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.)

2 answers

1. 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

   Answer ID
   534591

   Created
   April 21, 2011 11:29am UTC

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   URL
   https://questions.llc/answers/534591

2. 4.7 degrees

   Answer ID
   1205426

   Created
   April 10, 2015 1:50pm UTC

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   URL
   https://questions.llc/answers/1205426