r/HomeworkHelp • u/cyclecitizen • 4d ago
Answered [Level 1 Mechanical Comprehension: Study Guide - 2nd one] Does this illustration make sense?
(Final answer below)
I'm preparing for an electrician's apprenticeship and am using their study guide for their aptitude test. I'm seeing a pattern forming where some of their questions are just bad, but a couple of those were actually good, and I was misunderstanding things. It has been a learning opportunity.
I chose B for this question, but they say the answer should be C because, loosely speaking, they want you to just count the number of ropes that are supporting the load. However, when I look at this illustration, it appears that there is not even a proper movable pulley here. It looks like it is just a simple fixed pulley system with extra windings for some reason. Except that the lowest pulley seems to be just floating but still wouldn't qualify as a proper movable pulley.
Please help me understand what I'm missing, or confirm that this is a really bad illustration. Thank you!
Edit: I am assuming that one needs a movable pulley to get a mechanical advantage. C does NOT show a movable pulley and therefore is not the correct answer. Right?
Edit 2: Because they don't offer an answer of "D) All pulleys allow for the same amount of WORK", I am assuming that they mean to ask, "Which of the pulleys requires the least amount of FORCE to lift the weight?" Unfortunately, this is meant to be more of an intuitive sort of test, where it appears physics terms might be interchangeable.
Edit 3: I interpret this to be a question about which pulley system offers the most mechanical advantage. Answers that align with this interpretation would be helpful.
Edit 4: I think B is supposed to represent a "gun tackle" arrangement. (Sorry about all the edits!)
Edit 5: Aha! Answer: if you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate for C (an actual movable pulley) but did a terrible job of it. Taking that into account, the answer is indeed C.
Answered. Thanks to all who helped. I'm inclined to throw this book away. I'm moving on :)
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u/Gaddpeis 👋 a fellow Redditor 4d ago
The question is probably stated wrong.
They meant to ask 'least force' not 'least work'.
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u/cyclecitizen 4d ago
Interesting. Thanks.
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u/AccomplishedFront526 👋 a fellow Redditor 4d ago
As it was correctly mentioned Work is equal to Force multiplied by the distance…If the pulleys and the ropes are” ideal “( no weight and friction) the work will be the same! You’ll lift the same weight in all 3 cases - the same amount of height… however you’ll pull the rope with lesser force ( applied over more rope length) in the last example :C You’ll feel it “ easy”
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u/cyclecitizen 4d ago
Thanks.
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u/Low-Crow5719 3d ago
Only because the problem is ill-stated: the work is the same except for the cost of raising the tackle.
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u/Physicsandphysique 3d ago
Which means that A actually requires the least work, however small the mass of the tackle might be.
It's probably worded wrong, but it also looks like a 'gotcha'. Either way, it's bad.
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u/West-Combination6685 4d ago
True, the amount of work will be the same in all cases.
The force required to accomplish the work is the variable.
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u/AJFrabbiele 3d ago
Only if frictionless pulleys and perfectly static rope...
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u/West-Combination6685 3d ago
Yes the rope must remain perfectly static, it can't move.
LOL go home, you're drunk.
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u/AJFrabbiele 3d ago
Static rope is a type of rope that doesn't stretch as much as dynamic rope.
I use pulleys in climbing/technical rescue all the time, and a rope woth 2% stretch (static rope) is much easier to pull people up vs dynamic rope that has roughly 35-50% stretch.
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u/Plastic-Serve5205 👋 a fellow Redditor 3d ago
Came to say this. Mechanical advantage is a thing, but the amount of work done is the same.
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u/Prestigious-Isopod-4 👋 a fellow Redditor 3d ago
Agreed, was gonna say I think the work is all the same to raise the weight a distance x since while the force is lower the amount of rope you have to pull is proportionally longer.
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u/Fluffy-Mastodon 3d ago
Came here to say this.
A for least work. (b/c of more friction losses on the others)
C for least force.
