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Calculate the force of ball on an incline leaning on a wall

  1. Jun 23, 2015 #1
    Hi all,

    I'm working on a problem from the Feynman exercise book, and have been racking my brains for an answer, so would really appreciate some help here. The problem seems simple enough:

    A ball with a 3cm radius, weighing 1kg rests on an inclined plane (angle alpha) and also touches a vertical wall. Neglect friction.

    (see attached diagram)

    What is the force of the ball acting on the wall (Fw)?

    The answers in the back gives
    Fw= tan(alpha) kg.wt

    I got the force due to gravity acting down the plane, Fr = 9.81.sin(alpha). The horizontal component of this force, which to my mind is the force acting on the wall, is

    Frhor=9.81* sin(alpha)cos(alpha)

    What am I missing here?!!!

    Thanks!

    Amit
     

    Attached Files:

  2. jcsd
  3. Jun 23, 2015 #2

    SammyS

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    Hello Amit86. Welcome to PF !

    ball-in-corner-problem-png.85133.png

    The only forces acting on the ball are gravity, and the two forces supplied by the two surfaces. Right ?

    Can the vertical wall counteract the force gravity exerts on the ball?
     
  4. Jun 23, 2015 #3
    Hi, Sammy. That's correct.
     
  5. Jun 23, 2015 #4

    SammyS

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    There are two questions I asked.
     
  6. Jun 23, 2015 #5
    I imagine the vertical wall can counteract the force
     
  7. Jun 23, 2015 #6

    SammyS

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    (By the way, there is a "Reply" feature in the lower right-hand corner of the message screen that's helpful with dialogue.)

    Can the vertical surface produce a force on the ball that has a vertical component?

    (There's no friction.)
     
  8. Jun 23, 2015 #7
    As far as I can tell, I don't think it can. "both surfaces have negligible friction"
     
  9. Jun 23, 2015 #8

    SammyS

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    Right.

    Therefore, only the incline can provide a force which has the vertical component necessary to counter act the gravitational force. Right?
     
  10. Jun 23, 2015 #9
    I suppose that's true.
     
  11. Jun 23, 2015 #10

    HallsofIvy

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    You say things like "I imagine", "as far as I can tell", and "I suppose". Do you know in what direction gravity acts? Do you know in which direction the force from the wall acts?
     
  12. Jun 23, 2015 #11
    Of course I do; check the diagram. I am looking for some insight into where the tan(alpha) comes from. I've provided all the information given in the question, I need to get some sense of how to proceed with a solution, and would appreciate constructive advice.
     
  13. Jun 23, 2015 #12

    SammyS

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    This should help you to find the vertical force the incline needs to exert on the ball.
     
  14. Jun 23, 2015 #13
    okay thanks!
     
  15. Jun 23, 2015 #14
    Ok so I think I've got then...

    The vertical component of the reaction force of the plane = the total gravitational force (i.e 9.81 x 1kg), so the horizontal component of reaction force of the plane would be 9.81*tan alpha Newtons or

    Fw= tan(alpha) kg wt

    Thanks for your help!
     
  16. Jun 23, 2015 #15

    SammyS

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    Correct !

    Notice that this vertical force is greater than the vertical force that the incline exerts for the case when the ball is allowed to roll.
     
    Last edited: Jun 23, 2015
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