Why Can an Equation Be Homogeneous but Incorrect?

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SUMMARY

An equation can be homogeneous with respect to its units yet still yield incorrect results due to improper application or context. For instance, the formula for total length L = L1 - L2 is dimensionally correct but fails to represent the physical scenario accurately when applied to two rods of lengths L1 = 15 cm and L2 = 10 cm, resulting in an incorrect total of 5 cm. Similarly, the formula L = L1 L2 / (L1 + L2) also produces a dimensionally correct answer of 6 cm but does not reflect the actual total length. This highlights the importance of understanding the physical meaning behind equations, rather than relying solely on dimensional analysis.

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d1v1n1ty nb
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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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