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Energy, Distance and Force

Discussion in 'Electronic Design' started by Jim Thompson, May 18, 2005.

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  1. Jim Thompson

    Jim Thompson Guest

    I'm drawing a blank trying to remember how to use (IIRC) Hamilton's
    Principle.

    Isn't there some simple-minded way to take the energy at point A and
    energy at point B, and calculate the force required to get from point
    A to point B?

    ...Jim Thompson
     
  2. Tim Wescott

    Tim Wescott Guest

    Not the force, but possibly the work.

    Energy at point B = energy at point A + work to get to point B.

    In a perfect physics world that means you could either go one inch while
    exerting 10 tons, or you could go 20 000 inches while exerting one pound.
     
  3. Jim Thompson

    Jim Thompson Guest

    Defining the problem more simplistically... what is the force between
    the two plates of a capacitor, spaced "d", area "A", voltage "V"?

    ...Jim Thompson
     
  4. Tim Williams

    Tim Williams Guest

    Oh, electrostatic force?

    Don't know why you'd need to know this...this is first year textbook stuff,
    Jim... ;-)

    Lesse, one definition for electric field is the force divided by the charge,
    E = F/q where E and F are vectors.

    q = VC and C = e0*A / d (e0 = epsilon naught, permittivity of space), so:
    E = F*d / e0*V*A > F = E*e0*V*A / d
    E is also defined in volts per meter, so E = V/d. Thus:
    F = e0 * V^2 * A / d^2

    Force goes down inverse square with distance, and linear with area, I'd
    think voltage would be linear as well though. Eh, what do you expect for a
    usenet reply mmmh?

    Tim
     
  5. Terry Given

    Terry Given Guest


    Woodson & Melcher (part 1) gives:


    F = dW/dx (where the d's have melted and leaned to the left a bit)

    W = energy = .5CV^2

    C = Ae/x (3.1.54)

    F = AeV^2 (3.1.55)
    -----
    2x

    which is about what I guessed.

    Cheers
    Terry
     
  6. Terry Given

    Terry Given Guest

    and agrees with Tim, so must be right :)

    Cheers
    Terry
     
  7. Jim Thompson

    Jim Thompson Guest

    Of course it is. It's just that I'm coming up on 50 years since high
    school physics and, you know, use it or lose it ;-)

    ...Jim Thompson
     
  8. Jim Thompson

    Jim Thompson Guest

    [snip]

    Wow! Old times. I should buy that book as a keepsake if nothing
    else.

    I have White & Woodson, the predecessor.

    I worked as a technician in Professor Woodson's lab in MIT Building 20
    while I was a student at MIT.

    Melcher was a graduate student studying MHD under Woodson.

    Melcher also taught some EE courses that I attended.

    Melcher went on to become head of the EE Department, but died of colon
    cancer, IIRC, mid 80's.

    ...Jim Thompson
     
  9. Terry Given

    Terry Given Guest

    Hi Jim,

    I bought vol. 2 & 3, brand new, for $1 each while I lived in
    Taxachusetts - from a book clearing place, Hamiltons IIRC. Vol. 1
    arrived about a month ago, is older than I am, and cost about $20. They
    are an excellent treatment of electromechanical systems. I knew you
    would recognise them, which is why I used them ;)

    My copy of Zverev turned up this morning, and I eagerly await
    Motchenbacher (its in the mail....).

    Cheers
    Terry
     
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