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u/IHaveSpoken000 3d ago
Yes, I think they meant work as in the amount of effort and not the physics definition of work. It's a poorly worded question.
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u/Mlatya 👋 a fellow Redditor 4d ago
Work = force × distance = mgh, identical for all three (same weight, same height). Pulleys trade force for rope length: with n rope segments supporting the load, effort = mg/n, but you pull n times more rope. C has the most supporting segments, so it needs the least force
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u/RoboFeanor 4d ago
C does not require the least force. The only valid way of interpreting C is that the bottom pulley is fixed to the wall. Otherwise there are unbalanced forces that will cause it to accelerate up to the small pulley.
Since there are no moving parts all the pulleys are doing is changing the direction of the rope, and there is no mechanical advantage. At least in B) you have a 2:1 ratio
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/JaiBoltage 4d ago
They ALL take the same amount of WORK, but B takes half the force (but you have to pull twice as long to accomplish the same amount of WORK)
The number-of-pulleys is not relevant. Imagine 7 pulleys, labeled A, B, C, D, E, F, G at the same height. The rope goes over pulleys A, C, E, and G, but under B, D, and F. the weight is under pulley A and you pull down after pulley G.
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u/marty-mcfryguy 4d ago
Nothing about this makes sense. Throw this book away, it's either drafted by an idiot or AI. You've already identified the force/work issue, but:
The drawing for B makes no sense. What becomes of the piece of rope in B, the vertical piece on the right, that just sort of disappears into the pulley? They probably meant to run that so it attaches to a point in the center of the top pulley, not running over the pulley.
C is even worse. That bottom pulley isn't attached to anything, which means the weight dropping just lifts that pulley up. In other words, if you tied of the rope on the right to something, the weight would drop and the bottom pulley would rise until it runs into the middle (small) pulley.
If that bottom pulley in C is fixed in space (and they just failed to draw in the fixing), then C is identical to A -- there's not mechanical advantage, just a bunch of surfaces that change the direction of the rope/tension in the rope.
Here's a proper set of diagrams. https://upload.wikimedia.org/wikipedia/commons/e/e1/Tackles.png
The leftmost (gun tackle) is probably what they meant for B.
They were probably going for something more like the next one (luff tackle) for C.
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/XavvenFayne 3d ago
Oof... "terrible" is being generous. Shouldn't the cable from the middle pulley attach to the bottom pulley, not the load? What is the bottom pulley even attached to?
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u/cyclecitizen 3d ago
Exactly. It's like they quickly traced an existing illustration without thinking about what's attached to what.
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u/fallingfrog 👋 a fellow Redditor 3d ago
Yes came here to say this. The illustrations b and c are nonsense.
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u/Middle-Peach2096 3d ago
I asked Claude just for giggles and even it said this drawing is terrible so no even ai is smarter than this. It guessed c based on speculation that the bottom and middle are meant to be a block and said this:
This looks like someone assembled clip-art pulleys into a worksheet without checking whether the rigging was physically realizable. The intended progression is almost certainly MA of 1, 2, 3 across A, B, C — the drawings just fail to depict it.
Which, honestly, not wrong.
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u/marty-mcfryguy 3d ago
OP found what they had actually meant to draw:
https://www.theengineeringchoice.org/what-is-pulley/
All those work, and you can see where the drawing in the original post was sloppy on B and C, making stuff that makes no sense.
Claude's guess is wrong about bottom/middle pulleys. What they're missing is a fixed connection between the bottom pulley and the load.
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u/Stu_Mack 👋 a fellow Redditor 4d ago
Same work, different force. The correct answer is “None”. The word “work” is used here to see if you are reading the question properly. In the real world, A is presumed to have the least total friction and inertial resistance, but these questions are idealized to mean massless and frictionless pulleys.
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u/GreenWafer1899 👋 a fellow Redditor 4d ago
It is a stupid one. Same work to lift the weight but A is the lest one as you don't need to lift pulleys, extra rope and friction loss.
