balance beam question
balance beam question
(OP)
I have a balance beam question. See sketch. with the beam supported in the middle and a weight hung across it approximately 24" long. the left side drops down roughly 1/2". Is there a way to calculate the weight difference from one end to the other? Even if it is only a ratio. total weight is unknown.





RE: balance beam question
Sure, simple statics 101.
RE: balance beam question
How do you account for the fact that it isn't in equilibrium? How do you take into account that the bar tilts 1/2". Obviously if the bar tilts 1/2" with this uneven load, but say an 1" with another uneven load, how do you calculate the weight from side to side.
RE: balance beam question
Regards,
Mike
RE: balance beam question
Engineering is the art of creating things you need, from things you can get.
RE: balance beam question
RE: balance beam question
RE: balance beam question
RE: balance beam question
The green represents the weight being measured. The grey portion represents the balanced beam that hangs perfectly level when nothing is hanging from it. When the green object is hung from the beam, the system tilts 1/2" down on the left side. So the green object which appears to be balanced, is not actually balanced. There is more weight on the left side. How much more weight is on the left side? If the object weighs 10 lbs and it was balanced, then each side of the beam it hangs from would be seeing 5 lbs. Since the left side drops 1/2" the weight must be something like 7 lbs left and 3 lbs right? I would assume that if it was 8 lb/2 lb then it might drop say 1" and if it was 6 lb/4lb it might drop 1/4"?
What we are trying to figure out is that since all we know is that the left side drops 1/2" what does that mean the weight is on the left compared to the right?
Thanks
RE: balance beam question
RE: balance beam question
RE: balance beam question
you've got W2 = the weight of the green stuff, CG2
you've got (courtesy of Bradley) the total CG is -0.0208, so that W2*CG2 = -0.0208*(W1+W2) ... CG2 = -0.0208*(W1+W2)/W2
now if you want to express this as Wl = the weight of W2 on the left of the balance and Wr, the weight on the right, then
Wl+Wr = W2 and Wl*CGl+Wr*CGr = W2*CG2
and you can see you can't solve this without assuming something ... like CGr = -CGl = L/2
RE: balance beam question
Balancing that is 12*d where d is the difference between the left and right load.
So 12*d = W*e/48
and d = W*e/576
BA