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Study23
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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]?
 10 months ago
 10 months ago
Study23 Group Title
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]?
 10 months ago
 10 months ago

This Question is Closed

atlas Group TitleBest ResponseYou've already chosen the best response.1
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
 10 months ago

atlas Group TitleBest ResponseYou've already chosen the best response.1
[L/T]^a X[ML^2/T]^bX[M]^c = [M]^0X[L]^1X[T]^0
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
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
 10 months ago

shawmoes Group TitleBest ResponseYou've already chosen the best response.0
This is pure dimensional analysis, no computation is needed here. h/mp yields [M][L]^2/[T][M] . What does h/c(mp) yield?
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
@shawmoes \[\Huge \frac{ \frac{ [M][L]^2}{[T] } }{ \frac{ [L] }{[T} \times [M]} ?\] \[\ \Huge \text{Where would I go from there?} \]
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
\[\ \large \text{Would this be wrong?} \] \(\ \Huge h \times \frac{ 1 }{ mp }\times \frac{ 1 }{ c } \text{ ?} \)
 10 months ago

shawmoes Group TitleBest ResponseYou've already chosen the best response.0
Your notation is not right h/c(mp) gives : \[\left[ T \right]\left[ M \right]\left[ L \right]^{2}/\left[ T \right]\left[ M \right]\left[ L \right]\]
 10 months ago

shawmoes Group TitleBest ResponseYou've already chosen the best response.0
That's correct. If you simplify what I wrote above (which should be easy enough) you'll end up with [L]. Done.
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
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 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
Also @shawmoes, part (b) to this problem states to find a new quantity of dimensions [T]
 10 months ago

shawmoes Group TitleBest ResponseYou've already chosen the best response.0
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.
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
Ahhh... okay.
 10 months ago

shawmoes Group TitleBest ResponseYou've already chosen the best response.0
Try to figure it out. Start with knowing you have to eliminate [L] and [M] right off the bat.
 10 months ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
@shawmoes Could you help me out? Im having a bit of a difficulty..
 10 months ago
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