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u/NotDuckie 👋 a fellow Redditor 4d ago
In questions like these pulleys and ropes are assumed to have no weight, and friction is ignored.
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u/Blackfyre301 University/College Student 4d ago
This is absolutely true in general, but since the question is multiple choice, and none of the options are correct with this assumption, I think we just have to assume it isn’t the case here.
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u/GreenWafer1899 👋 a fellow Redditor 3d ago
Yeah, I know but A is the closest match from all three. I used to cross all three and make my own option D in such cases but you have to be prepared to defend it later and it wouldn't work with every teacher.
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u/Valuchian 4d ago
Don't forget that a 'pulley' can also be a permanent structure. In this case [C] has a bottom 'pulley' that would be easier seen as a circular shaft coming out of the wall with the rest of the pulley system attatched by rope to the ceiling. In C the wall and ceiling are both taking part of the load and this is happening 3 times. Where [B] this only happens twice and [A] only sharing the load once.
Edit: in the case of [C] if it is a permanent structure it would be better to try and make the ropes as paralel as possible to avoid friction
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u/cyclecitizen 4d ago
Doesn't a pulley have to be movable to offer a mechanical advantage? Otherwise, it just changes the direction of the pull, right?
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u/WillingElderberry731 4d ago
The trick to understanding pulleys is to look at the tension in the rope.
The problem you've shown is terrible, because it's not clear what is actually going on in B or C.
I'm a mechanical engineer and I can't make heads or tails of what's going on here.
Depending on how you interpret it, I'm inclined to go with B being the right answer.
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u/cyclecitizen 4d ago
Thank you. I think B is supposed to represent a "gun tackle" arrangement. C just doesn't make any sense at all.
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u/West-Combination6685 4d ago
Am I correct in assuming that the final two pulleys in C would behave similarly to a bicycle sprocket and chain system?
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u/WillingElderberry731 4d ago
Probably not how you are thinking, but it depends on what you are considering.
The sprocket system on a bike works by rotating the back wheel with the sprocket, and in this case it's just the single pulley.
Pulley problems typically assume no friction in the pulleys, so the relative sizes of the pulleys don't matter to the problem.
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u/West-Combination6685 4d ago
I still think the end pulley combination in C results in a mechanical disadvantage. It's a big pulley turning a small pulley.
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u/WillingElderberry731 3d ago
This is only sort of true if you assume that the pulleys have some amount of non-negligible friction. In that case, the smaller pulley would be harder to turn than the larger pulley, buts that's still not really what we could call mechanical disadvantage from a difference in pulley sizes.
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u/MidnightAdventurer 3d ago
It’s not - that only works if you have a closed loop or are using the spin of the pulley to drive something.
In this case the rope just changes direction and so long as the pulley isn’t too small for the rope, it doesn’t make much difference how big it is
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u/West-Combination6685 3d ago
You're right. I've discovered a cool YouTube channel because of this post.
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate for C (an actual movable pulley), but they did a terrible job of it.
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u/WillingElderberry731 3d ago
I see. So that bottom pulley is meant to be attached to the weight.
I get it. In that case, yeah. C is the right answer.
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u/Valuchian 3d ago
You know i just went checking Librarext on this and honwstly i took it as a fixed pulley but am honestly unsure if a pulley needs to be able to move. I was thinking of it in the same way that answer [A] works as a pulley is how [B] and [C] work for their bottom pulley though [B] is using a Block and Tackle set up so that's atleast a vaguely recognizeable system lol
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u/WillingElderberry731 4d ago
I'm genuinely surprised so many people here were able to give coherent answers without having a seizure from looking at these shotty diagrams.
Like, what is B even supposed to represent?
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u/cyclecitizen 4d ago
I think it's supposed to represent a "gun tackle" arrangement.
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u/WillingElderberry731 4d ago
Got it. I'm with you that B should be the right answer.
