem was way too overly complex and that the answer is "Justifiably Either", it's not A, it's not B, its either. The problem is flawed in my eyes and should have a more definite answer so no one is told they're wrong when they've made a solid case.
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@Skoteh90 . – Any problem with unjustifiable assumptions can be proved flawed. The problem is based on what happens generally with ceiling fans in our homes. There is no point of assuming their speeds as high as a race car or even more than that. Although, curious minds can surely think about these extreme cases and it is always a fun to debate about them. However, too many assumptions in the problem about these extreme scenarios will confuse the majority of the audience.
For your valid point, if we keep on increasing the speed of the fan the amount of static electricity will also increase and it will try to hold the dust particles strongly and won't allow them to slip off from their blades. We know that dust do stick to race cars as well as mentioned by Josh.
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@Rohit Gupta – I was choosing some wild number to illustrate better that higher speeds strip dust from surfaces. Just like using compressed air to clean surfaces. "There's no way the dust on top of A would stick to the fan as easily as the dust on fan B simply because it's moving." Compressed air doesn't charge the surface making the dust stick more. It removes it.
The amount of charge that can build up is related to the material the blade is made out of, it has limits too. I guess it depends if the charge limit gets hit before the speed limit and vice versa.
The question isn't if dust sticks to a race car, it's how much. How much more/less dust would stick if the race car wasn't moving with the same static charge and the same amount of dust. less? more? I guessed more from my experience with wind and dust and static but the answer isn't clear in my opinion.
Hi, Josh, would it be possible to get a "definitive" solution to this question? I got this wrong (no surprise there, my knowledge in these areas of Physics is pretty limited) but in reading the posted solutions there seems to be a lot of disagreement of why (or even whether) Fan A is the correct answer.
Also, out of curiosity, how is a question that provokes this much discussion considered "basic"? Despite my admitted lack of understanding of some parts of Physics, I will admit it bruised my ego a bit to realize I didn't know how to answer a basic question.
I would also argue that in room A, there would be more airflow, as that is how a fan works, by pushing air through it. In the air, there is dust, without airflow, the only dust that would get on the fan is that which is already above it. With Airflow (moving fan), it would circulate the air in the room, eventually passing much more dust through the fan, and effectively causing more dust to accumulate on the fan.
Most used fans I've seen that don't get cleaned have dust on almost every surface, as every surface is angled at least slightly and comes in contact with moving air. And most fans that don't get used or cleaned only have dust on the top, in reduced amounts even.
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This is true and another way to see the problem with increased air flow. It has another reason attached to it. Air friction charges the blades of the fan which attracts the dust and due to static electricity the dust particles held on to their place. Thus rotating fan will attract more dust.
I knew that whenever I keep something still for a very long time it gets dusty and since the fan b is still for a long time I thought it might get dusty. I think guess and check works best. How does this work? I would rate this problem a 10 because I don't know how to solve it. I felt like It was kind of hard but l didn't want to give up too easily.
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Air friction charges the blades of the fan which attracts the dust and due to static electricity the dust particles held on to their place. Thus rotating fan will attract more dust.
When the fan A rotates its blades suffers a lot of drag which charges its blades, this process is similar to charging of comb when we rub it in our hairs. Moving blades of fan get charged which then attracts the dust particles. The dust particle held on the moving blades without falling because of static electricity.
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Good point, I wonder if the static charge is stronger than the air pushing against the dust. Also in the "Assumptions: Upon sticking to the blade, dust is held by a strong electromagnetic force." So both the moving and nonmoving fan have this strong static charge. Where the nonmoving fan has no major airflow, just what the room provides by default from whatever the room's purpose is. Then how fast is the fan spinning? Are the blades able to hold a large charge or a small charge, plastic or metal? So many factors to take into account. :P
My experience shows that whatever the science behind it, the moving fan collects a lot more dust than the one which is still. And this dust is clingy, dark, and prone to making thick dust cushions on the leading edges, which anyone who has had to clean a fan can attest to!
The example you gave: "Person A running in rain vs identical person B walking in the rain. Who is more wet after the same amount of travel time." is not simpler than the fan case, if there is wind and you don't have a humpback and you're running against the wind you'd want to run with the same inclination of a falling drop. I answered A to the fan question because my unused fans require more cleaning than the ones that see more use.
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Let me make the rain question more defined for you. I was summarizing for the sake of simplicity. Add these stipulations. *Rain is falling straight down. *Human is average human and they are identical. *Rain that hits human stays on human. *It is a closed system. (Normal Rain + Normal Human) I believe it has much fewer factors, therefore simpler.
