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Circular motion in hemisphere

  1. Jun 7, 2012 #1
    1. The problem statement, all variables and given/known data
    As shown in attached figure, a small object is in uniform circular motion in a horizontal plane, on the smooth of a hemisphere (radius:r). The distance between the object's plane of motion and the hemisphere's lowest point is [itex]\frac{r}{5}[/itex]

    What is the speed of the object?


    2. Relevant equations
    ƩF=[itex]\frac{mv2}{r}[/itex] ....(1)

    Ncosθ=mg ...(2)



    3. The attempt at a solution

    From (1)
    and I get ƩF from FBD wrote in attached figure ƩF=Nsinθ

    From (2) I knew that N=[itex]\frac{mg}{cosθ}[/itex] ..(3)

    substitute (3) in (1) in got gtanθ=[itex]\frac{v2}{r}[/itex] ..(4)

    and I try to find tanθ from geometric of hemisphere

    First, I try to find the radius (let it is r') of this mass at r/5 from the lowest point of hemisphere

    If I look in the picture and use pythagoras r' = (r2-([itex]\frac{4r}{5}[/itex]))1/2
    ∴r' = [itex]\frac{3r}{5}[/itex]
    Thus; tanθ = 3
    substitute in (4) v = √3gr

    but the answer is [itex]\frac{3√5gr}{10}[/itex].......

    Or I get tanθ wrong or use wrong geometric condition of hemisphere ???

    help is appreciate

    Thanks :!!)
     

    Attached Files:

  2. jcsd
  3. Jun 7, 2012 #2
    Your tanθ should be equal to (3/5)r/(4/5)r=3/4

    tanθ=v2/r'g
    v2=3/4x3/5rg=3/4x3/5grx5/5=3.3.5gr/4.5.5
     
  4. Jun 7, 2012 #3
    Oh!!! thanks azizlwl :wink:

    i get it this is an easy one but i can't notice o:)
     
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