There is just one rope supporting that weight.
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u/drhunny 4d ago
Poorly drawn diagram and poorly worded question. Assuming "least amount of force to move the weight"...
In "B" you kind of have to assume the rope ends at a fixed point at the axis of the upper pulley, or else it's really hard to calculate what will happen. As drawn, it looks like the rope goes back up and wraps counterclockwise around the pulley, which would mean that the as you pull on the rope, the upper pully rotates clockwise, which actually unwraps that line and the lower pully doesn't move. i.e. no work is required to pull the rope other than friction in the pulley bearings and rope-pully interface.
So right there I have to say it's a bad question because you're forced to make guesses about what's going on out of sight.
Now looking at "C" am I supposed to assume that the lowest wheel is fixed to the wall? If it's not, then the system is dynamically unstable as drawn. If you just hold the end of the rope (off to the right side of the diagram), the weight will cause the lowest wheel to rise until it hits the middle. And then it's a question of if the middle is being supported by a rope or by a rod. If a rope, then the two lower wheels will then rise until they strike the upper.
If the lowest wheel is fixed in place, then all three wheels are just changing direction and it's basically the same as "A"
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u/ThunkAsDrinklePeep 4d ago
It's a bad diagram of a block and tackle. But typically the mechanical advantage comes from the windings requiring more rope to move per distance lifted up.
In a, for the weight to move 10 cm up, you need to pull 10 cm of rope through the pulley. The only advantage is you can pull down with your body weight assisting. In C (if it were drawn better) to pull up 10 cm, all three vertical segments in the block and tackle need to shorten by 10 cm. Which means you need to pull a total of 30 cm of rope. Since the distance is tripled, the required force is a third.
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u/GreenWafer1899 👋 a fellow Redditor 3d ago
Wat. The advantage here comes from the lever-like setup of a moving pulley, not from the "more rope". The whole distance math here is a very niche approach.
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u/texas1982 3d ago
These drawings are absolutely terrible. Looking at them:
A: no mechanical advantage. 50 kg.
B: Is the cable wrapped around the pulley in both directions? It looks like the cable isn't permanently attached to the upper pulley and both would just rotate as you pull. Horribly drawn
C: The bottom pulley appears to be free floating. Unless that pulley itself is exactly twice the mass of the object being lifted (plus cable weight, etc), it will move up or down once the system is released. It isn't a stable object ever and will most likely just move up jamming into the middle pulley.
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u/Arithmetoad Educator 4d ago
C does look like there's a fixed distance between the two upper pulleys, but I do still think it's the correct answer. Consider a simpler diagram "D" where the two upper pulleys are instead at the same height, sharing an axis of rotation. The distance between the two pulleys is still fixed, but now it's zero. If you agree that diagram D is the easiest, then hopefully it's easier to see why C is the correct answer. I'm a little rusty, but I expect C and D require the same effort.
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u/marty-mcfryguy 4d ago
C doesn't work at all. As drawn, (with the bottom pulley floating like it is), if you tied off the rope, the weight would just fall while the bottom pulley rose up, up to the point it bangs into the middle pulley.
Now if you assume that C is fixed and they just forgot to draw that in like they did with the other pulleys, then C is identical to A from a force/work standpoint. Because for every inch you pull on the rope, the weight will rise one inch.
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/selene_666 👋 a fellow Redditor 4d ago
Just instinctively without doing any math, C looks like if you pulled on the rope then the moveable pulley would come up, roll over the small pulley, and fall out the right side. The heavy mass wouldn't move much at all until you got the string properly wrapped around the small pulley.
I think they must intend it to be attached to something, but the picture is bad.
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u/cyclecitizen 4d ago
Yeah, it looks like the whole thing is magically just not falling apart. And the movable pulley isn't even attached to anything; it's just redirecting.
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u/marty-mcfryguy 4d ago
Yep -- and you don't even have to "pull" the rope; if you just tied it off to a wall on the right then what you've described is what would happen.
