As an American, you should know that symbol lb is sometimes used for force too. Or maybe you shold do some research yourself. See [en.wikipedia.org]Quote
nitewing76
Quote
hercek
Claim 1 of the document:
The last column of the table specifies unit as lb/in² for 1" wide belt.
Claim 2 of the document:
Note 7 specifies the formula for the belt elongation computation as BeltElongation = (BeltLength * TensileLoad) / TensileModulus.
Lets specify what should be the units for all the terms of this equation except the TensileModulus:
Lets put the units into the equation and derive the unit for their TensilaModulus:
- for BeltElongation it is in
- for BeltLength it is in
- for TensileLoad it is lb
in = (in*lb)/TensileModulus
TensileModulus = (in*lb)/in
TensileModulus = lb
That means that from the Note 7 we can deduce that their unit for TensileModulus is actually lb.
Claim 1 is different from Calim 2 because lb ≠ lb/in².
That is the contradicition in the document. The problem with contradictions is that anything can be deduced from them. I interpreted it one way and deduced elongation of about 1.85 mm (If I would assume load of only 29N instead of 57N), you interpreted it another way and deduced elongation of 230 nm which is about a wavelength of ultraviolet light. What interpretation sounds more probable?
You really need to stop assuming you are correct all the time and conduct some research before your next post. Please, take the time to verify your thoughts as being accurate. You're "assumptions" are the cause of your bad math.
BeltElongation = in...Yes
BeltLength = in...Yes
TensileLoad = lb...NO NO NO! TensileLoad = Force (F) = lbf* (in*s2) or N or kg*(m/s2) The Meaning of Force.
I used that symbol because the Gates document used it and we were discussing that document.
Moreover you used the symbol lb for force too! Do you emember? Your second to last post in history where you discussed the Young's modulus. I pointed it out to you in my previous message. Attention to detail is what you preach.
All the lowers of imperial units should listen to the professor big time.Quote
nitewing76
One time a professor said, "Never calculate Force in anything other than SI units, because it's too easy to screw-up the cancelations."
The math (as written in my message) is correct. If you do not believe so then read carefully this message: [forums.reprap.org]Quote
nitewing76
Did you ever stop to think the reason why the belt elongation being cubic centimeters seemed wrong to you was because your math is wrong?Quote
hercek
As for as the rest of your [A2's] computaion. It is correct. You just selected the other interpretaion of the document with condtradictions.
Except the last step. You have the last step wrong. If you would bother to continue to folow also the units in the very last step you would even notice the contradiction in the document since:
Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)Quote
A2
Belt Elongation = (1.0 meter * 28.57 N) / 124105648 N/meter²
Belt Elongation = 0.00000023 meter = 0.00023 mm = 0.000009 inch
Belt Elongation = 230e-9 * (meter*N) / (N/meter²)
Belt Elongation = 230e-9 * meter / (1/meter²)
Belt Elongation = 230e-9 * meter³
Ooops, belt elongation in cubic meters? Does not sound right to me.
If you still do not believe the math is correct then send a bug report to the maxima developers. They may have a good laugh about that.
But notice this was just continuation of A2's equations (and his interpretation of the crapy Gates document). I was showing him that if his equation (and therefore his interpretation of the document) would be correct then he can deduce non-sense (elongation in meter³). Which means his equations (his interpretation of the document) were not correct. That is proof by contradiction.
What you can dispute is my interpretation of this A2's equation: Belt Elongation = (1.0 meter * 28.57 N) / 124105648 N/meter²
Typically units are tied to their number with high priority so I interpreted it as: Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)
Bult let's say I should assume that value/unit pair priority is the same as multiplication (and therefore the same as division, all left associative). Then you still would get non-sense elongation unit of N²/meter. So my proof that something is wrong with A2's interpretation of Gates document would still be valid.