Thread: Calculating weight on fulcrum points

I was going to upload a picture but I couldn't, so I'll have to get creative.
This problem has been driving me nuts, and I don't really trust my answer. The question is, How much weight is on fulcrum A and Fulcrum B? I get 1380lb. for fulcrum B and 620 lbs. for fulcrum A. Is that correct?

Information: The block is 40 inches long. Fulcrum A is situated 2 inches in from the edge. Fucrum B is 12 inches in from the edge. That leaves 26 inches between the two fulcrums because the block is 40 inches long. The block weighs 2000 pounds. The two I's would be the fulcrums. In real life, the block is 3 dimensional, but I hope this picture makes sense.

0000000000000000000000000000000000000000
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-----------2000 pound concrete block----------------0
0-----------(this block is 40 inches long)--------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0000000000000000000000000000000000000000
....I............................................. ....I....................................
fulcrum A----------------------------fulcrum b

Originally Posted by SteveC

I was going to upload a picture but I couldn't, so I'll have to get creative.
This problem has been driving me nuts, and I don't really trust my answer. The question is, How much weight is on fulcrum A and Fulcrum B? I get 1380lb. for fulcrum B and 620 lbs. for fulcrum A. Is that correct?

Information: The block is 40 inches long. Fulcrum A is situated 2 inches in from the edge. Fucrum B is 12 inches in from the edge. That leaves 26 inches between the two fulcrums because the block is 40 inches long. The block weighs 2000 pounds. The two I's would be the fulcrums. In real life, the block is 3 dimensional, but I hope this picture makes sense.

0000000000000000000000000000000000000000
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-----------2000 pound concrete block----------------0
0-----------(this block is 40 inches long)--------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0-------------------------------------------------------------0
0000000000000000000000000000000000000000
....I............................................. ....I....................................
fulcrum A----------------------------fulcrum b

You are close. I get B= 36000/26 which is close to 1380. A is of course 2000-B.

Yes, the answer is indeed 36000/26 pounds for B. I see how you did that now. When I calculated it, I didn't carry out my decimals far enough, and writing the answer as a fraction is the "correct" answer anyway.

How certain are you that we got it correct (well, I almost did), because for some reason I still have some doubt.

if I'm not mistaken, it will resemble something like everything beyond the fulcrum plus everything up to halfway between the fulcrums goes to one, while the other half between them and beyond the other fulcrum goes to that other fulcrum. Right?

if I'm not mistaken, it will resemble something like everything beyond the fulcrum plus everything up to halfway between the fulcrums goes to one, while the other half between them and beyond the other fulcrum goes to that other fulcrum. Right?

No, the method the Dr. and I used involved looking at the block's center of gravity and where it lied between the two fulcrums. The blocks center of gravity would lie 18 inches from fulcrum A, and 8 inches from fulcrum B. 8+18 is 26. So fulcrum B would share 18/26 of the weight, and fulcrum A would share 8/26 of the weight.

Let me show you why your reasoning is false. Imagine one fulcrum point was directly in the middle of the block, and the other fulcrum was at the very end of the block. (it doesn't matter which end) Then you would assume that one fulcrum holds 3/4 of the weight and the other holds 1/4 of the weight. Well, this would obviously not be true because the fulcrum in the center would be holding ALL the weight.

Originally Posted by SteveC

Yes, the answer is indeed 36000/26 pounds for B. I see how you did that now. When I calculated it, I didn't carry out my decimals far enough, and writing the answer as a fraction is the "correct" answer anyway.

How certain are you that we got it correct (well, I almost did), because for some reason I still have some doubt.

I am absolutely positive. I can derive it. It is just a matter of showing that both the sum of the forces and the sum of the moments are zero.

wow... That was a bad mistake on my part, thanks for the correction.

Cool, I'm glad we've got this figured out then.

In case anybody didn't understand what DrRocket meant by the sum of the moments, I'll explain. Moment is another name for torque. If you consider the torques about fulcrum A, there is a torque exerted by the weight of the block acting at the center of mass a distance of 18 inches from A, so the torque is 2000*18. This is balanced by a torque in the counterclockwise direction exerted by Fb at a distance of 26 inches from A. So Fb=2000*18/26.

Fulcrum is eighteen inches from the center of the block and fulcrum is eight inches from the center of the block, and the sum of the weight of the fulcrums is proportional to the weight of the block, such that . This means that the ratio of the weight held on fulcrum is , and that of fulcrum is . We can find the weight of fulcrum through the following algebraic expression based on the previous information than and the weight of fulcrum through the expression , which results in and .

Oh wehh.. I heard fulcrum now, the last i heard it is when I was college..

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