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Study23

  • 2 years ago

DUE TOMORROW, THIS PROBLEM HAS BEEN GIVING ME TROUBLE ALL DAY! •• Really stuck with this problem, not sure what to do: Consider a system where the three fundamentally important quantities are the speed of light c with dimensions [L]/[T], Planck's constant h with dimensions [M][L]^2/[T] and the mass of the proton mp with dimension [M]. What combination of ratios and/or products of c, h, and mp will yield a new quantity of dimensions [T]?

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  1. atlas
    • 2 years ago
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    Raise these quantities to the powers a, b and c respectively and equate it to L You will get three equations using which you can solve for a b and c

  2. atlas
    • 2 years ago
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    [L/T]^a X[ML^2/T]^bX[M]^c = [M]^0X[L]^1X[T]^0

  3. Study23
    • 2 years ago
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    So how would I solve that? Would I have to find a b and c numerically? Do you mind showing me how? I'm still not clear

  4. shawmoes
    • 2 years ago
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    This is pure dimensional analysis, no computation is needed here. h/mp yields [M][L]^2/[T][M] . What does h/c(mp) yield?

  5. Study23
    • 2 years ago
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    @shawmoes \[\Huge \frac{ \frac{ [M][L]^2}{[T] } }{ \frac{ [L] }{[T} \times [M]} ?\] \[\ \Huge \text{Where would I go from there?} \]

  6. Study23
    • 2 years ago
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    \[\ \large \text{Would this be wrong?} \] \(\ \Huge h \times \frac{ 1 }{ mp }\times \frac{ 1 }{ c } \text{ ?} \)

  7. shawmoes
    • 2 years ago
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    Your notation is not right h/c(mp) gives : \[\left[ T \right]\left[ M \right]\left[ L \right]^{2}/\left[ T \right]\left[ M \right]\left[ L \right]\]

  8. shawmoes
    • 2 years ago
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    That's correct. If you simplify what I wrote above (which should be easy enough) you'll end up with [L]. Done.

  9. Study23
    • 2 years ago
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    So basically I want things to cancel out to get L in the end? So L is that answer, but the real answer per say is the steps behind getting [L]? So this just sounds complicated but isn't? @shawmoes

  10. Study23
    • 2 years ago
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    Also @shawmoes, part (b) to this problem states to find a new quantity of dimensions [T]

  11. shawmoes
    • 2 years ago
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    A dimensional analysis problem like this is purely figuring out ratios between variables , the answer is simply showing if your ratios give you [L]. No more proof is needed.

  12. Study23
    • 2 years ago
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    Ahhh... okay.

  13. shawmoes
    • 2 years ago
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    Try to figure it out. Start with knowing you have to eliminate [L] and [M] right off the bat.

  14. Study23
    • 2 years ago
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    @shawmoes Could you help me out? Im having a bit of a difficulty..

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