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Conservation of Energy/Motion Question

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data

    A small mass m slides down from rest at the top of a frictionless spherical surface of radius R=.5 meters. What is the speed of the particle at position x where it loses contact with the surface, and velocity makes an angle of θ=48.2 with the vertical?

    The answer choices are:

    (A) 1.28 m/s
    (B) 1.82 m/s
    (C) 1.93 m/s
    (D) 2.36 m/s
    (E) 2.58 m/s

    2. Relevant equations

    Conservation of Energy?

    3. The attempt at a solution

    I thought maybe start with PE1=PE2+KE, where h=2r, and then find the cosine component of the height when velocity is at that angle, to do: mg(2r)=(1/2)mv2+mg((cos48.2)+R), but that didn't work. I got .57, which is not even close to any of the choices.
     

    Attached Files:

  2. jcsd
  3. Feb 21, 2012 #2
    Hi Victorzaroni
    try equating component of weight with centripetal force
     
  4. Feb 21, 2012 #3
    Component of weight as in the cosine component or sine?
     
  5. Feb 21, 2012 #4
    see at the point when it leaves the contact
    mgcos(θ) will be equal to centripetal force o:)
     
  6. Feb 21, 2012 #5
    thanks. I get it now! It's 1.82, choice B
     
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