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Rotational Inertia Physics C

  1. Jan 12, 2015 #1
    Screen_Shot_2015_01_12_at_8_56_00_AM.png
    1. The problem statement, all variables and given/known data

    A solid sphere (mass of m, radius of r and I=2/5 mr2) is rolling without slipping on
    a rough surface with a speed of v. A ramp (mass of 2m and angle of θ) rests on a
    smooth surface and is free to slide on the surface. As the ball rolls up the ramp, the
    ramp begins to move. Provide all answers in terms of the given variables and any
    fundamental constants.

    A. What will be the speed of the ball/ramp when the ball reaches its highest point on
    the ramp?

    B. What distance L will the ball roll up the incline?

    C. What will be the speeds of the ball and the ramp after the ball rolls back down off
    of the ramp?

    2. Relevant equations
    Conservation of Momentum, Conservation of Energy

    3. The attempt at a solution
    A. mv=(m+2m)v
    mv=3mv
    vf=1/3v

    B.
    we now have vf which is v/3 we can solve

    ΣEi=1/2 Iω2+1/2mv2=

    1/2(2/5mr2)(v/r)2+1/2mv2=

    1/5mr2+1/2mv2=7/10mv2

    ΣEf=mgh+1/2*3mvf2=

    mgh+1/2*3m(v/3)2=

    mgh+1/6mv2=7/10 mv2

    h=8v2/15g

    L=(8v2/15g) cscΘ

    c. I would like guidance on how to solve c.
    I know it uses energy, but I'm stuck on this one
     
    Last edited: Jan 12, 2015
  2. jcsd
  3. Jan 12, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Once again, momentum and energy are conserved.
     
  4. Jan 12, 2015 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You'll need both energy and momentum for (c). It is probably easier to start in the frame where (ramp+ball) start at rest.

    Technical detail for (b): It is beyond the scope of this problem, but in general you will get losses due to internal friction when a ball hits an incline like that.
     
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