Question

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]?

Answer 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

Answer 2

[L/T]^a X[ML^2/T]^bX[M]^c = [M]^0X[L]^1X[T]^0

Answer 3

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

Answer 4

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

Answer 5

@shawmoes \[\Huge \frac{ \frac{ [M][L]^2}{[T] } }{ \frac{ [L] }{[T} \times [M]} ?\]
\[\ \Huge \text{Where would I go from there?} \]

Answer 6

\[\ \large \text{Would this be wrong?} \]
\(\ \Huge h \times \frac{ 1 }{ mp }\times \frac{ 1 }{ c } \text{ ?} \)

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Also @shawmoes, part (b) to this problem states to find a new quantity of dimensions [T]

Answer 11

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.

Answer 12

Ahhh... okay.

Answer 13

Try to figure it out. Start with knowing you have to eliminate [L] and [M] right off the bat.

Answer 14

@shawmoes Could you help me out? Im having a bit of a difficulty..