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Coursework help - Stokes Law equation + graphs

  1. Dec 1, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi there.
    For my A2 physics coursework I have been doing an experiment into stokes law, in which I dropped ball bearings of various diameters into a tube filled with a liquid, worked out their terminal velocities and then used Stokes Law to calculate the viscosity of the liquid. My results have been consistent and in line with my expectations. I then did another experiment, the reverse in a way, in which I used my calculated values for the viscosity of the liquids to find the diameter of ball bearing before measuring it to ensure I was gaining accurate results.

    However now I am at the stage of writing up my experiment report and I am a little unsure of what graphs to plot. I've been reading and it sounds as though I should plot a graph of radius2 over velocity, however I am unsure as to what this would show. For example, would the gradient show viscosity?

    2. Relevant equations
    The equations I've been using are μ=(d2g(Pρ-Ps))/18ν, where (Pρ-Ps) is the density of the ball bearing minus the density of the fluid, d is the diameter of the ball bearing, g is equal to 9.81 and v is the terminal velocity of the ball bearing. I believe this equation can also be written as μ=(2/9)*((Pρ-Ps)/v)*gr2, where r is the radius of the ball bearing.

    3. The attempt at a solution
    I have tried to rearrange the second equation in order to get r2/v, as the graph would be I think? leaving me with 9μ/(2(Pρ-Ps)g) = r2/v, which I think would mean that r2 ∝ 1/v?
    However I am confused as to what my graph would show (i.e what the gradient would be equal to etc) and whether I have rearranged the equation correctly.

    As a side note, I am unable to ask my teacher presently as I am currently off school ill and ideally I would like to have finished my report when I go back in.
    Any help would be much appreciated, thank you!
    Alex
     
  2. jcsd
  3. Dec 1, 2014 #2

    BvU

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    Hello Alex, welcome to PF :) Hope you get well soon.

    It's good practice to plot experimental results by using the y axis for what you measure and the x axis for what you vary. I suppose you measured the time it took the balls to fall from one level to a lower one. And you varied the diameter and the material of the balls.

    Another good practice is to try to plot results in such a way that a linear relationship is achieved (at least according to the prediction of the theory). Sometimes that means you need to square, to take a square root or a logarithm.

    If you look at your expression, you see you can write ##\displaystyle v = {d^2 \; \Delta\rho g \over 18\mu}## which looks like ##v = C\; d^2##, so you expect a straight line if you plot something that is proportional to v as a function of something like d2.

    Here, v = distance / time means that 1/time is a good one to plot vertically. The distance ##\Delta y## is the same in all cases (right?), so you divide that out in a later stage (*).

    For the horizontal axis, asw we saw, diameter d doesn't yield a linear relationship in the theory, but d2 does.

    With three materials you hope to get get three more or less straight lines, each with slope ##\displaystyle\Delta\rho g \over 18\mu \Delta y##. Draw the best possible straight lines to determine best values for these slopes.

    As a next step, you can claim you measured three slopes as a function of ##\Delta \rho##, so you can plot these slopes vertically and ##\Delta \rho## horizontally. That line is expected to have a slope ##\displaystyle g \over 18\mu \Delta y##. Again, draw the best possible straight line to determine its values. Finally, calculate ##\mu##.

    (*) because distance is the same for all measurements, the error in the slopes doesn't get smaller if you use more different ball sizes to get a better line. (The error in the distance is 'systematic' and not statistical)
     
  4. Dec 1, 2014 #3
    You have the right idea. Consider plotting v/r2 vs Δρ/μ (so that the left hand side is all geometric and kinematic, and the right hand side is all physical properties). The data should all lie on a straight line.

    Chet
     
  5. Dec 2, 2014 #4
    Thank you to both of you, you've helped me greatly!
     
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