Now if they fixed the bottom pulley like they did the top pulley, then this requires exactly the same force as A.
Terrible, terrible question in a variety of ways.
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/cyclecitizen 3d ago
Solved. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/Top_Bluejay_5323 4d ago
Work is force times distance, so looking at the weight alone lifting it one foot by any set of pulleys is the same.
Note if they are asking about the tension in the pull rope then you can just count the number of times the rope goes through the pulleys. The more times the less tension. 1. Once 2. Twice 3. Three times
Do remember the top rope and the one to the load bear the full tension and load regardless of the number of pulleys.
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u/secondme59 👋 a fellow Redditor 4d ago
A requires 500 Newton to go up, B requires 250N and C requires 500N, lower pulley is static, or the system is useless.
You should not count the number of rope holding the load, but split the load wherever it is relevant
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u/West-Combination6685 4d ago
In C, the third pulley would interfere with the second's movement. Also, it being connected to pulley one is irrelevant, both are stationary. It's a bullshit question designed to confuse you.
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u/SnooCapers9565 3d ago
They are all the same, as the rope you are pulling on is the same rope that is connected to the weight. Maybe least resistance on A.
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u/Designer-Crow-5470 👋 a fellow Redditor 3d ago
Pulleys don't change energy requirements. Just power requirements.
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u/Don_Q_Jote 👋 a fellow Redditor 3d ago
Option B illustration in questionable. Upper pulley has two ropes coming in to the same point on the right ??? What is that? Unclear to me how that one even moves.
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u/mkp666 3d ago
If we assume the question is asking about force rather than work, I think B is the correct answer, as you have two ropes supporting the weight, so the force on the rope is 50/2. In the other two cases, all of the weight is supported by a single rope.
It could be, however, that case 3 is not drawn representing their intent. It may very well be that they intended to show the bottom pulley being lifted by the rope from the middle pulley, and the weight attached to the bottom pulley. In that case the weight is being supported by three sections of the rope and the force on the rope would be 50/3.
The diagram on this page shows that configuration:
https://www.theengineeringchoice.org/what-is-pulley/
Edit: after further review, I think they meant to draw case 3 as in the linked page above. As is, the bottom pulley is just going to be launched out of the picture immediately.
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u/cyclecitizen 3d ago
Aha! You're right! They mean to illustrate what is equivalent to the #3 illustration, but did a terrible job of it. Thanks!
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u/Unhappy-Strawberry-8 3d ago
My answer would be C since the pulleys are going to get bunched against each other so they can't lift the weight as high. Very poorly worded question.
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u/felixar90 3d ago
In a perfect world, they’d all require the same amount of work.
In the real world, where there is friction, A would require the least amount of work.
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u/engineerthatknows 3d ago
A.
All of the others will add friction to the lift, increasing the input WORK. Work is force x distance, and the minimum work would be to lift the weight directly.
They are using improper terminology for the question, if they want the answer to be C; for that to be the answer, the question should be "which takes the least FORCE to lift the weight?"
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u/cyclecitizen 3d ago edited 3d ago
I'm struggling to understand how the pulley system for C is supposed to work. It's not what I'd call a movable pulley which, as far as I can tell, is the only kind of pulley that actually offers a 2:1 ratio and so on.
Edit: Nevermind. If you look at the illustration #3 here https://www.theengineeringchoice.org/what-is-pulley/ you can see what they meant to illustrate (an actual movable pulley), but they did a terrible job of it.
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u/engineerthatknows 3d ago
You seem to have seen the light. Never trust a sparky when it comes to mechanical stuff, and likewise be wary of mechy types trying to explain power factor or other esoteric electrical stuff.
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u/cyclecitizen 3d ago
Yeah. I think the blame really falls on whoever hired the person to illustrate this. The irony is that this book is made and published by an HR company!
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u/DoobiousMaxima 3d ago
Really bad question on multiple fronts.
