Mechanical Engineering: Particle Equilibrium (12 of 19) Pulleys and Mechanical Advantage
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In this video I will calculate the forces and the tension of pulley systems.
Next video in the Particle Equilibrium series can be seen at:
The free body diagram is key to the analysis. And it vastly simplifies the calculation. Just learnt something new ..... at age 70. Never too late
Yes. I am having fun learning things I didn't understand as a student. 🙂
I watched a similar video on this subject by DrPhysicsA, and I ended up being confused - many thanks for clearing up my confusion with your clear explanation.
you are awesome Sir I used to afraid from dealing questions on pulley system. but you clear my concept... thanks
That was the clearest explanation of pulliys I have seen.
Thank you, very much, for this very practical lesson!!!
This professor is the best!
These videos are really good I was feeling like there was something I was missing in regards to my education about pulleys and this is it. He really shows why pulleys work and not just how.
Glad you liked the video!
@@MichelvanBiezen
I have a question about the last 2 free body diagrams. On the 4th one; why did you split it beneath the middle pulley while on the 5th one you split it above the middle pulley ?
Edit:
Nevermind 😁 it was the last thing you said.
great. easy to understand by all. great explanation . thanks sairam sir
Michel, спасибо Вам и Архимеду!
a very clear explanation. thank you for making this video
If the second pulley had 4 pullies instead of 2 in the same sequence would the force be .25 vs .5? Similar to the 4th example?
Good theory. I remember the days at the end of junior school. That's cherished memory.thank you.
Thank you. Glad you enjoyed it and gave you some good memories. 🙂
You're really great sir
Great video, thank you :-)
God bless you
Flawless :) thank you
Wouldn't this be isnt as effective as the last part because you are lifting so you have to multiple the gravity? I didnt go to college and just looking but am i right?
Pulley system 2 was a mindblow to me. I managed to predict 50 newtons on each end of the rope because you taught us that all the ropes have to have the same tension, and i predicted 50 newtons on the left rope attached to the ceiling, but had no idea what the weight on the right rope attached to the ceiling would be and was really surprised at 150 newtons total force.
I think the way it works is like: In pulley system 1, we have 100 newtons of force pulling down (the weight), and 100 newtons of force pulling up (50n from ceiling 50n from person pulling)
But in pulley system 2, there is 150 newtons of force pulling down, the weight (100n), and the person pulling (50n). half of the weight is going into the ceiling, which means the other half HAS to be going into the pulley, and the person pulling is ALSO putting 50 newtons into the pulley, so it has to be holding 100 newtons.
Third pulley system predictions: it's gonna be 33 in each rope, the top pulley is going to be holding 66 newtons, and the person pulling would be lifting with 33 newtons. so 3x mechanical advantage.
Fourth pulley system predictions: The bottom pulley is connected to 3 ropes, so that has to be 33n in each rope. The middle pulley is 2 of those ropes, so that has to be 66n newtons from the middle pulley pulling on the cieling. The top pulley is holding 33n from just the weight, but if we also add the 33n from pulling on the rope it will be 66n. So middle pulley is 66n, top pulley is 66n, for a total of 132n on the ceiling
This feels wrong and like more mechnical advantage should mean more weight on the ceiling, but more mechanical advantage literally means we have to put less force into the system. we are only addding 33 newtons of down force into the system by pulling down with 3x advantage, where as when we had 2x advantage we had to put an extra 50 newtons of down force into the system. So more mechanical advantage weirdly enough means less strain on the system because it's being divided up more i guess.
Fifth pulley system predictoins: I flipped the video vertically and it seems to literally just be the fourth one but upsidedown, so that we are pulling up instead of pulling down. as an initial guess that should mean only 100n in the cieling cuz we are removing our downforce, but that shouldn't be possible cuz we are lifting a fraction of the 100n so the cieling can't be supporting all of it.
Oh i forgot to also add the upforce instead of just removing the down force. If we represent downforce as negative upforce, then we went from -33n to 33n, for a difference of 66n, but i only did a differnce of 33. So my initial guess should be that the ceiling is holding 66n.
Ok now to actually try to figure out whats going on: the bottom pulley is directly connected to the middle pulley, so pulling on the middle pulley by 1 is just as good as pulling on the bottom pulley by 1.
