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March 30, 2017

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Believe it or not, a plumb-bob does not hang exactly along a line directed to the centre of the Earth! Determine how far off true plumb a bob hangs in Cape Town. In which direction is the deviation (north, east, south, or west)? How would your answer differ for a plumb-bob in London? (Assume that the Earth is spherical.)

  • physics - ,

    What is centripetal acceleration as a function of latitude?

    w = 2 pi/24 hours = 2 pi /(24*3600) rad/s

    Ac = w^2 r
    r = Re cos (Lat)
    where Re is earth radius and Lat is latitude angle

    calculate Ac
    call tension in plumb bob line T
    then T will be off the direction to center of earth by angle A

    T vector - mg vector = m Ac vector
    draw those with mg toward earth center and Ac horizontal toward earth N-S axis

    Then |T| cos A = m |Ac| cos Latitude +mg
    and |T| sin A = m |Ac| sin Latitude

    approximate |T| by m g
    then sin A = (Ac/g) sin Latitude approximately

  • physics - ,

    4.7 degrees

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