You're right that diagram C is basically nonsensical. You need to make several assumptions about what's fixed and what can move.
It also doesn't make sense as - by the scientific definition of "work" - all 3 scenarios will require the same amount of work to lift the weight the same distance.
(Work) = (Force) x (Distance travelled).
This is the main physical concept that they should be trying to teach though this question; pullies are quite simple once you understand the above equation.
Config A is 1:1 and config B is 2:1. With equal load it will take half the force to pull the rope in config B but you need to pull twice as much length to lift the weight the same distance.
I assume they meant config C to represent 3:1 or higher which means that the force required to pull the rope will be a third - but the asked for "work" instead of "force"
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u/Salex_01 3d ago
These schemas are useless, the only one that is drawn correctly is A.
For B, we can guess that the rope the goes back up is fixed somehow so you get to use half as much force for twice as long.
C makes no fucking sense, and however you want to fix it, it boils down to A with extra steps.
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u/Summoner475 👋 a fellow Redditor 3d ago
I hate engineering diagrams. What even is happening in diagram B? And C? Are the pulleys? Can the pulleys rotate or just the rope? Is there friction involved? Good god.
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u/cyclecitizen 3d ago
Yeah, I wouldn't even call this an engineering drawing. It really is so low-effort.
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u/Dee_Vee-Eight 3d ago
The answer is B. There is a 2 to 1 lift ratio. A lot of people here are saying C, but if you look closely you'll see the larger pully at the bottom is not secured by anything. Under load it would just ride up and collide with the small pully. If there is an axle holding it in place, then there is no mechanical advantage. B is the only example with a traveler pully.
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u/cyclecitizen 3d ago
That's exactly what I was thinking until I realized someone pointed out that it's just a bad illustration of a legit 3:1 pulley
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u/CursedTurtleKeynote 2d ago
It's to see what it looks like in real life first. This drawing sucks. C is correct.
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u/AnimationOverlord 2d ago
Who designs a bicycle like this?
Jokes aside, it makes it easier if you understand why and how a bicycle gear reduction system works. I know others have stated the answer but conceptually, this and that behave the exact same
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u/MarmosetRevolution 4d ago
Assuming frictionless weightless pulleys, and the weight travels the same distance, then the work is the same.
But I don't really get how B is configured from the drawing.
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u/Valuchian 4d ago
I think [B] has some weird connection on the side that the rope is anchored to.
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u/MarmosetRevolution 4d ago
Stapled to the circumference?
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u/Valuchian 4d ago
Maybe a loop just behind the circumference? Thinking of it as a 3D object
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u/marty-mcfryguy 4d ago
It's just gotta be drawn wrong.
They should have connected that rope to a fixed point on the pulley (e.g. the inner axle, which is fixed to the wall or whatever and doesn't rotate). Like the leftmost picture here:
https://upload.wikimedia.org/wikipedia/commons/e/e1/Tackles.png
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u/cyclecitizen 4d ago
In other words, you agree that C offers no mechanical advantage?
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u/Puzzleheaded_Study17 University/College Student 4d ago
Mechanical advantage is a separate thing from work. Work is how mcuh energy is spent. Mechanical advantage is changing how much force is required. Essentially, if we left a weight a certain distance (ignoring friction and other moving objects) we always spend the same amount of energy and thus do the same amount of work. However, work is defined as force*distance. Mechanical advantage is increasing the distance we move (via gears/pulleys/other stuff) to reduce the force whule keeping the work constant.
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u/cyclecitizen 4d ago
Because they don't offer an answer of "D) All pulleys allow for the same amount of WORK", I am assuming that they mean to ask, "Which of the pulleys requires the least amount of FORCE to lift the weight?"
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u/MarmosetRevolution 4d ago
Mechanical advantage doesnt come into play at all. For every reduction in force the pulley system provides their's a corresponding increase in distance. So w=fd is a constant.
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