Assignment question: Conceptual bits megathread

Discussion in 'Physics & Math' started by Secret, May 25, 2014.

  1. Secret Registered Senior Member

    Messages:
    299
    NB: THESE ARE NOT ASKING HELP ON A HOMEWORK/ASSIGNMENT QUESTION, as all workings were shown, it is aimed to understand why the answer is so, so as to better understand (and in some case revise) the underlying physics which is crucial for assessing continuously the problem solving thinking logical flow when doing phsyics research
    View attachment 7125

    #1
    So I have this assignment/practice feedback (or rather a friend asked me about it), and its posted official worked solution

    However, because of memory failure I failed to understand why the air become less dense as you heat it up

    I try to re-convince myself by using the ideal gas equation
    PV=nRT (Van der waal's also works, but ideal gas is simpler and in this case using ideal gas will not result in a lost of generality)

    However, the solution seemed to suggest the volume of the air balloon is not changing (since the same V is being used), therefore using the above then ro=m/V=const.
    So what physical quantity of the gas that is affected by the temperature that result in the density change?

    Also is this a good way to convince people using easy to understand terms about why the Archimede principle is as described?
    Imagine if the force acting on the object by the fluid particles (the buoyancy) is less than the weight of the fluid (in this case air) displaced, then said fluid would not be displaced in the first place
     
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  3. Secret Registered Senior Member

    Messages:
    299
    View attachment 7277

    The answer key is given (despite using the same label for thedummy variable as the distance y (distance between point P and one end of the rod)

    Doing the integral in the answer given gives the answer we expect, so does by doing it with the change of variables y'=y+L and dy=dL
    But things gets weird when I use lambda as Q/L (since form the diagram, lambda is linear charge density, thus it should equal to Q/L where L is length of rod)

    For the dy integral it gives the expected answer, but for the dL integral it gives a diverging int(1/L', L'=0..L) term (diagram had not distinguish the dummy variable L' from the value L, sorry about that))

    what is the meaning of the diverging term, is it the potential right at one of the charge density (thus explained why it shoots to infinity)?
    and how to reconcile the results of the integrals since we are just changing the variables thus they should calc. to the same result?
    ===============
    EDIT: Nvm, the answer is poor presentation, cause it use the same letter as both the dummy variable and the values, and I am dumb enough to follow the ans's way of presentation

    Q/L, this L is fixed, but when integraring wrt dL, this other L (call it L') is a variable

    The lesson: do not use the same labels as both the dummy variable and the values

    ================
    Q
    View attachment 7289

    Trying to compute the E along the line from the centre of the rod to P
    when I am right at the edge of the rod, R=L/2 and I get infinity as expected
    But why does the E field within the rod not diverge to infinity as it is infinitely thin and should all consist of point charges (charge density) and isn't a point charge has E diverges right at the location of the point charge?
     
    Last edited: Aug 23, 2014
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