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October 9th, 2018, 11:51 AM   #1
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Dimensional Forms?

Hi All,

Struggling with the following question...

Determine the dimensional forms for the following quantities using only the dimensional primitives such as mass, length, time, etc.

i) work done (W) = force (F) x Distance ?
ii) power (P) = energy (E)/time (t)

Any help would be much appreciated.
Thanks.
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October 9th, 2018, 12:03 PM   #2
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Since you are struggling, let's start with something much more simple.


Can you tell me the dimensional form for speed in terms of distance (L) and time (T) ?

If not can you give me a formula for speed and we can start from there.
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October 9th, 2018, 12:11 PM   #3
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Quote:
Any help would be much appreciated.
Go on then, say something
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October 9th, 2018, 01:18 PM   #4
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Quote:
Originally Posted by NAC54321 View Post
Hi All,

Struggling with the following question...

Determine the dimensional forms for the following quantities using only the dimensional primitives such as mass, length, time, etc.

i) work done (W) = force (F) x Distance ?
ii) power (P) = energy (E)/time (t)

Any help would be much appreciated.
Thanks.
You need to specify all dimensional primitives.
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October 9th, 2018, 01:48 PM   #5
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Quote:
Originally Posted by mathman View Post
You need to specify all dimensional primitives.
What's a dimensional primitive: There is more than one system available.
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October 9th, 2018, 01:52 PM   #6
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(i) $[\mbox{ML}^2\mbox{T}^{-2}]$

(ii) $[\mbox{ML}^2\mbox{T}^{-3}]$

You might find this table useful.
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October 9th, 2018, 11:52 PM   #7
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Thanks Skipjack.
That table is very useful, appreciated.

Am I correct in saying that specific heat (c) = energy/mass x change in input.
Is = L²T² ?

I am struggling with this so bear with me, how to you actually derive this and show workings for each?
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October 9th, 2018, 11:55 PM   #8
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Studiot thanks for your reply.

I didn't look at this last night only now seeing it.
I have always calculated speed by distance / time.

Skipjack has helped greatly with the table and now it makes more sense, I am just trying to work out how each is derived.
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October 10th, 2018, 01:20 AM   #9
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Hi Skipjack

Is this correct for ii) or the one you've given?

(M L¯³T¯³)
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October 10th, 2018, 02:24 AM   #10
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You need an equation that leads to the dimensional formula.

For example, speed = distance/time, so its dimensional formula is $[\mbox{LT}^{-1}]$.

Hence momentum = mass × velocity has dimensional formula $[\mbox{MLT}^{-1}]$.

Similarly, force = rate of change of momentum has dimensional formula $[\mbox{MLT}^{-2}]$.

Energy (or heat or work or moment) = force × distance has dimensional formula $[\mbox{ML}^2\mbox{T}^{-2}]$.

Hence power = energy/time has dimensional formula $[\mbox{ML}^2\mbox{T}^{-3}]$.

Specific heat = energy per Kelvin has dimensional formula $[\mbox{ML}^2\mbox{T}^{-2}\Theta^{-1}]$.

Specific heat capacity = specific heat per unit mass has dimensional formula $[\mbox{L}^2\mbox{T}^{-2}\Theta^{-1}]$.

You may find occasional differences between authors as to what dimensional primitives are available. Also, some authors don't use the square brackets I've used above.

Note that although the word radian is used almost as though it's a fundamental unit, an angle is defined as a ratio of distances, so it's dimensionless.
Thanks from Benit13
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