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Finding Dimensional Homogeneity 
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#1
Aug2911, 11:06 PM

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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/s^{2}) V= velocity (m/s) R= radius (m) t= time (s) 2. Relevant equations 1. F=ma 2. F=m(V^{2}/R) 3. F(t_{2}t_{1})=m(V_{2}V_{1}) 4. F=mV 5. F=m(V_{2}V_{1})/(t_{2}t_{1}) 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/s^{2}) From here, I'm not really sure where to go. F=m(V^{2})/(R) becomes: N=(kg)((m/s^{2})/(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
Aug2911, 11:18 PM

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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
Aug2911, 11:31 PM

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#4
Aug2911, 11:35 PM

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Finding Dimensional Homogeneity



#5
Aug2911, 11:42 PM

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Am I to understand correctly that 1N= 1kg(m/s^{2}) And then using that I can compare left to right? And if the right side doesn't come out to kg(m/s^{2}) it is NOT dimensionally homogeneous? 


#6
Aug2911, 11:44 PM

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#7
Aug2911, 11:55 PM

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When I do the substitutions for F=mV it becomes: N=(kg)(m/s) or further: (kg)(m/s^{2})=(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
Aug3011, 12:00 AM

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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. 


#9
Aug3011, 12:04 AM

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#10
Aug3011, 12:12 AM

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



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