Sparky - 23-5-2005 at 11:43
I'm having some problems trying to fix a triple beam balance that I have. It's a conceptual problem - I can't figure out what is wrong
with it. Maybe I got carried away with trying to find the problem, but I can't figure it out.
I obtained a balance for free some time ago, but it is missing the 10 gram slider. So, I have attempted to make a 10 gram slider. I cut a piece of
brass and wrapped a copper wire around it. This mass hangs from the 10 gram bar, and acts as the slider.
I have adjusted the balance by changing the mass of the homemade slider, and by using the calibration screw. Now when all the sliders are at 0, the
scale reads 0. However, upon attempting to weigh something, I find that I do not get accurate results. They appear appear fairly precise though. The
scale tilts well, and doesn't appear to be broken in any way than having the slider missing (well, now it is replaced by a homemade one)
To examine the balance I decided to collect a set of data. I found the mass of an erlenmeyer flask, using a scale I trust. Then I put this erlenmeyer
on the balance and took a number of readings, putting in 50 ml of distilled water each time.
I examined the data and made a graph. I recorded the "actual" mass as that which I weighed with the trusted scale, and assuming that in fact
50 grams was added each time. The set is small, but it shows something:
http://pigscanfly.ca/pyropage/DataSet1Graph.gif
There is a cyclic trend, that is the error depends on if the slider is at the 20 mark or the 80 mark. I don't know what to do about this though.
It seems to me that the only parameter here to change is the mass of the slider. But if I do that, it will upset the 0 reading. So what to do? I
searched for manuals and information online but didn't find any addressing my problem.
Things I can see from the data are that the deviance from the accepted values becomes smaller (in absolute magnitude) as the mass measured grows. That
is, as I added more water, the readings of the scale became closer to the accepted value (and not just by percentage). The error becomes smaller,
but, as one would expect, not linearly.
As the slider is moved farther out, it seems the error is more than closer in. There isn't really enough data to show this for sure, (only two
points) but I am guessing it is the case.
So, there are distinct trends here, but I don't know what to make of them. Any ideas?
12AX7 - 23-5-2005 at 12:02
Hmmmm...maybe it hangs wrong? If it has the same mass as the original slider, there's no reason it shouldn't work now.
If you change its mass and change the zero reading, can't you balance that with a tweak on either side of the fulcrum?
Or just make a quickie new one. Pennies are 2.5 grams and nickels 5g.. 
(No kiddin- I have several 500g lead weights calibrated by smaller weights calibrated by pennies and nickels. They are all within 1%, and all with my
homemade scale.)
Tim
Sparky - 23-5-2005 at 15:56
Thanks for your reply, 12AX7.
I wanted to have a scale accurate to .1 grams, so using pennies in a balance scale isn't really any good for me. I already have a kitchen scale
accurate to 1 gram.
I fiddled around with the scale somewhat and found my answer. I haven't done an analysis to see exactly what the physics are behind the
situation, but I found empirically how to fix it.
There are really only two parameters to change, so I figured I should change them and see what happens.
I found that by having the 10 gram slider be heavier, the reading on the balance (of a known weight) went down. Of course in order to balance the
heavier slider at 0, the calibration screw had to be moved out more too. The thing is, that with the screw moved out fully, the slider was not heavy
enough - the scale still gave a reading above the actual value. So, I had to add weight (copper wire) to the screw side. Then add weight to the slider
side... I continued this until I achieved a reading whereby both the 0 setting and the known weight gave good readings. Testing it against my trusted
scale showed it to be accurate.
12AX7 - 23-5-2005 at 16:04
If you're too lazy to sit down with a pad and pencil and do the math, nothing beats the imperical method 
Physics is a simple torque problem (when unbalanced, it doesn't just move, it accelerates to a new position), in a regular scale the forces are
varied but yours has variable radius well. Tau = F cross r, when torques are equal, angular acceleration is zero. When unbalanced it will accelerate
to a new (stable) position depending on the method attaching to the beam. (This can be seen because the force vectors tilt closer to the radius,
reducing the acceleration. Likewise, if the vectors are attached above the fulcrum, it will be unstable (a change in position changes the
equilibrium) and as such very sensitive.)
Tim