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Force exerted on hemisphere

  1. Apr 29, 2016 #1
    1. The problem statement, all variables and given/known data

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    2. Relevant equations


    3. The attempt at a solution

    Using the fact that the sphere is in equilibrium in the 'y' direction , the force exerted by the floor N = 2mg .

    Now , if I consider the lower hemisphere then , vertical force exerted by top hemisphere + weight of lower hemisphere = Normal reaction from the floor .

    This means , vertical force exerted by top hemisphere on lower = mg

    Should this be the total force exerted on the lower hemisphere ?

    Thanks
     

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    Last edited: Apr 29, 2016
  2. jcsd
  3. Apr 29, 2016 #2

    TSny

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    Yes, the sphere as a whole is "in equilibrium in the y direction" since the center of mass of the sphere has no acceleration.

    However, does the center of mass of the lower hemisphere have any acceleration?
     
  4. Apr 30, 2016 #3
    It has centripetal acceleration ω2r ( r=3R/8) directed towards the center of the sphere i.e in +y direction (upwards)

    Taking + y to be upwards , 2mg - mg +R = mω2r , gives R = 5mg/8 downwards i.e option A)

    Is that ok ??
     
  5. Apr 30, 2016 #4

    TSny

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    Yes, I believe that's all correct.
     
  6. Apr 30, 2016 #5
    Thank you :smile:
     
    Last edited: Apr 30, 2016
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