Why Does Distance from a Pivot Point Reduce Effort in Mechanics?

[mechadv44]

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

 

[tiny-tim]

welcome to pf!

hi mechadv44! welcome to pf!

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

no, the energy is the same…

you can't get extra energy for nothing

only the force is less

 

[mechadv43]

same person who started thread, different name, sorry password problem..
I meant force though, can it be explained in plain english as opposed to just a formula why being further uses less force?thanks

 

[waynexk8]

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

Clue.

The crow bar end you are pushing on, goes further than the other end.

Wayne

 

[tiny-tim]

same person who started thread, different name, sorry password problem..

goodness! are there 44 of you?

I meant force though, can it be explained in plain english as opposed to just a formula why being further uses less force?thanks

force times distance equals work done (= energy supplied) …

if the two ends of the lever are at different distances from the fulcrum, so that they move different distances when the lever turns, then different amounts of force will do the same work, and will supply the same energy

 

[mechadv43]

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?

 

[Lsos]

I think I asked this question once, too. The answer I got was essentially that yes, that's just the way the universe works. Fortunately it's a very simple thing and you'll see manifestations of it everywhere in everyday life. It quickly starts to just "make sense".

Climbing stairs for example is easier than going straight up a wall. A door is easier to open if the handle is on the far side of the hinge. A piece of wood is easier to split when hit with the narrow end of an axe, a screw is easy to screw in and yet it holds things together very tightly, gears, levers, pulleys, even a winding road up a mountain...all take advantage of the fact that work is force x distance, and all these mechanisms simply trade distance for more force.

Unfortunately there are also a lot of concepts in physics where the answer is also "that's just the way it is", but they DON'T make any sense. You have to go in pretty deep to start getting to these concepts, though.

 

[russ_watters]

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?

Because conservation of energy requires it isn't a good enough answer?

 

[Michael C]

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?

"WHY" questions are very hard to answer. Feynman explains just how hard it is. When asked why magnets attract each other, he explains that he can't give a simple answer. If you prefer reading a text instead of watching a video, here's a transcript.

For your particular "why" question, maybe Archimedes can help.

 

[sankalpmittal]

I said that i already know that having a longer lever on the force side of the fulcrum 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?

The most important concept is (as already typed by russ_watters in previous post) law of conservation of energy.

This law states that total energy in the system remains constant , i.e. energy can neither be created nor be destroyed.

Effort E Newtons upward
|​

<-------------------------------------|-------------------------------------------------------->
|

Fulcrum​

Load​

(Axis of rotation)​

(L Newtons downwards)​

Now I am not taking in account load arm and effort arm because lever is not in equilibrium.
Here L >>>> E , so by conservation of energy :
Work Input = Work output
L*d = E*x
(* is multiplication )
L/E = x/d
since L>>>>E , so x>>>>d

x arc >>>>>> d arc covered in circular path with Fulcrum as axis of rotation here.

So here
L* d arc = E*x arc

As work = force * displacement

By conservation of energy we get this result.

Note : We talk about like
Load * Load arm = Effort * Effort arm , when lever is in equilibrium. Longer the effort arm , more the mechanical advantage. This is principle of lever.
Obviously think logically that one guy sitting at longer distance apply force less to counterbalance because distance being more will dominate the counter force effect !Its centre of gravity will be displaced and will be posed with less friction...
(And please we neglect friction ! ) Yes ! Centre of gravity will dominate at the side of the guy sitting at longer distance.

 

[HallsofIvy]

Let's say you have a lever of length 6 m and the pivot is 2 m from the object being moved so that your end of the lever is 4 m from the pivot. As you move the lever through angle \theta radians, you will have moved your end of the lever a distance 4\theta meters. At the same time the object will have moved a distance of 2\theta meters. Since work (energy) is "force times distance" and energy is conserved, the work you do, the force you apply to the lever times 4\theta must be equal to the force applied to the object by the lever times 2\theta:
F_{object}(2\theta)= F_{you}(4\theta)
which reduces to
F_{object}= 2F_{you}
Showing a mechanical advantage of 2 to 1- the force applied to the object is twice the force you apply to the lever.

 

[Studiot]

I'm suprised no one has mentioned the link from mechanical advantage to velocity ratio and mechanical efficiency.

