Help Me Understand Mechanical Advantage Please

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. Lets 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/lever...al/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 …
… 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

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

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

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

zoobyshoe

This was his last communique:

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

sankalpmittal

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

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.

mechaadv43

TY all, i'm not thinking clearly lately.
Simply, the weight sets on the fulcrum and i just have to move my proportion. the wight is also tranfered into the lever, as example, if i push a seasaw that's weighted on one side: if i push it from the end, there's more weight stored in the lever as opposed to if i push if from right next to the pivot.

got confused with experaments like nail and crowbar because they also use a big other factor of concentrating my force into a small area around the nail which i overlooked. Or for cutting a tree half way at the base then pulling it down from the top. once the tree's pulled past its 'spring' the force goes into the cut and the wood itself becomes the fulcrum untill it breaks.