Your used fans are in active rooms with dust cycling through them, I assume your inactive fans are in storage with no dust circulation. These two fans are in identical rooms and both have a strong electromagnetic charge attaching dust to them that cycles through the room. One fan is moving. One is not. They are ceiling fans so large blade side can catch more dust cycling through the room. Look closely at your fan, the dust collection is mostly on the front of the blade because of hair build up not just the blade itself. We have no hair in this problem. In my experience wind blows dust off of surfaces and surfaces collect dust. Of these two surfaces, one has wind and one does not.
My answer was "Justifiably Either" there is no obvious answer and for a "Basic" "Level 1" Classical Mechanics problem. I was pointing out an issue with the problem and providing an example. Too many factors, too many assumptions available.
Very well explained,this question obviously leaves a lot to our assumption,however, what brilliant thinks is that the density of dust in room is same and more dust is accumulated to the blades of moving fan as it sweeps greater surface area (or volume to be precise). 1. Collison of air molecules and dust particles ignored. 2.Electrostatic force is constant for both fans 3.Centifugal force does not act on dust particles or the electromagnetic force is stronger.
And Viola, answer is A.
Answer: Fan A
Reason:
Fan A create a tremendous amount of airflow, and dust is thrown around the room. But much lands on the fan and its blade.
Most dust particles carry an electrical charge, and can be attracted to one another.
The charged dust particles are attracted and cling to any surface that develops a charge. This can be electrical equipment, which directly carries electric current or a surface subjected to frictional forces, which result in a static electricity build-up. The latter is the case for ceiling fans. As the blades rotate, they experience frictional forces as they `rub' against the air; this knocks electrons around, causing the blades to build up a net charge. The charged dust particles then stick to the charged areas of the blades.
The dust sticks due to the electrical attraction.
Fan B is not answer because it's blades doesn't rotate.
Does this still work if the blades are metal and can dissipate any charge? Resorting to physics seems like such a boring way of arriving at a solution!
This question reminded me of my father's theory, which he told me when I was a kid, on walking slowly through rain rather than running. Slow walking he claimed meant that the rain would only fall on the top of your head and shoulders, whereas running meant that you would bash into the falling drops with the front of your body exposing a greater area to wetness.
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If the metal blade is electrically insulated from the motor and the current carrying wires, (and it usually is, because we do not want to get an electric shock if the fan is touched when it is running) then the metals cannot dissipate the charge and the same effect will be observed. Dust will accumulate.
As for the running/walking in the rain problem, the answer is not so simple. Although running will cause more of the falling drops to bash into the body every second, walking is slower and takes more time. These are two competing factors and it can be tough to decide which one wins.
Check out this problem set - Raindrops keep falling on my head for problems on this very topic.
For observation I must conclude the theory is not correct, or some critical information is missing. Given a room were dust is floating in the air, and properly grounded metal fans, it will build up on fan B much quicker. Because of the airspeed around the blades of fan A it can only hold a very limited amount of dust due to electrical charge. Most of the dust is blown off. Dust on fan B on the other hand will just stack up and stay on the blades due to minimal airflow in the room.
This question cannot be answered without stating the assumptions of the writer. Are we assuming all the dust sticks to the fan? Are we assuming laminar flow of air? Are we completely ignoring air resistance? Electrostatics? This is the first time I've seen a question so poorly stated on brilliant.org
You are so smart!
The reason is because the Fan A generally cleans all the dust of the Fan B since it gives out wind, and since fans only give out wind, therefore it doesn't effect itself so it remains dusty itself. This works when both fans are in one room as stated by the question itself: "Paul has two identical ceiling fans A and B in a room".
Here is a model of a fan:
This demonstrates the energy that is being released out which is clearing off the dust by pressure of the wind, as long as the blades of the fan has a low area to generate a great amount of pressure. This pressure can be used to remove the dust from Fan B but not itself.
This is a well tricky question where science beats logic !!! :))
The problem states that fans are ceiling fans and hence do not throw air on each other with enough pressure. So, I am afraid this is not the correct logic for this problem. The real reasoning is the moving blades gets charged due to air friction and hence attract more dust.
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This is the correct argument...as fan A rotates more than the other it will attract more dust
Agreed sir , is that frictional electricity you are talking about?
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Yes, the static charge that develops on the blades of the fan due to the friction of air.
From what I understand of propeller fluid dynamics--and please correct me if I'm wrong--the flow over the high pressure (lower) blade edge will be laminar. Thus, only dust in the contact lamina will be (successfully) electrostatically attracted: in farther laminae, dust will be retained within them, the retention forces overcoming electrostatic attraction force to the blade. There will be a degree of scouring within the contact lamina that removes already-attracted dust. I suspect that, over time, the scouring rate and accumulation rate will come to equilibrium.
