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How to calculate the mechanical advantage of a lever?

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  • How to calculate the mechanical advantage of a lever?

    How do you calculate the advantage or the difference in power or lifting force of the two different lever systems in the picture?

    If you click on the picture it shows a bigger picture.
    How to become a millionaire: Start out with 10 million and take up machining as a hobby!

  • #2
    I think this is what you are looking for.

    https://www.engineersedge.com/calcul...ver__14631.htm
    My recommendation?

    No matter what I tell you, get a second opinion.

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    • #3
      Ratio of fulcrum to force and fulcrum to load.

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      • #4
        Same advantage, different direction. Just the ratios of the distances to the fulcrum as Jim said.
        Richard

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        • #5
          Originally posted by rohart View Post
          Same advantage, different direction. Just the ratios of the distances to the fulcrum as Jim said.
          Not the same. Move the fulcrum to the midpoint and it will be obvious that it's not the same.

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          • #6
            In one case it is a straight ratio, in the other there is an additional "1" in there...

            If the lever is 9 units long, fulcrum 1 unit in, then you have in one case 8:1, but the other case you have 9:1.
            1601

            Keep eye on ball.
            Hashim Khan

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            • #7
              You could use moments, simple force x distance clockwise, equals force x distance anti-clockwise, fulcrum is the datum or where moments are calculated about.
              (Works really well with beams and cantilevers, saves going all bows notation and vectors, though levers can be treated as vectors instead of scalars, ie magnitude and direction)
              More than one way to do most things though memory is fuzzy about it!
              Mark

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              • #8
                Jim Williams stated it succinctly. His explanation can be treated in scalar or vector form as well!

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                • #9
                  It is a simple ratio, as Jim Williams suggested. But you have to null out the difference in the weight of the lever on either side of the balance point as you change the balance point. Making the lever lightweight minimizes the need to do this, but there is still an error. Marv Klotz may have a formula that includes this factor, I don't know. I know that this leverage idea is great for weighing heavy things with a bathroom scale. It doesn't take a lot of figuring to set the position of the balance point to say 1 to 10. Every 100 you read on your scale is then 1000- lbs or kgs, doesn't matter.

                  As I can see it, it's a matter of the ratios plus the balancing of the lever.
                  I seldom do anything within the scope of logical reason and calculated cost/benefit, etc- I'm following my passion-

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                  • #10
                    I found the math online and lo and behold it is the same force required for both as long as the spacing is the same. Thanks for the help.
                    How to become a millionaire: Start out with 10 million and take up machining as a hobby!

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                    • #11
                      Same force, except gravity helps you a "little" bit with the red one, and fights you a "little" bit with the blue one due to the weight of the lever itself.

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                      • #12
                        Shouldnt be the same force. The ratios are different.

                        Ed
                        For just a little more, you can do it yourself!

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                        • #13
                          So many things that factor in - and like Darryl stated the weight of the lever is everything - technically the red diagram might lift the weight itself just with the lever - and assuming the lever is made of the same thing the blue might take double the effort than just lifting the weight without even figuring in the leverage ratios...

                          and why does the blue have an unusable hole drilled in it?

                          but for strictly ratio's sake - measure the amount of travel that the handle end moves, in comparison to the amount the weight gets lifted - done deal,

                          keep in mind even if you get identical there's also a friction formula as not all fulcrums and pivots are created equal and some have more "bearing speed" and pivot travel in comparison to others even though it "appears" that the work load is identical...

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                          • #14
                            Originally posted by A.K. Boomer View Post
                            So many things that factor in - and like Darryl stated the weight of the lever is everything - technically the red diagram might lift the weight itself just with the lever - and assuming the lever is made of the same thing the blue might take double the effort than just lifting the weight without even figuring in the leverage ratios...

                            and why does the blue have an unusable hole drilled in it?

                            but for strictly ratio's sake - measure the amount of travel that the handle end moves, in comparison to the amount the weight gets lifted - done deal,

                            keep in mind even if you get identical there's also a friction formula as not all fulcrums and pivots are created equal and some have more "bearing speed" and pivot travel in comparison to others even though it "appears" that the work load is identical...
                            The blue has the same holes as the red. I just modeled one and copied it.
                            How to become a millionaire: Start out with 10 million and take up machining as a hobby!

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                            • #15
                              An additional one? I think I know where you got that, but there is no reason to add that complication. If you measure FROM THE FULCRUM to points where you have the LOAD and the FORCE, then it is a simple ratio of those two lengths, as has been stated several times already.

                              You are talking about a lever with TWO assumptions: 1. the length of the lever is fixed (9 in your example) AND 2. the distance to the load is fixed at ONE. If you place those TWO constraints on the levers, then yes, you will get different ratios and different mechanical advantages. BUT, the simple ratios of the two distances are still the way to calculate the 8:1 and 9:1 ratios that you cite. If you just follow that simple rule, you will get the correct result for ALL types of lever.

                              It IS a simple ratio. You just must measure your distances correctly in each case.



                              Originally posted by J Tiers View Post
                              In one case it is a straight ratio, in the other there is an additional "1" in there...

                              If the lever is 9 units long, fulcrum 1 unit in, then you have in one case 8:1, but the other case you have 9:1.
                              Paul A.

                              Make it fit.
                              You can't win and there is a penalty for trying!

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