 

[jambaugh]

Here's a way to understand mechanical advantage in general terms. Energy is always conserved. [edit: as mentioned by Tiny-Tim]

When using any kind of pulleys or gears or levers, the power transferred through (work per unit time) is constant and so the work done over an interval is constant.

So, for example if you have a lever, applying a force F on one side and moving a distance \Delta x, it yields an amount of work \Delta W = F\Delta x
That must be equal to the work done on the other side of the lever so you get:
F_1 \Delta x_1 = F_2 \Delta x_2
You can thus use mechanical advantage to double the force but it will halve the motion.
(classic lever with fulcrum 2/3 at 2/3 the length so the two sides has a 2/3 : 1/3 or 2:1 ratio.

Apply 10 Newtons to one side and you'll get 20 Newtons on the other... however move the one side 5 cm and the other side will only move 2.5 cm.

10*5 = 20 * 2.5 = 50 Newton cm = .5 Newton m = 0.5 joules.

You can also generalize to pressures and change of volume torques and angles of rotation and also to voltage and flow of charge.

Work = force times \Deltadistance = pressure times \Deltavolume = torque times \Deltaradian angle = voltage
\Deltacharge
likewise time rate of change of work which is power is:
power = force times speed= pressure times volumetric flow rate = torque times angular speed = voltage times current.

This assumes the ideal case with 100% transmission efficiency. Friction and other loss effects will suck up some of the energy or power in an actual example.

So assume you want to lift an engine block which masses 1/2 a metric ton=500kg.
It thus weighs 500kg x 9.8m/s^2 = 500 x 9.8=4900 Newtons. (Multiply mass times gravitational acceleration to get weight as a force)

You wish to lift it 2 meters. That means you want to do 9800 Joules of work. (Joule = Newton Meter)

You can do this with a 5:1 pulley system where you pull on the rope with a 100kg lifting force (980 Newtons=1/5 the force) by pulling with that force 5 times as far (10 meters).

You can also do this with a pneumatic lift applying say 1 torr = (100,000 Pa = 100,000N/m^2 = 100,000 Joules / meter^3)
by displacing .098 cubic meters= 98000cc's.
(or use 100 torr displacing 980cc's that's a bit under 1 atmosphere pressure)

Or use a 240V electric wench which will require 9800/240 ~ 40.83Coulombs. (at 10Amps that will lift it in 4.083 seconds.)

Mechanical advantage is a matter of spreading the work out over a greater amount of motion so it requires less force. In the end though work input = work output.

Archimedes said “Give me a place to stand and with a lever I will move the whole world.” what he neglected to say was “but not very far ; ) ”

 

[mechadv43]

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?

thanks

 

[sankalpmittal]

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?

thanks

See the post of Michael C i.e. post 9 , it has link to a good site which has your answer I think.

Here is my answer :
I think you are confusing principle of lever with law of conservation of energy.

http://www.astarmathsandphysics.com/o_level_physics_notes/o_level_physics_notes_moments_the_lever_principle_html_210ae596.gif

Now see , in above image that lever is balanced at fulcrum with distance d > distance D
Now since lever is balanced , then anticlockwise moments equals clockwise moments.

Then ,
w*d = W*D
since w<W and d>D
Then
W/w = d/D
Now see that resultant force will act on the point which divides the ratio of distance "d+D" in d:D.
As we know that d> D so the resultant force will dominate at the side of distance d.
Hint : Here centre of gravity will be at midpoint of distance "d+D" that is at the side left of fulcrum in this system ! Also think about section formula of coordinate geometry.
W/w = mechanical advantage as well
M.A. = d/D
Hence the mechanical advantage will be with the small stone of weight w.

Does this help ?

Edit : Tiny-Tim thought that you were asking about law of conservation of energy in which work input equals work output. That's different matter although here it applies as its a universal law. Halls Of Ivy too answered your question in different way. jambaugh too had a great explanation.

 

[jambaugh]

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?
thanks

Meditate on the idea that Force is a Rate of work per distance. Say it out loud, "Force is work per distance!"

As I move a lever I am doing a given amount of work, since the lever transforms distance traveled it "dilutes" or "concentrates" the work per distance i.e. the force.

