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In dimensional analysis, how do we go from [T]^1 = [L]^a [M]^b ([L]^c/[T]^2c), knowing that a = 1/2 b = 0 and c = 1/2, to t = (constant) sqrt(h/g)? How do we know there's a constant and where does it come from? Wasn't L supposed to cancel itself out?
 one year ago
 one year ago
In dimensional analysis, how do we go from [T]^1 = [L]^a [M]^b ([L]^c/[T]^2c), knowing that a = 1/2 b = 0 and c = 1/2, to t = (constant) sqrt(h/g)? How do we know there's a constant and where does it come from? Wasn't L supposed to cancel itself out?
 one year ago
 one year ago

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JeshaiahBest ResponseYou've already chosen the best response.0
Actually, the equation was [T]^1 is directly proportional to [L]^a [M]^b ([L]^c/[T]^2c), which means that dividing [T]^1 by [L]^a [M]^b ([L]^c/[T]^2c) would give you a nonzero constant. The constant has no dimensions, and does not affect the final dimension of the answer. Unfortunately, this also means that the constant cannot be identified by dimensional analysis. The only way to find the constant is to substitute in each value in the equation and calculate the value of the constant from there.
 one year ago

SaikamBest ResponseYou've already chosen the best response.0
Yes. For example, in the equation \[s = ut + \frac{ 1 }{ 2 }a t^{2}\] the constant 1/2 has no dimension and would not be shown in the dimensional equation. And regarding your second question, L DOES cancel out since \[L ^{a} * L ^{c} = L ^{1/2} * L ^{1/2} = 1 (dimensionless)\]
 one year ago
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