I see 3 things coming out of the bottom pulley, one of them being our up force, so i FEEL like we should be lifting 33n but one of the things coming out of the bottom pulley is just a direct connection to the middle pulley.
So really, if we consider that pulling on the middle pulley is just as good as pulling on the bottom pulley, and we consider that the middle pulley has 2 connections to the top pulley, and the bottom pulley has 1 connection to the top pulley, that's just as good as if the bottom pulley had 3 connections to the top pulley. We also have 1 connection to the person pulling the rope, who is applying an up force. so it should be 25 newtons of force being pulled, and 75 newtons on the ceiling.
Time to see if my predictions were right i guess
Ok I think I got every answer correct, but I messed up visualizing the free body diagram on the fifth pulley system. Thank you for these videos!
Glad you figured it out! 🙂👍
I watch your videos from Turkey dear Michel Van Biezen from Istanbul Technical University and your teaching is very professional and clear. I want to say that you should consider adding a subtitle to your videos because the translation of TH-cam algorith is not very clear and it may make a mistake and give us a wrong word. I encountered with lots of videos which was translated bad. Respect from Turkey.
Hi Ismael, welcome to the channel and thank you for the suggestion. At this time we don't have the time to work on subtitles, since both my wife and I work other jobs besides making these videos, but later after we retire, we may want to do that on the more viewed videos.
Excellent video!
Thank you. Glad you liked it. 🙂
these pulleys look scary but are really easy to solve
thank you
I understand that each side of a rope takes part of the weight but ultimately the ceiling mount should be the weight of the object divided by the mounting string in the pulling string???
The force on the ceiling will be equal to the weight + force (when pulling down) or will be equal to the weight - force (when pulling up).
Wait, so... arranging our pulleys a certain way has the consequence of imparting a net gain of force on the point of contact with the fixed plane? We effectively make the object to be displaced _heavier_ than it actually is? That's weird..
Well, you´re not really making the object heavier. In short: the upwards forces need to balance completely with the downwards forces. The amount and arrangement of pulleys does not change that.
When pulling upwards, the force we apply should be subtracted from the force the ´fixed plane´ needs to apply to keep the weight non-moving. If we pull in the opposite direction (downwards) then our force is acting in an opposite direction from the 'fixed plane' force. In order to make up for us pulling on the ceiling in addition to the weight, it needs to counteract that with an equal and opposite reaction.
I have a question... If in diagram 2 you switch the load and the ceiling around, do you then go from having 2:1 mechanical advantage to a 3:1 mechanical advantage?
Not sure what you mean by: "if we switch the laod and the ceiling around". We'll have to make some more examples of different pulley combinations to illustrate some other setups.
Hello my professor, is there a ploycope or document with this lectures and exercises?
No, not yet. That is something we are considering doing in the future.
Can someone explain why the load is attached to one pulley instead of one end of the rope?
Thank you
When you take a simple example with one pulley, you will see that the tension on the rope is half the weight of the load, but if you place the load on the rope on the other side, then the tension will equal the full weight of the load.
Is there any relationship between load and pulley diameter, sir please explain
The pulley diameter matters in compound pulleys.
Yes they do matter when the pulley has mass.
Thank you for your prompt reply🙂
You are welcome.
Great
It would be interesting to give the ratio of the load lifting speed to the speed of the driving force F if for example we have a winch with a motor.
The ratio for the speed (or distance traveled) is the same as the force required to lift the load. If you need 1/4 the force you will have to pull 4 times as far.
Not sure if you'll even see this, but here goes: In the 4th example, how can the amount of weight supported by the attachment point at the ceiling (133N) be more than the amount of weight being hauled (100N)??
100 Newton came from the mass of the object and another 33 came from external force that is acting on the end of that rope (the line with arrow) I understood it rightaway when thinking like this 😄
You have to apply force to pull it down remember?
Because you have that force (F) included as weight to carry by the ceiling
Only movevable pulley can reduce the force
What is the mechanical advantage of example 2? Is it 2? And how about the MA of example 1? Is it 2 as well? I need a confirmation so badly... please reply
The mechanical advantage is defined as the weight lifted divided by the force required to do so. The first two examples: mechanical advantage = 2:1 The third example MA = 3:1 The last example MA = 4:1
@@MichelvanBiezen thanks prof michel...you saved my day
lots of doubts analysing the first diagram
1.how pulley is fixed
2. rope fixed ?
