Go Back   Physics Help Forum > College/University Physics Help > Special and General Relativity

Special and General Relativity Special and General Relativity Physics Help Forum

Like Tree10Likes
Reply
 
LinkBack Thread Tools Display Modes
Old Oct 24th 2017, 02:22 AM   #11
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,152
Originally Posted by oz93666 View Post
Energy stored in a capacitor = 1/2 C V squared

Energy stored in an inductor = 1/2 L I squared

Energy stored moving mass = 1/2 m v squared

Energy stored in a stationary mass = m c squared

????
I wouldn't use the word "stored" for the last three but they really don't have anything to do with each other as far as I know.

-Dan
Pmb likes this.
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.
topsquark is offline   Reply With Quote
Old Oct 25th 2017, 01:30 PM   #12
Senior Member
 
Join Date: Aug 2010
Posts: 232
Originally Posted by oz93666 View Post
Energy stored in a capacitor = 1/2 C V squared

Energy stored in an inductor = 1/2 L I squared

Energy stored moving mass = 1/2 m v squared

Energy stored in a stationary mass = m c squared

????
I'm not clear why you posted this or what your question (????) is. Those all "look alike" because they are all for energy and so the right hand side must have the units of energy: mass times distance squared over time squared.
topsquark likes this.
HallsofIvy is offline   Reply With Quote
Old Oct 25th 2017, 02:08 PM   #13
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 684
You also missed one.

Strain energy = 1/2 stress x strain



and I echo HallsofIvy's question why did you post this?
topsquark likes this.
studiot is offline   Reply With Quote
Old Oct 25th 2017, 02:17 PM   #14
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,181
Originally Posted by HallsofIvy View Post
I'm not clear why you posted this or what your question (????) is. Those all "look alike" because they are all for energy and so the right hand side must have the units of energy: mass times distance squared over time squared.
He was perfectly clear. He asked

Is the "Energy stored in a stationary mass" = m c squared ?

But topsquark is quite correct when he said that he wouldn't use the term "stored" because it implies that a specific amount of energy has a location, which it doesn't. One can't literally speak of the energy stored in a capacitor just as you can't literally speak of the kinetic energy stored in a moving bullet. That doesn't mean that its not wide;ly used in that way by the best professional physicists that exists. Its a matter of convenience, i.e. an easy way to picture something or speak of something.

Last edited by Pmb; Oct 25th 2017 at 02:20 PM.
Pmb is offline   Reply With Quote
Old Oct 25th 2017, 03:32 PM   #15
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 684
Pete, oz was not the OP here - he made a comment.

There is a common theme with all those formulae posted and the 1/2 arises for the same reason in each case, but this link was not elaborated upon.
studiot is offline   Reply With Quote
Old Oct 25th 2017, 04:39 PM   #16
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,181
Originally Posted by studiot View Post
Pete, oz was not the OP here - he made a comment.

There is a common theme with all those formulae posted and the 1/2 arises for the same reason in each case, but this link was not elaborated upon.
I know. However, when a sentence ends with question marks it makes it a question, rhetorical or otherwise.
Pmb is offline   Reply With Quote
Old Oct 26th 2017, 01:14 AM   #17
Senior Member
 
Join Date: Apr 2017
Posts: 115
I was just wondering why this format pops up so often , always a half then one item , and another item squared ....

let me refresh my mind about Dimensional analysis .... everything can be looked at in terms of M (mass) ....L (length) ... and T ( time)

equations have to balance ...

energy measured in Joules has units M L2 T-2 (that's M ... L squared ... T to the minus 2)

velocity , measured in meters /sec has units L T-1 ...

so the formulae E= 1/2 m v2 analysed dimensionally has ...

M L2 T-2 on one side and M ... L T-1 .....L T-1 , on the other side ...both sides equal

Inductance in farads has dimensions L !!! ... LENGTH very curious

Current has dimensions M1/2 L 3/2 T-2 !!!!! ( that's square root M ...L to the power 3 over 2 ... T to the minus 2) .... isn't that strange????

Energy in a inductor = 1/2 L I squared ....put the dimensions in and it all balances nicely ....!!!

Capacitance in farads has dimensions L - 1 ( L to the minus 1)

Voltage has dimensions M1/2 L 1/2 T-1

What does it all mean ????
oz93666 is offline   Reply With Quote
Old Oct 26th 2017, 05:39 AM   #18
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,152
Originally Posted by oz93666 View Post
I was just wondering why this format pops up so often , always a half then one item , and another item squared ....

let me refresh my mind about Dimensional analysis .... everything can be looked at in terms of M (mass) ....L (length) ... and T ( time)

equations have to balance ...

energy measured in Joules has units M L2 T-2 (that's M ... L squared ... T to the minus 2)

velocity , measured in meters /sec has units L T-1 ...

so the formulae E= 1/2 m v2 analysed dimensionally has ...

