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Homework Help: Work & energy - friction

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    A ball is released from height h. The friction coefficient between the straight part and the ball is 'u'. I need to find the smallest h so that the ball doesn't fall off the track.
    The angle alpha=45 degrees.

    2. Relevant equations
    Work of non-conservative forces = Change in mechanical energy

    3. The attempt at a solution
    I calculated the work done by the friction force while the ball is going down the straight part.

    X=the length of the straight part.

    We get that:

    since cos(alpha)/sin(alpha)=1

    Now I want to say that Wf=change in mechanical energy, so:


    when v=the velocity of the ball when it reaches the end of the straight part. We get:


    Now to the second part, the frictionless rail. Since all the forces are conservative now:


    When V1^2=g*h(1-u) -----> (the velocity we found before)
    V2=the velocity at the top of the loop

    So I want that V2>0, so after some work we get:


    but when I put in a numerical answer I'm told that I'm wrong. Is there a mistake in my solution?

    Attached Files:

  2. jcsd
  3. Dec 3, 2009 #2
    The condition v>0 at the top is not sufficient for the ball to stay on the track.
    You need to have the reaction force acting on the ball at the top to be >=0.
  4. Dec 3, 2009 #3
    yeah you're right I forgot, thanks..
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