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Help Me Understand Mechanical Advantage Please

by mechadv44
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jambaugh
#19
Feb10-12, 07:20 AM
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Quote Quote by JHamm View Post
I think the OP is asking, not for a way to prove that levers supply a mechanical advantage, but for how the atoms in a lever interact so that the forces at one end are different to the forces at the other.
i.e. what is the cause of mechanical advantage?
Ahhhh, yes that's a different question. For that it is important to understand (if I'm lifting you with an off center see-saw) that it is not my downward force which lifts you but rather the force the fulcrum is pushing upward to both lift you and oppose my downward force.

It is the same force that keeps us from falling to the center of the Earth though gravity is trying to make us do just that.

It is also an important consideration when setting up a mechanical advantage system. You can have a strong lever and good advantage but if you use a weak fulcrum it will break before you lift your load.

Ultimately to get a full understanding I think one should study vectors and understand how the various directed forces add up and cancel.
sophiecentaur
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Feb10-12, 11:34 AM
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Quote Quote by JHamm View Post
I think the OP is asking, not for a way to prove that levers supply a mechanical advantage, but for how the atoms in a lever interact so that the forces at one end are different to the forces at the other.
i.e. what is the cause of mechanical advantage?
I think that is taking things much too far in one go. All in one breath you're supposed to have a grasp of inter-atomic forces / quantum mechanics AND the Principle of Moments. Moments are soooo much easier to cotton on to that they are taught to 13yr old kids. QM is seldom grasped until Degree level.

'Looking back' one can often see a link between elementary and advanced stuff but only when 'you know the answer anyway'.

Also, I am not at all happy about the term "Kinetic energy of the Load arm" in the first post. Moments have nothing at all to do with MASS or Kinetic energy. They relate FORCES and DISTANCES. If you consider Power, then you should be discussing Force times Speed - which is measured in Watts, in the end.
JHamm
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Feb10-12, 08:20 PM
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Quote Quote by sophiecentaur View Post
I think that is taking things much too far in one go. All in one breath you're supposed to have a grasp of inter-atomic forces / quantum mechanics AND the Principle of Moments. Moments are soooo much easier to cotton on to that they are taught to 13yr old kids. QM is seldom grasped until Degree level.
I agree the question is somewhat innapropriate, it's just what I think he was trying to ask us.
zoobyshoe
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Feb10-12, 10:33 PM
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Quote Quote by mechadv43 View Post
Sorry if the answer’s already posted and I’m just not bright enough to see it. But, what I’m really asking is can a person (the smartest person ever for argument’s sake) move a lever with mechanical advantage and actually understand/feel it in their mind how it‘s requiring less force, or is it ‘just how the universe works?’ Is it how sankalpmittal said, center of gravity will dominated at the longer side of the lever?
This might help: if you can understand how a magnifying glass takes the harmless light from some given area and makes a very small, intense, not so harmless, hot spot that can start a fire, then mechanical advantage is the same principle. The magnifying glass takes light from a large area and concentrates it into a very small area. Likewise, a lever takes the small force which is "spread out" over a long distance and concentrates it into a much smaller, but more forceful working distance. The "hot spot" created by a magnifying glass only exists in a much reduced area, the increased force of the lever only acts over a much reduced distance. Rather than a "force multiplier" think of it as a "force concentrator", because that's exactly, and more precisely, what it's doing. You are taking something that is "spread out" and concentrating it. This is why the input = the output, and there's no violation of any conservation laws. All you're doing is concentrating what you have.

