# Homogeneous but incorrect?

1. Nov 9, 2006

### d1v1n1ty nb

im posed with the question why an equation may be homogeneous with respect to its units but still be incorrect? i cant think of way to explain this can anyone help me out? Thanx

2. Nov 9, 2006

### vanesch

Staff Emeritus
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.

...

3. Nov 9, 2006

### d1v1n1ty nb

Thanx, thts a good way to describe it. Is there any well known common formulae that fits this trend?

4. Nov 9, 2006

### Office_Shredder

Staff Emeritus
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.

5. Nov 9, 2006

### Staff: Mentor

A well-known formula that doesn't work? No...

6. Nov 9, 2006

### vanesch

Staff Emeritus
Pick a pile of exam copies of first year students

7. Nov 10, 2006

### HallsofIvy

Except that it is probable that none of those will be dimensionally correct either!

8. Nov 10, 2006

### vanesch

Staff Emeritus
:rofl: :rofl:
Right !