3.how load is being lifted
4.drawing free body diagram ..how different is it from previous first diagram n first diagram of this video where tentions get divided
1. pulleys are fixed to the ceiling
2. ropes are held in place by the force (as indicated)
3. loads are held in place by the forces (as indicated)
4. The free body diagrams are the same as any free body diagram.
At 2:23, You show there is "(150 total), 100N pulling on ceiling", when the total load is 100N shared by 2. it should be 50N?
When you are pulling UP, the ceiling only has to carry the weight MINUS the force of pulling UP.
When you are pulling DOWN, the ceiling has to carry the weight PLUS the force of pulling DOWN.
How can you get more than the load with a suspended load? # 3.
The additional load came from the external force pulling the end of that rope (line with arrow)
can anyone explain how we draw the free body diagrams which determine the strings that are aiding at pulling the weight at the bottom? for example, in the example second from the left, why do we determine that only two strings are in effect, and not the third string? I feel like in an exam i could just as easily encompass the 3rd string in the free body diagram and wouldnt get the answer of 50N.
many thanks
Essentially you can draw them anywhere you like. The guidance is that you draw them such that the boundary cuts through the strings (or forces) that you are interested in. In a tatic case (like this) the sum of the forces pulling upward must equal the sum of the forces pulling downward.
@@MichelvanBiezen Thanks Michel. appreciate it. I think asking the question, which strings are pulling the object in the opposite direction - is helpful. thanks so much for taking the time to reply!
which questions are asked to engineer in Pulley industry?
1: What is the rated capacity of the pulley as the sum of the two tensions?
2. What is the coefficient of friction the pulley makes with the axle?
3. What is the range of cord diameters that can pass around the pulley?
4. What is the radius of the cord around the pulley?
5. Can you provide a drawing that shows the mounting interface of the support bracket, so that I can work it in to my drawing?
I have question in the last question, my friend and I cut between 3 ropes. We manage to have tension of 66N instead of 75N
@Priya pari In this example friction and the weight of pulley doesn't exist
I have the same question just like yours. I suspect that there should be a criteria for deciding a free-body diagram, which in this lecture the professor didn't teach.
My guess would be that a free-body diagram must containt all ropes directly or indirectly pulling the thing.
Since a norm of tension force on a rope is constant everywhere and every rope lifting the weight is actually one rope, the answer is the weight divided by the number of ropes in the diagram.
@
Oliver Rusta
If you cut ropes at the level where there are only three ropes (just above the lowest pulley), the middle rope will have tension not the same as the lateral ropes, but two times greater.
@@user-lr8od4uz1n Not necessarily. In the example #2, the last part of the rope is ignored because it does not touch a movable pulley. In general, only movable pulleys play a role in distributing a force. Non-movable pulleys only change the direction of the force.
@@user-lr8od4uz1n the criteria I use is I draw a box around the parts that begin to move when the rope is pulled.
When it comes to mechanical advantage, does it matter if the pulley is fixed or not?
There are different pulley arrangements. Some have the pulleys fixed and others do not.
Thanks!
Welcome!
Can a 2000 lbs weight dropping 2 ft, lift a 500 lbs weight 8 ft (ignoring friction)?
Yes, with the correct pulley system you can.
fantastic...how do you determine the 100N the weight
The 100N weight is just arbitrary. (It is a nice round number)
Why did you use the second pully in the free diagram on pully system 5 and didn't use the second pully on pully system 4?
On system 5, the bottom 2 pulleys are connected, so they act as a single sub-system.
Why in example 3 the force on the ceiling is higher than the object itself?
Because there is the force applied in addition to the weight
Wait why at 4:57 is it 67 Newtons..shiuldnt it be 33..and ifnits,double then it should,be 66..where did he get 67 from?
@@leif1075 it's actually two 33.333... N pulling down, so according to the free body diagram for that single pulley, the force pulling up should be 66.666...N ≈ 67N
@@leif1075 100/3=33,3333333333333333333333
33,33333333333+33,333333333333=66,66666666666666=67
I can understand the first four questions, but why should the middle pulley be included in the analysis of the fifth question?