I think anyone who has ever jacked up a car ought to be able to form the intuitive understanding you ask about. You are doing all this winding of the crank (with a screw jack) covering much distance with your hand, while the car, conversely, moves upward very, very slowly by comparison. The jack is "collecting" all the force you apply and slowly concentrating it to raise the car. With each turn of the crank you apply a certain force over, say, 3.1416 feet (if the crank circle radius is 6 inches, say) and the jack concentrates all that force that was spread out over all that distance to something compact that actually raises the car about 1/8 of an inch.
sankalpmittal
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Feb11-12, 02:31 AM
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Quote Quote by sophiecentaur View Post
Also, I am not at all happy about the term "Kinetic energy of the Load arm" in the first post. Moments have nothing at all to do with MASS or Kinetic energy. They relate FORCES and DISTANCES. If you consider Power, then you should be discussing Force times Speed - which is measured in Watts, in the end.
Are you referring to my post , post 17 ?
Why do you think that moments has nothing to do with kinetic energy ? Kinetic energy is the energy possessed by a body or an object by virtue of it being in motion. When we apply force on effort arm on one side , then we are applying muscular energy to it. Aren't we ? Energy is conserved and so that energy sets the effort arm in downward motion , say. Being in motion it has to possess kinetic energy. This in turn sets load arm in upward motion , and so it also must possess kinetic energy equal to effort arm due to law of conservation of energy which is a universal law.

Moreover , whenever we do work , we say or we mean in Newtonian physics , that if an only if that object covers some displacement. Hence there is momentum in that object and being in motion it must have kinetic energy.

Moment of an arm is the turning effect of that arm also known as torque. It is force times perpendicular distance of line of action of force from point of rotation.
So its different from the force. Nonetheless , if there is moment (clockwise or anticlockwise) , there is kinetic energy. Right ? Please correct if I am wrong..

__________________________________________________________________

So OP is asking about interaction of molecules ? Then its quite obvious that total weight downward equals sum total of weight of all the atoms downward. So if one side arm is greater than other , then at that side already there are more atoms and hence greater downward weight. So we apply less additional weight for the both side to be in equilibrium.

Also centre of gravity will be at midpoint of lever and hence will dominate at side which has greater lever arm.

But we assume the lever weight massless in practical applications and in theories of textbooks and in studying laws like law of lever by Archimedes. Do we not ?
sophiecentaur
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Feb11-12, 04:38 AM
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In my opinion, if you are trying to help someone to understand something about Physics then we are duty bound to use the correct and well defined terms. If we don't then we can confuse them and leave them worse off than they were in the first place.

You want to talk about "kinetic energy of a force"? Well, perhaps you could quote a reputable source in which the term is used. That would be the acid test. I certainly never came across such confusion in a textbook.

A lever doesn't have to be moving for the force to be 'multiplied'. No Mass is mentioned in the Principle of Moments. I know there is a method for working out forces in structures that is referred to as 'virtual work', in which you allow the structure to distort by an infinitessimal amount and then discuss the 'force times distance' involved. That does NOT involve the movement of masses (KE).

You may have a 'feeling' about this and this may be your personal way to get closer to the subject but please don't assume to be enough of an authority about it to instruct others in this approach. It is basically flawed because it mixes dimensions in a very dodgy way.

I will withdraw my objection if you can give me a credible reference, though.
sankalpmittal
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Feb12-12, 11:42 PM
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Quote Quote by sophiecentaur View Post
In my opinion, if you are trying to help someone to understand something about Physics then we are duty bound to use the correct and well defined terms. If we don't then we can confuse them and leave them worse off than they were in the first place.

You want to talk about "kinetic energy of a force"? Well, perhaps you could quote a reputable source in which the term is used. That would be the acid test. I certainly never came across such confusion in a textbook.

A lever doesn't have to be moving for the force to be 'multiplied'. No Mass is mentioned in the Principle of Moments. I know there is a method for working out forces in structures that is referred to as 'virtual work', in which you allow the structure to distort by an infinitessimal amount and then discuss the 'force times distance' involved. That does NOT involve the movement of masses (KE).

You may have a 'feeling' about this and this may be your personal way to get closer to the subject but please don't assume to be enough of an authority about it to instruct others in this approach. It is basically flawed because it mixes dimensions in a very dodgy way.

