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Object hung from two ropes - determine weight

  1. Sep 9, 2012 #1

    bcalkins

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    Original Problem:
    sin(45)(425N) + sin (60)(601N) = 821N
    The problem is, no scale is perfect. Let's assume for the time being that the angles are quite accurate, but you know based on your past experience that these scales can be off by as much as 2 N. This uncertainty propagates through any calculation that involves the measured quantities.

    By how much (in N) could your estimation of the weight of the box be off?

    Hint: The easiest way to do this is by finding the highest and smallest possible values of the weight that can result from the range of values of the measured forces.

    What I'm doing - but wrong answer:
    sin(45)(423) + sin(60)(599) = 817.8553853
    sin(45)(427) + sin(60)(603) = 824.147914
    Subtract higher from lower = 6.29300

    Where am I going wrong?
     
    bcalkins, Sep 9, 2012
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  3. Sep 9, 2012 #2

    Nessdude14

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    Let me try re-phrasing the question: How much do the maximum and minimum values differ from the calculated weight?

    The value you found (6.29) is the difference between the maximum and minimum values. Neither value (min or max) will actually differ from the real weight by that much, since the real weight is somewhere in the middle.
     
    Nessdude14, Sep 9, 2012
  4. Sep 9, 2012 #3

    bcalkins

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    So would the correct answer be 6.29/2=3.14?
     
    bcalkins, Sep 9, 2012
  5. Sep 9, 2012 #4

    Nessdude14

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    Actually, the minimum and maximum don't differ from the calculated weight by the same amount. One value has slightly more error than the other. Try finding the difference between the calculated weight and each of the min/max values.
     
    Nessdude14, Sep 9, 2012
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