The free body diagram indicates that there are four ropes at the top supporting the weight on the bottom. The sum of the tensions must equal the weight of the object.
In the last example, what if the FDB boundary was cut around the pulley with the weight?
The tensions in the 3 strings will still add up to the 100 N weight.
@@MichelvanBiezen But that would be 33 N (each).
I'm not sure if the weight supported by the ceiling can be less than 100N.
For the example where the force is directed upward, the tension at the ceiling will be less than 100 N
What about the weight l mass of the pulley(s) in addition to the given load?
In most examples we ignore the mass of the pulleys. If they have mass you do have to add their mass to the free body diagrams. (We probably should add some example videos)
@@MichelvanBiezen why ignore the fact? Please teach correctly.
In almost all cases, the mass of the pulley is insignificant to the mass of the object. That is why the mass of the pulley is ignored.
Thanks sir
You are welcome!
Haha, this is interesting
I hope it's as easy as it's here when I try to solve one myself 😄
It looks like you managed quite well
@@MichelvanBiezen what exactly do you mean? It looks like you managed quite well 🤔
You figured it out quickly by taking a look at the diagrams. 🙂
Oh yes, you're right. I understood everything well despite this been the first time I'm seeing a solution of it's kind. Thank you for making learning easy @@MichelvanBiezen
last one is important
Newtons are smart way for geniuses to understand. Simple lbs. Would be easier to understand which one would be better or easier to pick up most weight with minimum force numbers. 25 newton's...
Appreciate your time and upgrade of my IQ
You are welcome. 🙂
I’m confused with number 2 being more than the total of the weight
The ceiling must hold the 100 N weight and the 50N downward pulling force. (Draw the free body boundary around the the whole thing.)
Does that F mean Fig Newton?
No, it has nothing to do with fig newtons. The namesake of the fig newtons is town in Massachusetts that is a suburb of Boston, which has nothing to do with Isaac Newton.
F stands for force, and its units in the SI system are in Newtons, named for Isaac Newton who is credited with the fundamental laws of motion. It is just a coincidence that fig and force both start with an F.
Thanks a lot. Sir u are very cute
God bless ur soul daddy
Thank you
ولك يسعد دينك
thank you
@@MichelvanBiezen غالي❤️
What makes learning fun? This hurt a little.
Last example why tension is not 33N?
When you look at the free body diagram, the weight is supported by 4 strings at the top of the diagram, each holding 25 N
I am still confused by this. Why do you draw the free body diagram to include the pulley above the pulley that's attached to the weight? If you draw the FBD as you did in the previous 4 examples, there would only be 3 forces pulling up on the pulley while the only downward force would be the weight of the mass. Therefore, if you draw it like that, the tension would be 33N. So my question is, why do you draw the FBD different in the last one vs the other 4 examples?
BruinPrideee - I think the fbd includes the free hanging ones and excludes those who are hanging solely from the ceiling
@@bruinprideee9970 if the free end of the string is pointing upward, that will be included in the FBD.. If the free end of the string is pointing down, it wont be included in the FBD..
Drawing a dashed line around a region on the blackboard is not drawing a free body diagram. You have to actually draw the forces.
Excelent 🇧🇷 🇧🇷 🇧🇷 🇧🇷 🇧🇷
Thank you.
Someone correct me if im wrong, but if i hang 100n from the ceiling then the force on the ceiling is 100n, plus the weight of the pulleys and rope. So if his formula which seems right, IS right. The he should have said "plus the weight of the pulleys" . Because they are not light and several will get above 50 lbs quickly.
For the purpose of understanding the principle of how the pulleys work, we are ignoring the weight of the pulleys.
Newton is the unit of force. Weight meaning mass should be measured in kilograms.
weight does NOT equal mass weight = m x g (mass x acceleration due to gravity)
@@MichelvanBiezen I agree, but go to the store and for 10 N of sugar?
