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An object rolling along a hemispherical bowl

  1. Jul 10, 2007 #1
    1. The problem statement, all variables and given/known data

    A uniform solid sphere (moment of inertia = 2/5 mr^2) of mass 1.5kg and radius r = 0.473m, is placed on the inside surface of a hemispherical bowl of radius R = 2.77m. The sphere is released from rest at an angle of 66.9 degrees from the vertical and rolls without slipping.
    a) How much potential energy has the sphere lost when it reaches the bottom of the bowl?
    b) What is the translational velocity of the sphere when it reaches the bottom of the bowl?
    c) What is the angular velocity of the sphere when it reaches the bottom of the bowl?

    2. Relevant equations

    KE = 1/2 Iw^2. PE = mgh.

    3. The attempt at a solution

    For part a, do I just do (1.5kg)(9.8)(2.77sin66.9)?
    After I find PE, I will just equate it with 1/2 mv^2 to find the translational velocity and 1/2 Iw^2 to find the angular velocity?

    Any help is appreciated. Thank you!
     
  2. jcsd
  3. Jul 11, 2007 #2

    olgranpappy

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    part a looks fine. part b is not fine. the total energy initially is PE + KE_trans + KE_rot. this must equal the total final energy PE_f + KE_trans_f+KE_rot_f. Part a is the value of PE and PE_f=0.

    thus set PE = KE_trans_f + KE_rot_f

    not equal to each individually.
     
  4. Jul 11, 2007 #3

    Dick

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    And find a relation between the angular velocity and the linear velocity, since it 'rolls without slipping'.
     
  5. Jul 11, 2007 #4
    I got it. Thank you so much!
     
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