# Question about lever



## NiGHTS (Mar 10, 2020)

Hello.

Attached is an image of a simple lever with a two weights *13 lb* and *1.5 lb* on a lever weighing *12 lb*. I've calculated the center of gravity of the entire thing to be *54.62"* from left. What I am trying to figure out is the weight of the far right-hand end of the lever when the fulcrum is *26.5"* from left.

Any help is appreciated! Thank you.


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## Edgy Cheesy Graphite PE (Mar 10, 2020)

You say you're trying to figure out the "weight of the far right-hand end of the lever when the fulcrum is 26.5" from the left". What I think you mean is what the reaction force right there would be if there was a support there? The weight of the lever is the weight of the lever, it doesn't change, but the reaction forces supporting the lever (which is how hard the lever is pushing down at specific points .... which equal how hard the supports are pushing back up) vary by location.

But that's semantics. It's a pretty simple problem. You have to take the sum of the moments about a point, and that sum of moments have to equal zero. But to do that you must know the distance to the far right location, I think that's the 204", but not 100% sure from the picture. If so just take the sum of the moments about the fulcrum.

Sum Moments: 0 = 13 lb * (26.5"-3.5") - 1.5 lb * (118.7"-26.5") - R * (204"-26.5")    _*error because this equation doesn't include the weight of the level*_
Solve for R

I've written the equation assuming R is going down (as drawn), if the value is negative, then R is in the opposite direction as the assumption (up).

I hope this makes sense.


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## NiGHTS (Mar 10, 2020)

Jean, I highly appreciate your intricate reply.

I will start by saying that indeed my ability to explain this problem is limited by an incomplete formal education on the subject of mechanical engineering, to which I soon hope to satisfy time permitting. In the meantime this question I've introduced to you is a simplified example of a real-life issue I am trying to find a solution for. That being said and after reading your response, I will attempt to clarify my original post.

I read about "reaction force", though I am having a hard time relating that term to my "weight" question. I would appreciate if you could help me relate it better; I'm interested in learning about it!

I've attached another image. This time hopefully less confusing. At the far right side is an imaginary scale and I am interested in predicting what it will measure given the following criteria. The lever itself weighs 12 lb and is 204" in length. Your formula seems to indicate that the lever's center of gravity is at 204", though it's actually at 102". Does changing the last factor in your formula to R * (102"-26.5") make it so that solving for R will accurately predict what will appear on the scale?

Also, note the length of the green weighted object. Though I don't mention it in my drawing, does its distributed weight affect this prediction? I've only included its center of gravity as I assume that is enough. Am I wrong in this assumption?

Again, your help has been incredible and I egarly await your response!


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## Edgy Cheesy Graphite PE (Mar 11, 2020)

Ah, I misunderstood the original diagram, so I didn't include the weight of the lever at all.

Here's the corrected equation:

Sum Moments: 0 = 13 lb * (26.5"-3.5") - 12 lb * (102"-26.5") - 1.5 lb * (118.7"-26.5") + R * (204"-26.5")  
Solve for R.
R is the reaction force at the right side at the scale. The force that the scale is pushing up with which equals the weight the lever is pushing down with.

To give a more thorough explanation, it would helpful to have some background on your knowledge level. When I have more time, I'll try to post a more complete explanation.


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