I agree, but go to the sore and order 10 N of sugar
@@nielsmadsen2185 weight is not mass !!! As a dog is not a cat that is way you can't buy 10N of sugar
In the US we buy pounds of sugar which is indeed a unit of weight and not mass. However there is nothing wrong with buying kg of sugar by adjusting the scales so they convert the 9.8 N of sugar they are measuring and depicting it as 1 kg.
Pulleys all pull their own weight.
Drawing #4 is wrong. A 100n weight can not pull down with 133n.
The drawing is correct. The 100 N weight is beying pulled UP, and the force downward required is 33 and 1/3 N (Rounded to 33 N).
@@MichelvanBiezen How can 100n pull down with 133n? I have several pullies and rope, I can build this to see what weight reads on my scale.
We now have about 1/2 dozen videos on different pulley combinations. Try to duplicate some of these examples to see how it works.
#2 look to me wrong 2 rope should still only have a total of 50 not 100
the video is correct. Thanks for checking
What bothers me is w is a force and not a mass.
w = m g (just like F = m a).
Just seeing a hanging mass represented in N and not kg whereas N is a vector. Just an odd representation, but I understand.
Ahh, I see. I think it is just a matter of getting used to it. When I moved to the US it took me a while to get used to pounds and miles. 🙂
Sorry 100 pulley will not lessen the weight even a gram if it is fixed only movevable pulley can lessen the weight
The weight of the object will not change, but the force required to lift is will.
Not true. You can not reduce a single line anchorage compared to the weight no matter how many pulleys you use. You only reduce the force need to lift it.
Yes, you can. If you are pulling UP the force on the single ceiling line is the weight MINUS the force needed to pull UP.
Notice how he alternates his examples between pulling UP and pulling DOWN. For pulling up, the force on the ceiling is the weight minus the pulling up force while for pulling down that force is added to the weight.
In conclusion divid the weight by the numbers of pulley and you get your answer
When the pulleys are in this arrangement, yes.
Michel van Biezen which other arrangement do you know?
Hey genius! 3,4,5 are 100 ceiling weight.
The values shown in the video are correct for example 3, 4, and 5. (They are not equal to 100N)
ΔΙΟΡΘΟΣΕΤΟ ΔΑΣΚΑΛΕ.ΕΙΝΑΙ 37,5 ΚΑΙ ΟΧΙ 33
The weight on the ceiling is wrong in every diagram except the first one. Or are we talking force needed which is not the same. No amount of pulleys with reduce the overall weight nor increase the weight. (Not including the weight of the equipment used) Left to right three and 5 are 100% wrong no amount of pulleys will reduce the weight of the single ceiling fixture ! ILLOGICAL Unless someone can explain ?#
The video is correct.
Imagine a tree branch as a pulley. You are holding a 100kg man off the ground with your own 100kg body. It's 1:1 so you need 100kg of force to lift (hold) 100kg weight. The BRANCH however is holding twice your weight.
Diagram 1 also reduces the weight (on ceiling) - that is, as long as you are holding the rope and sharing some of the weight. If you tie it off, the weight on the ceiling now goes up to equal the weight of the load.
The video is correct and explains it perfectly.
@@ianbrown_777 A tree branch doesn't need to be 100 kg itself to support a 100 kg person.
For instance, a standard 8 ft long, 2x12 plank has a mass of about 17 kg. But even a 100 kg person wouldn't hesitate to stand on it, as it can support a lot more than 100 kg of load as it spans its length across two support points.
@@carultch Correct. I'm not talking about how much the branch weighs - just the extra weight on it. I was just trying to explain in another way to the OP how the weight on the ceiling fixture will change (- either up OR down) depending on the system you attach to it.
Wow! The fourth pulley system - the tension on the ceiling cannot exceed the weight. Draw a free body around the weight and all the pulleys. The sum of forces in the vertical direction must be zero. Therefore the tension on the ceiling is 100N up as the weight pulls 100N down (of course ignoring the weight of pulleys and rope).
A good way of looking at it.
That’s a wrong way of looking at it. There are 2 downward forces on the pulley attached to the ceiling, F which is the applied force to keep the rope tight and the weight of the object. F is being applied downwards so it will get added to the weight hence the 133 N force on ceiling. It’s easier to understand if you imagine hanging a second weight of 33 N where F is being applied. So the force on ceiling will be the sum of 2 weights