 

[sankalpmittal]

Refer this image : http://postimage.org/image/51wfdnhwn/

Mathematical reason :

Kinetic energy of load arm = Kinetic energy of effort arm
By this we get :\
Mass of load/Mass of effort =Inverse Ratio of square of velocities
By image we get
Mass of load = 4 times mass of effort
As velocity of effort is twice the velocity of load
So Velocity ratio = 2
For an ideal machine
Mechanical advantage = Velocity ratio
So
Load = twice of effort
From this we can get that acceleration in effort is twice of load.

Also power input = power output
or work input equals work output
So greater the arm less is required force for lever to be in equilibrium.

Theoretical reason : Since angle θ is same in both triangles (see image) and base of effort side is double of base of load side then its obvious that effort arm will cover greater arc distance than load arm. Since work input equals work output , we have to say that effort must be half of load for same work distance. Less mass more acceleration. Also note arc distance by effort is twice of that of load ,as ratio has to be maintained. Also note that initially both arms are at rest.

 

[JHamm]

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?

 

[jambaugh]

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]

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]

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]

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]

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 possesses kinetic energy. This in turn sets load arm in upward motion , and so it also must possesses 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]

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]

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]

. . . . .
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 textbook 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]

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]

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]

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]

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]

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 !

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]

He wants to analyze molecular interactions ?

No, he does not:

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

I meant force though, can it be explained in plain english as opposed to just a formula why being further uses less force?thanks

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]

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,

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]

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]

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]

didn't robert frost write a poem on how going a shorter distance gives a greater force? …

i took the path less travelled

and that made all the difference​

 

[sophiecentaur]

There are some things which just do not have explanations within a limited set of knowledge. One can't just 'demand' the terms that can be used.
No one would try that sort of thing with Maths or Software so why assume it can work with Physics?

 

[kjamha]

First off, I want to apologize for not being as technical as I should be, but I'll do my best. Let's say your kid brother is on a see saw and he weighs 100 lbs. In order to raise him up 4', you need to push down your end of the see saw with a force of 100 lbs for 4 feet. Think of pushing down on your end of the see saw for 4 feet as a certain amount of energy that you need to exert. No matter what, if you want to raise your kid brother up 4', you need to exert that amount of energy. If you double the length of your end of the see saw, you can stretch out the amount of energy that you need to expend, it will be easier because you will push down with a smaller force - if fact, you will only have to push down with half the force, but it will take twice as long (you now need to push down for 8'). You still deal with the same amount of energy, but you don't have to exert all of that energy so quickly. You can spread it out - thin it out.

 

[zoobyshoe]

OK, mechadv24, I think I have figured out a good explanation of why distance from the fulcrum makes a difference without the use of any formulas and also avoiding any mystifying reference to "force multiplication". The explanation is a comparison of three different simple situations, and I even drew pictures:

Fig. 1

Figure 1 illustrates a stone block of weight 50 lbs supported on a massless board resting on two supports The board is understood to be level with the horizon, and the stone block is located with its center of gravity exactly over the center of the board. The board is exactly centered on the two supports. The stone block is of uniform size and density such that its center of gravity is congruent with its center of volume.

All these things being true, we should be able to conclude that each support bears exactly one half the 50 lb weight of the stone block, that is: 25 lbs per support.

Since each support bears half the weight, any thing substituted for one of the supports will also bear half the weight. If we substitute a man for one of the supports, that man will be maintaining a 50 lb weight off the ground by supporting 25 lbs of it himself and letting the other support bear the other 25 lbs.

The man might, then, lift or lower the 50 lb weight by what ever distance the other support allows, by only manipulating 1/2 of it himself. This is a second class lever (click and check out the little animated second class lever) :

http://www.elizrosshubbell.com/levertutorial/second.html

Fig. 2

In figure 2 the stone block has been pushed all the way over to the right. Its center of gravity is now directly over the center of the right hand support.

In this position the right support is bearing the full weight of the block. The left side support is holding none of the block. To prove this, we could remove the board, and the block would rest on the right hand support and not fall.

If the left hand support is holding none of the weight, then any thing we substitute for it would also be holding none of the weight. Likewise on the right. Any thing we substitute for the right side support will be supporting all of the weight, 50 lbs.

A man substituted on the left would be holding none of the block, and a man substituted on the right would be holding the total weight of the block.

Fig. 3

In figure 3 we have moved the block to a place between the positions illustrated in figures 1 and 2. Since the right hand support bore 1/2 the weight in fig. 1, and bore the full weight in Fig. 2, it must now, logically, be bearing something between half the weight and the full weight, based exclusively on the fact the block is now resting between the the two former positions.