On the low-pressure edge, depending upon pitch and speed, my understanding is that flow will be somewhat turbulent (so-called "swirl"). Dust will be attracted, but it will also be scoured off by the turbulence. Here I would expect a much lower rate of attraction (low pressure = lower dust density, plus less friction = less charge generation), and, if anything, a higher rate of scour than the high-pressure edge.
Thus, for both flat edges of the moving fan blades (the leading edge will be permanently scoured clean, and irrelevant in surface area), dust is being removed as well as accumulated. Unfortunately, the dynamics are unquantifiable without a specific ceiling fan specification (blade dimensions, materials, profile, pitch; rotation speed; distance from ceiling) and fixed environmental data (ambient airflow; temperature; humidity).
By comparison, the upper surface of the unmoving fan has few practical limits to the degree of accumulation over time, convection or sudden air currents (say, from opening and closing of doors or from open windows) being about the only forces liable to remove any of the cumulative dust burden.
My contention is that it's not possible to make a clear comparison with the static fan model, which is much more quantifiable, so I don't believe there can be a strict yes/no/equal answer to this question. My own belief is that--presuming relatively low ambient airflows--the static fan will accumulate more dust than the moving fan, over an extended period.
The problem is this is not my experience, which is that the longer the fan is stationary the more dust it acquires...
This problem also states that the fans are in separate rooms, so the wind generated by A does not effect B at all.
Go With Fan A
fans are in different rooms, please read the ques carefully, science beats you not logic :P
Last summer Air Contioning in my dorm stop to work for several days. I have to use a fan similar to picture. After using a few night I saw that the border of attack of the blades were full of lint and dust, it surprise me at first but I realized the same happen with the fans of desktop PC, I believe that moisture in the air is the culprit making the dust stick into the border of attack. Indeed PC power unit failure happens for the same reason...we forget usually to blow away the dust.
I created this problem after noticing it in my home as well. The fan that is used more often gets a lot dirtier than the others. I searched for it on google and found the reason for this is static electricity. The fan blades get electrically charged when they rotate and attract more dust particles.
The repetitive motion of the fan generates an air current that goes out and downward from the fan, into currents that are being pushed up and towards the fan. So any dust that gets kicked up will probably find it's way to the top of the fan, where the forces of static electrical charge (caused by the blades continuously rubbing dust particles in the air) can take over in sticking the dust particles to the rotating fan blades.
Right, the rotating fan causes air currents which bring dust towards it. The rotating fan becomes charged, which help the particles to stick to it better. Both factors add up resulting in the moving fan gathering more dust.
If we change the ceiling fan by a cooling PC fan. Any IT engineer can easily notice that the working cooling fan has accumulated more dust then the still one. Thus for me A is correct answer.
The answer is apparently Fan A
I approached this by considering "where does dust come from?". Because dust usually comes from people and other things on the ground, I figured dust would only get up above the fan's blades if air was being circulated. Assuming (dangerous) there are no other factors to influence circulation, I believed the fan being on was the only way for dust to rise and stick to the fan. and circulating the dust in the air. But I agree with most other people in that this question had too many unknowns and either solution could be defended.
The rotating fan causes air currents which bring dust towards it. Another factor is that the rotating fan becomes charged, which help the dust particles to stick to it better. Both factors add up resulting in the moving fan gathering more dust. The normal rotation speed of a ceiling fan isn't high enough to overcome the electrostatic force of attraction between a dust particle and the fan.
Answer: Justifiably Either. "Brilliant" thinks it's A.
Reason:
So I understand what the question was getting at where both fans have the same amount of dust fall on top of them at any given moment. Where fan A has the added dust from hitting the front of each blade as it rotates. So fan A has more dust colliding with its surface at any given moment so in total, most dust.
But...
There's no way the dust on top of A would stick to the fan as easily as the dust on fan B simply because it's moving. The dust hitting the top of each fan is much more significant because of the larger surface area. Fan A reduces that larger amount of dust from sticking by moving air against its surface, also by creating angular momentum that can launch dust off. (Ex: if the fan was spinning at 1000 RPM no dust would be able to attach to its surface, it would all be stripped away)
This question is confusing and does not state that these important factors should be ignored. It can be assumed as I did because they never gave you a fan speed, surface areas of the blade faces, or likelihood of the dust to stick. But they need to make that obvious for those who don't think it's safe to make these assumptions and try to take into account all factors.
Improvements: Add disclaimer that airflow does not inhibit the dust ability to attach to the fan and that angular momentum is not significant enough to throw dust off of the fan. Or use the equivalent problem that avoids these issues:
"Person A running in rain vs identical person B walking in the rain. Who is more wet after the same amount of travel time."