I will withdraw my objection if you can give me a credible reference, though.
Sir , my textbook says that we can always correlate work and energy which is given in work-energy theorem. Also , my textbook says that whenever there is motion there is kinetic energy and whenever there is momentum (angular or linear) , there is kinetic energy. Work done is force times displacement covered in the direction of it. Momentum is motion possessed by that body. Hence body will have momentum when we do work on it and thereby it will have kinetic energy.

Talking about moments or torque it is force times perpendicular distance of line of action of force from point of axis. Of course it has same unit as that of work which is Newton metres in SI system. We also say that
1 Newton metre = 1 Joule
But we cannot say that work and moments are same. Thay are entirely different.
Yet when lever arm moves downward , say and other arm moves upward , then lever as whole suffers clockwise couple. Yet there is motion in it and so kinetic energy.
Is there not ?

Sir , please tell me what's wrong in my previous post , post 23 and tell me where that analogy fails.
Thanks...
sophiecentaur
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Feb13-12, 03:27 AM
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Quote Quote by sankalpmittal View Post
. . . . .
Sir , please tell me what's wrong in my previous post , post 23 and tell me where that analogy fails.
Thanks...
I think the main problem is that you have Implied a connection between Force and Mass which is not there and used that to draw a false conclusion.

Of course there is often an 'association' between Force and Kinetic Energy in machines of all sorts. However, there is more to Physics than mere associations. We try to do better than that.

Firstly, I notice that you haven't quoted a reputable reference for the expression "Kinetic energy of a Force" and I am not surprised. The text book you quote from states the 'real' relationships and does not even imply that 'your' phrase is valid. You have constructed your own argument by extending too far from what you have read in the book.

One simple way to demonstrate your inappropriate use of KE in the context of levers is to consider a simple 2:1 length lever with balanced masses (Ratio 1:2). If you allow some movement (say the large mass moves downwards) and do some simple calculation for the KE of each mass, you find that the smaller mass will have TWICE the KE of the larger mass. The velocity will be twice and the mass is half, so the mv2/2 is NOT the same in each case. So, although we have done a calculation involving this lever, it really doesn't lead to any useful conclusion and definitely not an equation that is of any use for solving a 'balance' problem. There is some other form of Energy which would need to be considered as well.

Another nail in the coffin is to consider Friction. When you turn a wrench against a very sticky thread, your hand / body may have some kinetic energy but what is moving on the other implied end of the lever? A nut, with a mass of just a few grams, rotating very slowly. Any energy that you may be putting into the system is not turning up as identifiable Kinetic Energy (there will be some KE in the form of internal energy - heat - but this is outside of your analysis and doesn't count). Work has been done but KE is not relevant - or only a tiny part of the situation.
zoobyshoe
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Feb13-12, 04:50 AM
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Quote Quote by sophiecentaur View Post
One simple way to demonstrate your inappropriate use of KE in the context of levers is to consider a simple 2:1 length lever with balanced masses (Ratio 1:2). If you allow some movement (say the large mass moves downwards) and do some simple calculation for the KE of each mass, you find that the smaller mass will have TWICE the KE of the larger mass. The velocity will be twice and the mass is half, so the mv2/2 is NOT the same in each case. So, although we have done a calculation involving this lever, it really doesn't lead to any useful conclusion and definitely not an equation that is of any use for solving a 'balance' problem.
I am glad you pointed this out because I tried it and you're right. The fact the lever arms have kinetic energy seems, therefore, to be completely beside the point. Bringing it into the mix does not serve to clarify anything.
sophiecentaur
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Feb13-12, 05:00 AM
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Quote Quote by zoobyshoe View Post
I am glad you pointed this out because I tried it and you're right. The fact the lever arms have kinetic energy seems, therefore, to be completely beside the point. Bringing it into the mix does not serve to clarify anything.
Glad someone took my point. Not only does introducing KE miss the point but it's a potentially seriously confusing thing to introduce.
This is a great example in which someone's own visualisation of a situation, which may work fairly well for them, personally, in many circs should not be used as a tool for 'explaining things' unless it is 'rock solid'.
If anyone takes the huge step of 'explaining' something on a forum like this, they are taking on the mantle of TEACHER. God knows, there are enough professional teachers who actually struggle with many of the basics that they are expected to teach and what they have told students can be to blame for a lifetime of subsequent conceptual problems.
jambaugh
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Feb13-12, 07:14 AM
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Quote Quote by sankalpmittal View Post
Moment of an arm is the turning effect of that arm also known as torque. It is force times perpendicular distance of line of action of force from point of rotation.
So its different from the force. Nonetheless , if there is moment (clockwise or anticlockwise) , there is kinetic energy. Right ? Please correct if I am wrong..
On this, slightly. The force moment is as you say a torque a generalized force. It does not imply kinetic energy when there is no rotational motion. One note as to why torque and energy have the same units, since a generalized force is work done per generalized motion if the units of that motion are pure numbers (as with radians) then the units of force will equate to units of energy. Technically though there is a distinction. As said, force is not work. The proper units of torque would be e.g. newton-meters per radian = Joules per radian.