By the same logic, the left hand support must now be bearing something between half the weight and none of the weight.

And, any thing we substitute for either support will be bearing the same fraction of the weight borne by the support it replaces.

If we put a man over onto the right, he will be supporting more than half of the weight but less than the full weight. If we substitute a man for the left hand support, he will be supporting more than none of the weight, but less than half of the weight.

The exact proportions are exactly what you'd think, but it is only necessary to show that the placement of the stone alters what each support must bear. We can arrange it, as I've shown, that both bear the same amount, or that one bears the full amount while the other none, and we can arrange for everything in between. As we push the block closer and closer to the right hand support, that support bears more and more of its weight. (Because if it doesn't, then there must be some threshold, some point where it suddenly changes from bearing half the weight to all of the weight. If you can prove there is such a threshold, why it should exist, and where it is, I think we'd all be amazed.)

As I said, this is a second class lever. We can turn it into a first class lever: If we lengthen the board in Fig. 3 past the right hand support by an amount equal to the distance between the center of gravity of the block and the right support, we can put the weight out onto this new extension, and a man over on the left will now have to press down with 1/4 the weight to sustain the weight. And, we will have turned the second class lever into a first class lever (Fig 4):

As before, the sturdy fulcrum is really providing most of the support (3/4 of it in this case) and the weight or person on the left must now push down where before they pushed up.

In conclusion, having viewed the weight on supports as a second class lever, and then having turned the second class lever into a first class lever, I hope I have demonstrated why the distance from the fulcrum at which the force is applied makes a difference. The lever is analogous to a weight resting on two supports, and, the relative distances of the supports from the center of gravity of the weight determine what fraction of the total weight a given support of that weight must bear. This same relationship follows in some way, shape, or form into the lever proper, and into all examples of mechanical advantage in all its manifestations.

 

[sophiecentaur]

The above is all fine but it makes the basic assumption of the Principle of Moments from the start - it's just not explicit. WHY should there be an equal share in the first example?
'Stands to reason', or the principle of moments?
Also, it involved an awful lot of writing and diagrams.
The point of expressing things in the way the Physics does is that it gets it all into just a line or two of argument / explanation - probably with some of the ultimate shorthand -Maths. We have been heading that way since Galileo's time, with good reason.

 

[JHamm]

But the OP doesn't want to just know that it IS true, I'm sure (s)he already knows that, what they're after is an explanation on how it can be true, what makes it true; while a few lines of maths is the best way to show that something is true, it doesn't make a very convincing statement about how or why. In this case the only way to explain to the OP what they're after is through diagrams because that is really what they're asking for.

 

[tiny-tim]

i'm with zoobyshoe on this

the original question was …

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

… why does being further away make it easier?

zoobyshoe points out that if you're far enough away (but not too far! ), then the force needed is exactly zero …

it follows logically that in between, the force needed will be less, but not zero

i think that's a very good answer! ​

 

[sophiecentaur]

But the OP doesn't want to just know that it IS true, I'm sure (s)he already knows that, what they're after is an explanation on how it can be true, what makes it true; while a few lines of maths is the best way to show that something is true, it doesn't make a very convincing statement about how or why. In this case the only way to explain to the OP what they're after is through diagrams because that is really what they're asking for.

I can appreciate this to an extent but this concept of 'understanding' is actually not much more than reconciling a new idea with our already established ones. There is an enormous temptation to assume that the familiar is 'obvious, per se, and that the next step along the road is different. It's not; it's just not familiar yet.
A lot of people post questions on this forum which ask for explanations and there are always a lot of contribution answers that involve highly personal and quirky models. These sorts of answers can come from all sorts of directions which may be nothing like the start point of the original questioner's understanding. The more involved the answer, the more chance of it being taken 'wrongly' - and that could be wrong, either in the comprehension of what the contributor meant or actually wrong, because the Science is flawed.

Why is it that Maths is used so often in 'conventional explanations'? It's because there is least risk of misinterpretation. There is a common standpoint for both the asker and the responder. As Feynman frequently said (and he is GOD on this forum) - there are no real answers to the "WHY" question. There are levels of explanation available which can satisfy different levels of scrutiny.
If someone tries to give an answer to a 'why' question, they are duty bound to give a caveat ("this is my interpretation") unless their answer is straight out of some reputable source.

