# Finding Dimensional Homogeneity

1. Aug 29, 2011

### Physics_Grunt

1. The problem statement, all variables and given/known data
Which one of the following equations is dimensionally homogeneous?

Where:

F= force (N)
m= mass (kg)
a= acceleration (m/s2)
V= velocity (m/s)
t= time (s)

2. Relevant equations

1. F=ma
2. F=m(V2/R)
3. F(t2-t1)=m(V2-V1)
4. F=mV
5. F=m(V2-V1)/(t2-t1)

3. The attempt at a solution

Through what I can gather from my textbook and the internet, I started by entering what I know. So:
F=ma
becomes:
N=(kg)(m/s2)

From here, I'm not really sure where to go.

F=m(V2)/(R)
becomes:
N=(kg)((m/s2)/(m))

And again, I plug everything in but in my textbook at this point is where they determine if it is or isn't dimensionally homogeneous.

I would really appreciate any guidance on this, I realize it's a super basic question, but you've got to start somewhere! Thank you.

2. Aug 29, 2011

### PeterO

Homogeneous usually means "made up of the same types" or words to that effect.

If you express each quantity in base units - m , kg , s - you could compare left to right.

hint: there are two formulas which look very similar, but with one variable different. I would suspect one of those.

3. Aug 29, 2011

### collinsmark

Try that one again. It seems you forgot to square something or forgot to divide by something. One of the two.

4. Aug 29, 2011

### Dick

Uh, V^2 dimensions are m^2/s^2. You try it again.

5. Aug 29, 2011

### Physics_Grunt

Okay, so further googling turned up this(http://physics.nist.gov/cuu/Units/units.html" [Broken]) handy chart.

Am I to understand correctly that 1N= 1kg(m/s2) And then using that I can compare left to right? And if the right side doesn't come out to kg(m/s2) it is NOT dimensionally homogeneous?

Last edited by a moderator: May 5, 2017
6. Aug 29, 2011

### Dick

Yes. And I don't there is just one that is homogeneous.

Last edited by a moderator: May 5, 2017
7. Aug 29, 2011

### Physics_Grunt

I think the question may have been mis-typed on my handout. I think it should read "which one of the following is NOT dimensionally homogeneous?"

When I do the substitutions for F=mV it becomes:

N=(kg)(m/s) or further:

(kg)(m/s2)=(kg)(m/s)

Because the (m/s) on the right is not squared as it is on the left, would this be a correct example of an equation that is NOT dimensionally homogeneous?

8. Aug 30, 2011

### PeterO

That is the task for all but the third one, where the left hand side is not simply F, but has time with it.

I would have the units of F as kgms-2

Perhaps made clearer as kg m s-2 or kg.m.s-2

Often these are actually written "dimensionally" using [M] for mass, [T] for time and [L] for length.

then we would have [M][L][T]-2

That certainly takes care of countries that use pounds instead of kg, and feet instead of metres.

Oh and rest assured - only one of the examples is not homogeneous - perhaps you left the word not out of your original post.

Last edited by a moderator: May 5, 2017
9. Aug 30, 2011

### PeterO

certainly would.

10. Aug 30, 2011

### Physics_Grunt

Thank you all. Your explanations made it click in my head and I think I have it now.