If one wants to get super technical, mathematically a torque (or other gen. force) differs from work in that it is a linear operator mapping differentials in one coordinate to differentials in another not a stand alone quantity. You see that in the way force is measured, you have to do a little bit of work over a little bit of displacement to see the ratio. Look explicitly at how a scale or a torque meter works. (or a volt meter, or a pressure meter...)
sophiecentaur
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Feb13-12, 07:52 AM
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Quote Quote by jambaugh View Post
On this, slightly. The force moment is as you say a torque a generalized force. It does not imply kinetic energy when there is no rotational motion. One note as to why torque and energy have the same units, since a generalized force is work done per generalized motion if the units of that motion are pure numbers (as with radians) then the units of force will equate to units of energy. Technically though there is a distinction. As said, force is not work. The proper units of torque would be e.g. newton-meters per radian = Joules per radian.
In the dreaded Imperial system, this is taken care of by using foot pounds for work and pounds feet for torque. That could be the one single way in which Imperial is better!!
sankalpmittal
#31
Feb13-12, 10:05 AM
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Quote Quote by sophiecentaur View Post
One simple way to demonstrate your inappropriate use of KE in the context of levers is to consider a simple 2:1 length lever with balanced masses (Ratio 1:2). If you allow some movement (say the large mass moves downwards) and do some simple calculation for the KE of each mass, you find that the smaller mass will have TWICE the KE of the larger mass. The velocity will be twice and the mass is half, so the mv2/2 is NOT the same in each case. So, although we have done a calculation involving this lever, it really doesn't lead to any useful conclusion and definitely not an equation that is of any use for solving a 'balance' problem. There is some other form of Energy which would need to be considered as well.

Another nail in the coffin is to consider Friction. When you turn a wrench against a very sticky thread, your hand / body may have some kinetic energy but what is moving on the other implied end of the lever? A nut, with a mass of just a few grams, rotating very slowly. Any energy that you may be putting into the system is not turning up as identifiable Kinetic Energy (there will be some KE in the form of internal energy - heat - but this is outside of your analysis and doesn't count). Work has been done but KE is not relevant - or only a tiny part of the situation.
I am glad that you pointed out the mistake. I retried that and came to the conclusion that your calculations were correct. Again I checked my post 17 where I stated that KE of load arm equals KE of effort arm. Taking the values in the image on that post I calculated the kinetic energies rather than just applying law of conservation of energy.

I found that kinetic energy of load arm was not equal to kinetic energy of effort arm.
*Sigh* , this proves that I applied wrong concepts !
Thanks !

