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Homework Help: Help with Dimensional Formulae

  1. Jul 22, 2009 #1
    hey guys, i was wondering if you guys could help me with a few things.
    1st, how to work out dimensional formulae questions, i can not get my heard around it, and im sure with some help i can nail it,

    how do u give the dimensions for ENERGY


    give the dimensions of the following; (p = density)

    a) VA / v
    b) v^2/3 A
    c) p^3v / A^2
    d) if v = LT^-1 what it 3v
    e) 3A^3 + 2V^2

    cheers guys and i hope u can help me sort this problem out :) :)
  2. jcsd
  3. Jul 22, 2009 #2
    there are many equations for energy, dont know what one to break down into its dimensions!!
  4. Jul 22, 2009 #3


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    Pick any one. They should all give you the same dimensions. Try KE=(1/2)*mv^2.
  5. Jul 22, 2009 #4
    ah i see, m = M, v^2 = L^2 T^-2
  6. Jul 22, 2009 #5
    But this is where the concept of applying dimensions to energy can get pointless. Yes, you can break kinetic energy into the units kg*m2/s2, but what does this tell you about the amount of energy required to heat 1 ml of water 1oC? The units of that would be kg*oC.

    Energy can be expressed mechanically as:
    • F*d
    • 0.5*m*a
    • 9.8N/kg*m*h
    • etc.

    In mechanics, one could say that energy has the units kg*m2/s2, but that will only makes sense in mechanics.

    kg*m2/s2 = kg*oC
    then we can cancel kg and
    m2/s2 = oC

  7. Jul 22, 2009 #6


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    No, actually. If you are using SI base units then kg m^2/s^2 are the units of energy, period. Not just in mechancs. Why would you think that kg C would be units for an "amount of energy" in that context? That is just wrong.
  8. Jul 22, 2009 #7
    hey guys, i can see where u are coming from, i spend an hour or 2 just going through questions and found that if you know the formula for of something for example (Force) = m x a, then is is just stripping it down to its most basic units, m = M and being that a = change in velocity per unit time = LT^-2 thus FORCE = MLT^-2

    cheers guys :)
  9. Jul 22, 2009 #8
    How do you measure the amount of energy is absorbed by an amount of water? You know nothing of time or distance, you just know that xkg of water heated up yoC, so it must have absorbed energy. We calculate the energy by multiplying the mass of water by the temperature change, thus the units of our answer would be kg*oC, which we convert (using the correct proportional constant) to J.

    My point is that reducing complex units to their components (1N = 1 kg*m/s2) does not always work. With mechanics, yes, but to say that the basic SI units of energy are kg*m2/s2 is to deny that energy is something else entirely. The SI unit for energy is the Joule. This, of course, is derived from the N*m, and ... but it does not make much sense to say the water absorbed zkg*m2/s2. We'd just leave it at zJ.
  10. Jul 22, 2009 #9


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    You seem to have managed to bypass one of the big physical insights of the 19th century.http://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat How did you manage that?
  11. Jul 22, 2009 #10
    The original question was:
    I never stated that energy in water molecules is different than energy due to position of objects (gravity) nor due to their relative speeds (kinetic), so please don't reply with sarcasm.

    Yes, you can simplify all units to their base SI units, and for the introductory student this is good practice in mechanics. When you get into heat, it gets more complicated, and to think of the 4,186 Joules that it takes to heat 1kg of water 1oC (or K) as in some way equal to 4,186 kg*m2/s2 is open the door to potential confusion (e.g. "you mean the 1 kg of water is accelerating at 4.186 (m/s)/s for one meter?")

    The original questioner answers in mechanics. I'm just trying to warn him that this won't always be so easy.

    Perhaps, instead of saying:
    I should have said "...applying dimensions (base SI units) to energy can lead to confusion outside of mechanics."
  12. Jul 22, 2009 #11


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    Energy is kg*m^2/s^2. Period. Always. That's 'dimensions'. Sorry about the sarcasm, but sure, you use different methods to deal with different forms of energy. I still don't see how using SI units leads to confusion about this. That's why I said 'use any formula you want'. You could have used a thermal formula. You still get kg*m^2/s^2.
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