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

[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 until it breaks.

 

[zoobyshoe]

TY all, I'm not thinking clearly lately. Simply, the weight sits on the fulcrum and i just have to move my proportion (plus pivot friction).

Yes! You are basically dividing the weight into four parts (in my drawings) and you only have to deal with one part yourself. The fulcrum bears the weight of the other 3/4.

Lifting the full weight 1/4 the distance you push is the same as lifting 1/4 the weight the full distance you push. The advantage of the lever is that it let's you handle the weight a quarter (or whatever fraction) at a time instead of having to lift the whole thing the whole distance all at once. In the end, you have done exactly the same amount of work, so there's no net gain.

experaments like nail and crowbar also use a big other factor of concentrating my force into a small area around the nail, which is easy to understand.

Yes. You are dividing the work it takes to pull the nail between yourself and the wood near the nail where the hammer presses down. The nail is the "weight" and you are making the board bear most of it while you apply some fraction of it. And, the force on the hammer comes out the other side as a much larger force on the nail because the distance over which it's applied is much shorter. It's been "concentrated" into a smaller distance.

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 until it breaks. most of the force is just figting the 'spring' too.

Yes. And the falling part of the tree, itself, becomes both lever and applied weight (force). The length of the tree (from fulcrum to center of gravity) vs the length of the cut is described by the Law of the Lever.

Now, having gone this circuitous route, I sudden thought of the ultimate "intuitive" demonstration that distance from the fulcrum matters, and kick myself for not having thought of it first:

Stand up and put your feet about a foot apart. Slowly shift your weight to one side until all your weight is on one foot. You will be able to physically feel the pressure gradient in your feet as one foot bears more and more of the weight and the other less and less. It's directly tied to the distance of your center of gravity from either foot.

It's so obvious I couldn't see it, but everyday physical experiences like this are why most people automatically "get" why the distance from the fulcrum makes a difference as soon as they hear it said.

 

[mechaadv43]

uh, I'm so confused still. sorry to be a burden with my apparent stupidity (unless what I'm trying to 'get' isn't all that simple.i might take an iq test when i figure this out to hopefully find I'm not as dumb as i feel!) Formulas don't help me much, but I understand the concepts now. It's something i need to 'get' out on my own, but hoping it can be guided. this isn't a big joke, i don't get it still.
I'm drawing a blank on a simple experament:
A large tupperware box & a container of cat litter tied to the end of a 7 foot pole.
Putting the pole on the tuperware and sliding the pole to and fro.
-when the distances of my hand and the litter to the box are equal, I'm pressing as hard as the litter weighs. that's very easy to understand.
-when the litter's closer to the box than my hand, it's easier to hold.
-When my hand's close to the box and the litter is far, I have to press down like 10X the weight of the litter to lift it. Lifting it the hard way seems will be easier for me to understand.

 

[zoobyshoe]

uh, I'm so confused still. sorry to be a burden with my apparent stupidity (unless what I'm trying to 'get' isn't all that simple.i might take an iq test when i figure this out to hopefully find I'm not as dumb as i feel!) Formulas don't help me much, but I understand the concepts now. It's something i need to 'get' out on my own, but hoping it can be guided. this isn't a big joke, i don't get it still.
I'm drawing a blank on a simple experament:
A large tupperware box & a container of cat litter tied to the end of a 7 foot pole.
Putting the pole on the tuperware and sliding the pole to and fro.
-when the distances of my hand and the litter to the box are equal, I'm pressing as hard as the litter weighs. that's very easy to understand.
-when the litter's closer to the box than my hand, it's easier to hold.
-When my hand's close to the box and the litter is far, I have to press down like 10X the weight of the litter to lift it. Lifting it the hard way seems will be easier for me to understand.

Sounds to me like your experimentation exactly agrees with the formula.

 

[mechaadv43]

i meant don't understand the formulas.

 

[zoobyshoe]

i meant don't understand the formulas.

Do you want to?

 

[eapst28]

The same amount of work is done. Displacement of the bar at the far end is, let's say 3x, and displacement at the work end is only x. Therefore you can move more mass on the "x" end and the same amount of work is done at both sides.

 

[mechaadv43]

ha, i finally get it. doing it the hard way helped. if the weight is say 6 feet from the fulcrum and my end only has to be pushed down 4 inches to make it level, then all the energy needed for the weight to go up about a foot and a half is = to the energy i need to push my end down only 4 inches, thus I push harder, but for less distance. The fact that advantage end moves a larger arch/distance was almost unbelievable with only a 7 foot pole, it's harder for me to realize it, it's easier for me to see when I took the spot right past the pivot.

 

[zoobyshoe]

ha, i finally get it. doing it the hard way helped. if the weight is say 6 feet from the fulcrum and my end only has to be pushed down 4 inches to make it level, then all the energy needed for the weight to go up about a foot and a half is = to the energy i need to push my end down only 4 inches, thus I push harder, but for less distance. The fact that advantage end moves a larger arch/distance was almost unbelievable with only a 7 foot pole, it's harder for me to realize it, it's easier for me to see when I took the spot right past the pivot.

Excellent! You see the trade off in distance and force!

Technically what you're pushing down with is not 'energy' but force. The weight on the other side is also applying force. Getting on the wrong side allowed you to actually feel how much force the other side exerted being 6 feet from the fulcrum. That was a good idea to try.

 

[mechaadv43]

oh, i thought it was considerd 'energy' only because i brought the weight to a level standpoint.
Anyway, using no weight at all was also simpler.just took a broom stick and put all but 3 inches over a pivot that was high off the floor, then pushed down on the short 3 inch side only about 2 inches and the other side went up like 4 feet to make it level. Another thing, if i put a lever under a couch sticking under 2 inches from the pivot but my lever end is 4 feet from the lever, i can make the couch go up about an inch very easily, but i in no way lifted the couche's full weright untiill it's totally off the ground, i just used the same force it would take to lift the couch an inch, plus pushing down on a lever is easier than bending over and pulling up on the couch. it's elementary to me now, just wasn't thinking straight. TY

 

[zoobyshoe]

I think the moral of the story is, "Mechanics is something you should try at home."