Quote Quote by jambaugh View Post
On this, slightly. The force moment is as you say a torque a generalized force. It does not imply kinetic energy when there is no rotational motion. One note as to why torque and energy have the same units, since a generalized force is work done per generalized motion if the units of that motion are pure numbers (as with radians) then the units of force will equate to units of energy. Technically though there is a distinction. As said, force is not work. The proper units of torque would be e.g. newton-meters per radian = Joules per radian.

If one wants to get super technical, mathematically a torque (or other gen. force) differs from work in that it is a linear operator mapping differentials in one coordinate to differentials in another not a stand alone quantity. You see that in the way force is measured, you have to do a little bit of work over a little bit of displacement to see the ratio. Look explicitly at how a scale or a torque meter works. (or a volt meter, or a pressure meter...)
Thanks for this detailed explanation. This clarifies hell lot of things.

Yet I cannot find answer to OP's question. He wants to analyze molecular interactions ? In other words , I think he is looking for theoretical reasoning rather than mathematical deductions.

I guess I have the answer but this involves considering of mass of lever. I searched , googled etc. but cannot find answer to his question.

Here is my answer ( please correct if wrong) :
We know that centre of gravity is the point where total weight of body is supposed to act.
Let one arm of lever be longer and other be shorter. Then its quite obvious that total weight downward equals sum total of weight of all the atoms downward. So if one side arm is greater than other , then at that side already there are more atoms and hence greater downward weight. So we apply less additional weight for the both side to be in equilibrium.

Also centre of gravity will be at midpoint of lever and hence will dominate at side which has greater lever arm.

But we assume mass of lever to be massless , do we not ?
Am I correct ?
zoobyshoe
#32
Feb13-12, 11:24 AM
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Quote Quote by sankalpmittal View Post
He wants to analyze molecular interactions ?
No, he does not:

Quote Quote by mechadv44 View Post
ok, I know that being further away and using a fulcrum/pivot point from an object being moved takes less energy. i.e using a 4 foot crow bar to pry open something. But i can't grasp the concept of why being further away makes it so much easier. thanks
Quote Quote by mechadv43 View Post
I meant force though, can it be explained in plain english as opposed to just a formula why being further uses less force?thanks
Quote Quote by mechadv43 View Post
I said that i already know that having a longer lever on the force side of the folcrum requires less force. what i'm asking is WHY WHY WHY does it make it easier? why is a longer lever so special if still moving the same object!?Is this just something that exists and can't be explained?
He doesn't understand why distance from the fulcrum makes any difference.

He understands that it does make a difference, and he knows the formula, he doesn't understand why it makes a difference. Since he knows the formula, restatements of the formula are uninformative to him. He wants a simply stated explanation of the reason.
jim hardy
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Feb13-12, 11:48 AM
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But, what Iím really asking is can a person (the smartest person ever for argumentís sake) move a lever with mechanical advantage and actually understand/feel it in their mind how itĎs requiring less force,
sure - just grab a lever and go do it. There's nothing like "feeling it" to cement a concept in place.

Have your little brother stand on a 2X4 and lift him at various distances from his feet..
zoobyshoe
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Feb13-12, 12:30 PM
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Quote Quote by jim hardy View Post
sure - just grab a lever and go do it. There's nothing like "feeling it" to cement a concept in place.

Have your little brother stand on a 2X4 and lift him at various distances from his feet..
Or pull some nails out of a board with a hammer or crowbar. I think most people already have such an intuitive grasp of mechanical advantage from actual experience that the formula makes perfect sense the first time they encounter it.
mechadv43
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Feb13-12, 02:08 PM
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thanks. I'll try to understand this. i tried crowbarring some nails before starting thread..I won't give up now knowing that it IS understandable that the greater distance but less force on my end of the lever will move an object with all the concentrated force but for a shorter distance.
tiny-tim
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Feb13-12, 02:51 PM
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didn't robert frost write a poem on how going a shorter distance gives a greater force? Ö
i took the path less travelled

and that made all the difference


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