So, the idea of moments can be discussed with maths OR with arm waving BUT neither discussion will yield a totally bomb proof "why" answer. The best it can do is to satisfy the questioner in some way. However, the Maths answer will allow the questioner to extend the knowledge further but the arm waving one cannot be relied on to do so; it may totally lack substance.

A caveat, here. Maths is only a model, of course and can yield nonsense results if it isn't interpreted appropriately. That even applies to some very simple situations.

 

[sankalpmittal]

Ok , zoobyshoe ,

Here are the answers which I have figured out (which involve reasoning which I hope OP has been looking for) :

ANSWER 1 :

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.

http://postimage.org/image/i5170vxjr/

ANSWER 2 :

All I can ask you is to meditate the idea of force (as said by jambaugh) which is work done per unit displacement ! What if you have lighter body and heavier body in which you are doing equal work. Obviously you apply less force on lighter one. Hence in case of lever , work input equals work output. Greater arm covers more arc distance so you apply less force and vice versa in case of shorter arm. (Why ? same analogy... where you return to relative masses on which force due gravity is acting which is mg and yes , arm distance is directly proportional to arc distance covered by corresponding lever arm.) Edit : Please anyone reply whether I am correct or not ! I have been posting this post thrice in this thread ! xD

 

[zoobyshoe]

Ok , zoobyshoe ,

Here are the answers which I have figured out (which involve reasoning which I hope OP has been looking for) :

ANSWER 1 :

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.

http://postimage.org/image/i5170vxjr/

ANSWER 2 :

All I can ask you is to meditate the idea of force (as said by jambaugh) which is work done per unit displacement ! What if you have lighter body and heavier body in which you are doing equal work. Obviously you apply less force on lighter one. Hence in case of lever , work input equals work output. Greater arm covers more arc distance so you apply less force and vice versa in case of shorter arm. (Why ? same analogy... where you return to relative masses on which force due gravity is acting which is mg and yes , arm distance is directly proportional to arc distance covered by corresponding lever arm.)


Edit : Please anyone reply whether I am correct or not ! I have been posting this post thrice in this thread ! xD

The only real objection I had to your previous posts was bringing kinetic energy into it. You know Occam's Razor? "Entities should not be unnecessarily multiplied." The fact the arms have kinetic energy was an unnecessary complication in sorting things out.

What you posted above is fine with me, but I already understand it. Mechadv24 has some sort of interesting mental blind spot that prevents him from grasping it with the usual amount of explanation.

It's off topic under the present circumstances, but it occurred to me there probably is a real situation where you might want to analyze a lever in terms of kinetic energy, and that would be if you were making a trebouchet:

http://en.wikipedia.org/wiki/Trebuchet

where you want the kinetic energy of the long arm and its sling to be maximized. I haven't thought that through yet, though.

 

[jambaugh]

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.

When did the OP last post? Are you sure his question has not yet been answered to his satisfaction?

 

[zoobyshoe]

When did the OP last post? Are you sure his question has not yet been answered to his satisfaction?

This was his last communique:

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.

In other words, he's provisionally accepting it on faith.

 

[sankalpmittal]

When did the OP last post? Are you sure his question has not yet been answered to his satisfaction?

No I am not. The OP's question has been answered several times in this thread. I gave my answer in post #44. zoobyshoe gave the answer in post #39. But the main problem is that OP is finding those answers unsatisfiable though. He wants something else but I don't know anyways.

My answer in post 44 is more theoretical and reasonable than mathematical which I hope OP has been looking for. I think my answer is easily understood here because its purely physics and yes , there are no absurd complications inserted like kinetic energy (*types this sentence being addressed to zoobyshoe particularly*). In that answer , I have used only correct and well permitted terms to avoid misunderstanding and wrong judgments.

 

[mechaadv43]

I'm pretty sure zoobyshoe's post made it click for me. i need to digest the concept a little more to be certain for myself, but that's all i was wondering. thanks for drawing that all out instead of just like MS paint.

 

[zoobyshoe]

I'm pretty sure zoobyshoe's post made it click for me. i need to digest the concept a little more to be certain for myself, but that's all i was wondering. thanks for drawing that all out instead of just like MS paint.

Well, that's good news. Let me know if you hit any more snags.

I draw all the time so that's my preferred way of tackling it. Paint would have been foreign to me.