M L2 T-2 on one side and M ... L T-1 .....L T-1 , on the other side ...both sides equal

Inductance in farads has dimensions L !!! ... LENGTH very curious

Current has dimensions M1/2 L 3/2 T-2 !!!!! ( that's square root M ...L to the power 3 over 2 ... T to the minus 2) .... isn't that strange????

Energy in a inductor = 1/2 L I squared ....put the dimensions in and it all balances nicely ....!!!

Capacitance in farads has dimensions L - 1 ( L to the minus 1)

Voltage has dimensions M1/2 L 1/2 T-1

What does it all mean ????

I have highlighted the incorrect statements. Somehow or other you have lost the charge unit, Coulomb. (Or, if you like, the unit for current, Amperes.) Capacitance has the unit of farads in MKSA units, not inductance. Inductance is measured in henrys. It is little mentioned (at least I haven't heard it much) but capacitance is largely a geometric property of a collection of surface charges, so it should be somehow related to length units. (Yes, I'm not being very precise in saying that.) But capacitance only has units of length in the esu system of units.

Remember that Nature isn't perfect and Physicists have a tendency to define it to be perfect anyway. So similar formulas do tend to crop up fairly often. We also have things that come up from time to time without any great reason except that they turn out to be useful. Kinetic energy, for example, is defined in terms of mass and speed. The formula doesn't have to be $\displaystyle 1/2 mv^2$ (it could be defined as $\displaystyle mv^4$ for example), but if we define it as $\displaystyle 1/2 mv^2$ we get a nice little result: the work-energy theorem.

There are a number of properties that can be approximated by a Taylor series (I don't know what your Math level is but it's first semester Calculus.) Say we define the property to be calculated as f(x). This can give a similar form as well when we are sitting at an equilibrium point, defined to be where the first derivative vanishes. The Taylor expansion then reads as
$\displaystyle f(x) \approx f(0) + \frac{1}{2}f''(0)x^2$

You can see the $\displaystyle AB^2$ form in the second term.

I don't know any other way to say it. The formulas are defined in such a way to be as useful as possible.

There is something else to mention. Many of these formulas are for perfect systems but as I said before, Nature isn't perfect. The energy stored in the magnetic field of an inductor is not always $\displaystyle 1/2LI^2$. This is only a "constitutive" definition of the magnetic field energy and can break down in certain materials. It's more of a first order approximation. Many of your formulas are defined that way.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

Last edited by topsquark; Oct 26th 2017 at 05:50 AM.
topsquark is offline   Reply With Quote
Old Oct 26th 2017, 06:58 AM   #19
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,181
Originally Posted by oz93666 View Post
I was just wondering why this format pops up so often , always a half then one item , and another item squared .......

What does it all mean ????
I've often wondered the same thing. But you did take note that it doesn't always appear that way, just in certain cases. Certainly not in the case for the relativistic expression for total inertial energy and kinetic energy. And it also doesn't appear in the case of potential energy in classical mechanics in general. The expressions you noted, i.e. energy associated with an inductor and capacitor, are sort of (or exactly) potential energy.

The only answer I've come up with is its just the result of calculating the energy and for no other apparent reason. At least not to my knowledge. I can ask this question to an authority on the subject whom I know if you'd like?
oz93666 likes this.

Last edited by Pmb; Oct 26th 2017 at 07:11 AM.
Pmb is offline   Reply With Quote
Old Oct 26th 2017, 06:59 AM   #20
Senior Member
 
Join Date: Apr 2017
Posts: 115
Originally Posted by topsquark View Post
I have highlighted the incorrect statements. Somehow or other you have lost the charge unit, Coulomb. (Or, if you like, the unit for current, Amperes.) Capacitance has the unit of farads in MKSA units, not inductance.
Ah ...yes a typing error , inductance in Henrys , of course ...

But I think that's the only error ......charge , coulomb is not a basic unit it has the dimensions ... M1/2 L 3/2 T-1 http://www.phys.ufl.edu/courses/phy2...049-Ramond.pdf

A very curious sentence in your post ..."The formulas are defined in such a way to be as useful as possible"
oz93666 is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Special and General Relativity

Tags
emc2, energy, potential



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Potential energy Justusphung Energy and Work 4 May 5th 2016 12:50 AM
about potential energy ohm Energy and Work 9 Apr 8th 2010 03:51 PM
Is the increase in kinetic energy equal to the decrease in potential energy? s3a Energy and Work 1 May 28th 2009 07:02 PM
Electric Potential Energy and electric potential Problem Rainy2Day Advanced Electricity and Magnetism 0 Feb 9th 2009 04:10 PM
potential energy JOHNH Advanced Mechanics 3 Nov 19th 2008 05:16 PM


Facebook Twitter Google+ RSS Feed