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Math Problem No Numbers ?

  1. Apr 24, 2005 #1
    Given: W = J/s, J = Nm, N = kgm/s2, Hz = 1/s
    Convert W²/NJHz to mks and simplify. Make sure to list every step.

    can someone please guide me.....this is what I have so far...im not sure if im doing it right though....


    J/s² underline meaning over.....
    kgm/s² * Nm* 1/s



    is this right.....
     
  2. jcsd
  3. Apr 24, 2005 #2
    What is an mks???

    I can but I need a little help from you.

    Also try this thread.

    The Bob (2004 ©)
     
  4. Apr 24, 2005 #3
    thx bob...i dont know but I will email my teacher and ask him...
     
  5. Apr 24, 2005 #4
    PM me when you have found out.

    The Bob (2004 ©)
     
  6. Apr 24, 2005 #5
    MKS it a measure system. You are already working with MKS.
     
    Last edited: Apr 24, 2005
  7. Apr 24, 2005 #6
    Maybe you need to convert to cgs...
     
  8. Apr 24, 2005 #7

    jtbell

    User Avatar

    Staff: Mentor

    No, I think he's just supposed to reduce it to the simplest possible combination of meters, kilograms, and seconds, after substituting for watts, joules, etc.
     
  9. Apr 24, 2005 #8
    In that case it is fairly simple.

    Write W as Js-1, J as Nm, N as kg ms-2 and Hz as s-1.

    [tex] \frac{W^2}{N \times J \times Hz} = \frac{(Js^{-1})^2}{kg \ ms^{-2} \ \times \ Nm \ \times \ s^{-1}}[/tex]

    Now it is time to start using your basic knowledge of maths to multiply and divide this out.

    [tex] \frac{J^2s^{-2}}{\frac{kg \m}{s^2} \ \times \ Nm \ \times \ \frac{1}{s}} = \frac{J^2}{s^2} \div (\frac{kg \m}{s^2} \ \times \ Nm \ \times \ \frac{1}{s}}) = \frac{J^2}{s^2} \div \frac{kg \m \times Nm}{s^2 \times s}[/tex]

    [tex]= \frac{J^2}{s^2} \times \frac{s^3}{kg \m \times Nm} = \frac{J ^2 \ s^3}{kg \m \times Nm \times s^2} = \frac{J ^2 \ s}{kg \m \times Nm} = J^2 \ s \ kg^{-1} \ Nm^{-1}[/tex]

    This is what I get however I feel that the (Js-1)2 = J2s-2 might be said to be wrong by someone more in the know than I am on units. However this is what I think until I am told otherwise.

    If this does not make too much sense then look at the thread I mentioned in the second post. It will explain things more clearly.

    The Bob (2004 ©)
     
  10. Apr 24, 2005 #9
    First convert all your 'givens' to MKS, starting with the most basic (Hz).

    MKS means everything is meters, kilograms, and seconds. If something is on the 'bottom' of a fraction, rewrite it as being multiplied times the top, only make the exponent negative. Example: [tex]\frac{4}{x^2} = 4x^{-2}[/tex]

    [tex]Hz=(s^{-1})[/tex]
    [tex]N=(kg)(m)(s^{-2})[/tex]
    [tex]J=(kg)(m^2)(s^{-2})[/tex]
    [tex]W=(kg)(m^{2})(s^{-3})[/tex]

    Now just plug them into your big equation:

    [tex](W^2)(N^{-1})(J^{-1})(Hz^{-1})[/tex]

    For [tex](W^2)[/tex], all you have to do is double all the exponents of that part once you substitute, so [tex](W^2)=(kg^2)(m^4)(s^{-2})[/tex].

    Now, that's one part that I've done for you. I'd like to see you substitute the rest in on your own. Just remember, that when you've determined, for example, [tex]J=(kg)(m^2)(s^{-2})[/tex], then [tex]J^{-1}=(kg^{-1})(m^{-2})(s^{2})[/tex]...all the exponents switch signs. When multiplying like terms, add their exponents. For example, [tex](m^4)(m^{-3})=(m^{-1})[/tex]. I put parentheses around everything so I don't get confused by two-letter variables.
     
  11. Apr 24, 2005 #10
    lol...still kinda confused..but this seems righter then me (oops is righter a word)....

    so this is right...
     
  12. Apr 24, 2005 #11
    oh thx kingnothing i just saw ur reply...i will work it out now...and post my answer.....thanks to all that replied
     
  13. Apr 24, 2005 #12
    I see what you have done. My method, in my eyes, is fine but I simply need to learn the conversions (as N and J are the same as you have written and I would not have expected).

    Cheers.

    The Bob (2004 ©)
     
  14. Apr 24, 2005 #13
    so is ur way right too the bob?! u guys r losing me
     
  15. Apr 24, 2005 #14
    hey guys i did all the work on paper....my final answer is

    (kg4)(m7)(s-11)

    please tell me thats right?!?!
     
  16. Apr 24, 2005 #15
    [tex]=(kg^{4})(m^{7})(s^{-11})[/tex]

    i hope this latex stuff works....
     
  17. Apr 24, 2005 #16
    Personally I got m kg-1 s-1.

    The Bob (2004 ©)
     
  18. Apr 24, 2005 #17
    I got [tex]m^1 * s^{-1}[/tex] in other words, meters per second.

    Bob, how did you get an extra kg on the bottom?

    Watts squared yields kg^2, then on the bottom Joules and Newtons both have kg^1 so there is no kg on top or bottom.
     
    Last edited: Apr 24, 2005
  19. Apr 24, 2005 #18
    Here is my workings:

    [tex]N = kg \ ms^{-2}[/tex]

    [tex]J = Nm = kg \ ms^{-2} \times m = kg \ m^2 s^{-2}[/tex]

    [tex]W = Js^{-1} = kg \ m^2 s^{-2} \times s^{-1} = kg \ m^2 s^{-3}[/tex]

    [tex]\frac{W^2}{J \times N \times Hz}[/tex] [tex]= \frac{(kg \ m^2 s^{-3})^2}{kg \ m^2 s^{-2} \times kg \ ms^{-2} \times s^{-1}}[/tex]

    [tex]= \frac{kg^2 \ m^4 s^{-6}}{kg \ m^2 s^{-2} \times kg \ ms^{-2} \times s^{-1}}[/tex]

    [tex]= \frac{kg^2 \ m^4 s^{-6}}{kg^2 \ m^3 s^{-5}} = m s^{-1}[/tex]

    So I agree with KingNothing and I realised my mistake was a missing squared on my kilograms. :frown:

    Stupid me.

    The Bob (2004 ©)
     
    Last edited: Apr 24, 2005
  20. Apr 24, 2005 #19
    Alright, it's time to check my answer to prove to you villains that I'm right. :P
    meters=5
    kg=8
    seconds=3

    Watt=(8)(5^2)(3^-3)
    Watt^2 = 54.87 (about)
    Newton = (8)(5)(3^-2)
    Newton = 4.44
    Joule = (8)(5^2)(3^-2)
    Joule = 22.22
    Hz = (3^-1)
    Hz = .33

    Newton * Joule * Hz = 32.56
    Watt^2 = 54.87

    So, Watt^2 over Newton * Joule * Hz = 1.69


    And with my simplification, 5/3 = 1.6666666

    Tada!
     
  21. Apr 24, 2005 #20
    All credit to you. :biggrin: I said you were right and I was simply checking my method for joejo as I got the impression it made sense to him/her.

    The Bob (2004 ©)
     
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