A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years 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?
 2 years 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?

This Question is Open

Jeshaiah
 2 years ago
Best ResponseYou've already chosen the best response.0Actually, 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.

Saikam
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. 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 \[L ^{a} * L ^{c} = L ^{1/2} * L ^{1/2} = 1 (dimensionless)\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.