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Need help finding force components.

  1. Apr 9, 2005 #1
    I am having a problem with this question. I cant figure out how to approach it.


    A solid sphere of mass m and radius r rolls without slipping along the track. it starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r.

    What are the force components on the sphere at he point P if h = 3R?

    How would I go about solving this problem? I attached a picture of the situation.
     

    Attached Files:

  2. jcsd
  3. Apr 9, 2005 #2
    Well you need to split up this problem. First, the sphere moves down the incline under the influence of gravity (thus, there will also be a normal force)

    Then, secondly, it moves along a loop, which is circular. Then, there must be some centripetal force and also gravity right ???

    regards
    marlon
     
  4. Apr 9, 2005 #3
    You know, just to elaborate, there is a great classic associated with this figure. Suppose we let a point particle of mass m (the solution is analoguous for a solid object, you only will need to incorporate the rotational inertia I) slide down the incline from heigth h. What will this h be as a function of radius r, in the case that the object must STOP at the top of the loop.

    Well, first we study the motion along the incline : energy conservation learns us :

    mgh =1/2mv² and thus v² = 2gh

    Then, we study the loop : there will be both gravity and centripetal force (mv²/r) on the object. At the top : mv²/r = mg (the centripetal force must eliminate gravity. Well, actually this is the centrifugal force, directed along the opposite direction of the centripetal force) : mg = (mv²)/r and thus v² = gr

    Again applying energy conservation between bottom and top of the loop learns us :

    1/2mv² (here v² = 2gh) = mg2r + 1/2mv² (here v² = gr)

    This eaquation gives : mgh = mg2r + mgr/2 --> h = 2r + r/2 = 5r/2

    regards
    marlon
     
  5. Apr 9, 2005 #4
    Im still not seeing how I would do this. You said to split it up into two parts but what exactly am I trying to find in these two seperate parts?

    I am assuming the first part, when the ball is rolling down the incline, I am trying to find the velocity, right?
     
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