October 9th, 2018, 11:51 AM  #1 
Member Joined: Feb 2018 From: England Posts: 61 Thanks: 0  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. 
October 9th, 2018, 12:03 PM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
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. 
October 9th, 2018, 12:11 PM  #3  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
 
October 9th, 2018, 01:18 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723  Quote:
 
October 9th, 2018, 01:48 PM  #5 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  
October 9th, 2018, 01:52 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,973 Thanks: 2224 
(i) $[\mbox{ML}^2\mbox{T}^{2}]$ (ii) $[\mbox{ML}^2\mbox{T}^{3}]$ You might find this table useful. 
October 9th, 2018, 11:52 PM  #7 
Member Joined: Feb 2018 From: England Posts: 61 Thanks: 0 
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? 
October 9th, 2018, 11:55 PM  #8 
Member Joined: Feb 2018 From: England Posts: 61 Thanks: 0 
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. 
October 10th, 2018, 01:20 AM  #9 
Member Joined: Feb 2018 From: England Posts: 61 Thanks: 0 
Hi Skipjack Is this correct for ii) or the one you've given? (M L¯³T¯³) 
October 10th, 2018, 02:24 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,973 Thanks: 2224 
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. 

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