Why Can an Equation Be Homogeneous but Incorrect?

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An equation can be homogeneous in units yet still yield incorrect results due to the misuse of dimensional analysis. For example, calculating the total length of two rods using L = L1 - L2 or L = L1 L2 / (L1 + L2) both produce dimensionally correct outcomes, but the logic applied leads to incorrect answers. This highlights that dimensional correctness does not guarantee the physical validity of a formula. The discussion also touches on the challenge of finding well-known formulas that fit this trend, with no specific examples provided. Ultimately, the conversation emphasizes the importance of understanding the context and application of equations beyond just their dimensional consistency.
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im posed with the question why an equation may be homogeneous with respect to its units but still be incorrect? i can't think of way to explain this can anyone help me out? Thanx
 
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Consider a rod with length L1 = 15 cm and another rod with length L2 = 10cm.

Now put the two rods one after the other.
Consider the following formula: the total length of the two rods L = L1 - L2 = 5 cm.

This formula is dimensionally correct, and the answer is wrong.

Another formula:

the total length equals L = L1 L2 / (L1 + L2) = 150 cm^2 / 25 cm = 6 cm

Again, the formula is dimensionally correct, but gives the wrong anwer.

...
 
Thanx, thts a good way to describe it. Is there any well known common formulae that fits this trend?
 
Force is ma = kgm/s2

So imagine we have an object with mass m and length L just sitting there for some period of time t. Then the net force F=m*L/t2 doesn't actually turn out to be 0.
 
d1v1n1ty nb said:
Thanx, thts a good way to describe it. Is there any well known common formulae that fits this trend?
A well-known formula that doesn't work? No... :confused:
 
d1v1n1ty nb said:
Thanx, thts a good way to describe it. Is there any well known common formulae that fits this trend?

Pick a pile of exam copies of first year students :biggrin:
 
Except that it is probable that none of those will be dimensionally correct either!
 
HallsofIvy said:
Except that it is probable that none of those will be dimensionally correct either!

:smile: :smile:
Right !
 

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