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Physics Practical: Check proportionality

  1. Aug 16, 2015 #1
    1. The problem statement, all variables and given/known data
    image.jpg image.jpg image.jpg

    For part d), how to show that they are inversely proportional to each other ? The mark scheme states:

    "Correct calculation to check inverse proportionality. √h x cosϑ = k. Sensible comments relating to calculations to within 20% or their own value and suggested relation."

    What do they mean by 20%?
    2. Relevant equations
    Percentage uncertainty = (uncertainty/measured value) x100%

    3. The attempt at a solution
    My values are,

    √h = (2.95±0.1) cm, cos θ = 0.50. k1 = 2.95 x 0.50 = 1.475
    √h = (2.30±0.1) cm, cos θ = 0.64, k2 = 2.30 x 0.64 = 1.472

    I calculated the percentage difference of k,
    ((1.475-1.472) /1.472 ) x 100% = 0.2%

    Then I calculated the uncertainty of √h = (0.1 / 2.30) x 100% = 4.3%

    This is the method I followed from a textbook, so what does the 20% in the mark scheme represents ? Hope you all understand what I'm doing here..
  2. jcsd
  3. Aug 16, 2015 #2


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    2017 Award

    Staff: Mentor

    The square root of a height should not have centimeters as units.

    A 20% uncertainty which the quoted text might suggest would be very large.

    I don't like the way the problem is set up. With just those two measurements, it is not reasonable to draw any conclusions about the relation between h and θ.

    Fun exercise: calculate the height h which allows tilting the bottle by 90 degrees without tipping over. Is this realistic?
  4. Aug 17, 2015 #3
    Oh yeah, was not aware, sorry.

    Hmm.. what do you mean tilting the bottle by 90 degrees?
  5. Aug 17, 2015 #4


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    2017 Award

    Staff: Mentor

    Which height h corresponds to θ=0? Is that realistic?
    What happens if you reduce h a bit more?
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