- #1

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- Summary:
- In what cases does dimensional analysis fails? And also is there like any preferred situation or an 'ideal' situation in order to use dimensional analysis? Thanks in advance!

It possible a diagram would be really really helpful

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- Thread starter VVS2000
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- #1

- 84

- 8

- Summary:
- In what cases does dimensional analysis fails? And also is there like any preferred situation or an 'ideal' situation in order to use dimensional analysis? Thanks in advance!

It possible a diagram would be really really helpful

- #2

berkeman

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Is this a schoolwork question?

- #3

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- #4

berkeman

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Well, a number of quantities are dimensionless, but I'm not sure that represents a failure. Can you think of some dimensionless constants or quantities that are used commonly?Summary:In what cases does dimensional analysis fails?

Also, these two PF Insights articles would probably be good background reading for you to help understand dimensional analysis better...

https://www.physicsforums.com/insights/learn-the-basics-of-dimensional-analysis/

https://www.physicsforums.com/insights/make-units-work/

- #5

Vanadium 50

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I just thought well obviously this won't work for evert case so I just wanted to know what are those cases.

That's like asking when addition doesn't work - when it's the wrong tool for the job. Maybe you need to subtract or to multiply.

Dimensional analysis cannot tell you if the circumference of a circle is 6r, 2πr or 7r. It can tell you it is not 1/r or r

- #6

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Thanks for the links!Well, a number of quantities are dimensionless, but I'm not sure that represents a failure. Can you think of some dimensionless constants or quantities that are used commonly?

Also, these two PF Insights articles would probably be good background reading for you to help understand dimensional analysis better...

https://www.physicsforums.com/insights/learn-the-basics-of-dimensional-analysis/

https://www.physicsforums.com/insights/make-units-work/

- #7

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No no not like that. What if sometimes we don't know the nature of the opposing quantity. How are you going to proceed then?That's like asking when addition doesn't work - when it's the wrong tool for the job. Maybe you need to subtract or to multiply.

Dimensional analysis cannot tell you if the circumference of a circle is 6r, 2πr or 7r. It can tell you it is not 1/r or r^{2}.

- #8

Vanadium 50

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What if sometimes we don't know the nature of the opposing quantity.

I don't understand.

- #9

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Like in damping of harmonic oscillations.I don't understand.

- #10

berkeman

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What do the overall dimensions of the quantity in the exponent need to be? So what does that tell you about the dimensions of λ ?Like in damping of harmonic oscillations.

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

- #11

Vanadium 50

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I still don't understand. Perhaps you could use complete sentences? Maybe even paragraphs?

- #12

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For example damping in oscillations. What if we dont know the nature of damping? How do you find the equations of motion?I still don't understand. Perhaps you could use complete sentences? Maybe even paragraphs?

- #13

Vanadium 50

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How do you find the equations of motion?

What does that have to do with dimensional analysis?

- #14

berkeman

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Please see post #10.For example damping in oscillations. What if we dont know the nature of damping? How do you find the equations of motion?

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I am asking using dimensional analysis how do you find the eqaution of motion thenWhat does that have to do with dimensional analysis?

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Sorry I am new here. Post 10 where?Please see post #10.

- #17

berkeman

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- #18

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That's actually really helpful. Thanks.

- #19

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So I cannot use dimensional analysis in such cases?That's actually really helpful. Thanks.

- #20

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So I cannot use dimensional analysis in such cases?

- #21

berkeman

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Like in the Hyperphysics equations? Sure. Can you show the dimensions for each of the terms in the initial differential equation? And then show how that helps to define the dimensions of λ in the end?So I cannot use dimensional analysis in such cases?

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I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambdaLike in the Hyperphysics equations? Sure. Can you show the dimensions for each of the terms in the initial differential equation? And then show how that helps to define the dimensions of λ in the end?

- #23

berkeman

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Okay, but what are the dimensions (or units) for each of the terms in these equations?I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambda

- #24

Chestermiller

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The dimensions of c are...?I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambda

The dimensions of m are...?

The dimensions of ##\lambda## are...?

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