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Help with physics problem

  1. Nov 26, 2005 #1
    the question:

    You have a supporting point and a ball connected by a
    string of length 100cm. There is a peg at a distance d
    below the supporting point. You release the ball from
    rest at an instance when the ball is totally
    horizontal to the point, it swings along an arc. When
    the string catches on the peg, the ball swings upward
    but does not complete a circular path around the peg.
    Instead, the abll leaves its circular path, and
    strikes the peg.

    1) Find the distance d below the point of support at
    which the peg should be placed for this to happen.

    2) You have to find a function d(theta) at which the
    peg needs to be placed for this to happen.
     
  2. jcsd
  3. Nov 26, 2005 #2

    Integral

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    Staff Emeritus
    Science Advisor
    Gold Member

    Perhaps the reason this question has not been replied to is that the final part is not clear. How does the ball strike the peg? Could you post a picture showing the situation?
     
  4. Nov 26, 2005 #3

    lightgrav

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    Homework Helper

    This is a tough problem.

    Finding the speed of the ball at the bottom is easy (use E conservation).

    after string hits peg, the ball motion is circular up past horizontal,
    but you don't know the effective length of the string L = (1[meter] - d).

    Call theta the angle above the horizontal at which ball leaves the circle.
    ball is a 2-d projectile after that, from (x = L cos theta , y = L sin theta)
    with velocity components (- v sin theta , v cos theta) , to peg at (0,0),

    This is much easier problem in the forward direction (given d, where does ball cross x=0 line) . maybe you program it into a calculator or spreadsheet, then change d until it hits peg ...?
     
  5. Nov 27, 2005 #4
    i agree with Integral....

    wouldn't the diameter of the ball and the peg matter?
    i can picture a solution with peg of 1 cm diameter and ball of 2 cm diameter, and the peg 96 cm vertically below the "supporting point".....
    :rofl:
     
  6. Nov 27, 2005 #5
    plusaf, the peg and ball are considered points
     
  7. Nov 27, 2005 #6
    there are 3 concepts involved:

    1. conservation of energy at the point when the ball leaves the smaller circle

    2. speed at the point when the ball leaves the smaller circle.

    3. freefall.

    can someone who knows physics work it out for me. the concepts are quite simple. But the algebra i did was extremely messy.
     
  8. Nov 27, 2005 #7
    Integral, obviously, there is no outside fore so there is only one way the ball could hit the peg...
     
  9. Nov 28, 2005 #8

    lightgrav

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    Did you define the angle above the horizontal that the circle becomes parabola?

    you should know the speed there will depend on L and d.
    I think that 2/3 d = L sin theta , and v^2 (at transition) = L g sin theta .
    I had to solve a quadratic in sin^2 theta , to hit the peg.
    So there are two angles, for a 1-meter string, if I've not made a sign mistake.
    (yeah, the algebra stinks. Some problems are best done on computer ...
    say, do you have access to Maple ...?)
     
  10. Nov 28, 2005 #9
    i'm on it

    agree
    somehow i couldn't agree. i imagined the ball stopped vertically at one point above the peg. and that makes the velocity components (vy=0, vx= something). and from that, i worked out that
    d=100 - {(2*vx^2*sin(theta))/([cos(theta)]^2*g)}

    i'm working the vx. i'm trying to understand how the energy conservation work. when the vertical component of velocity is zero, the horizontal is not.
     
  11. Nov 28, 2005 #10
    ehm... when i say theta, i mean
    "the angle between the horizontal line along the peg and the point where the ball starting to leave the circular path.
    and also, i was assuming that the peg was "straight" below the supporting point
     
    Last edited: Nov 28, 2005
  12. Nov 29, 2005 #11
    the peg and the ball problem

    First let us imagine the string does not break(it is not mentioned in the problem, but if u imagine this it is relatively simpler). now at certain angle above the horizontal this happens. the angle can be foundby equating the gravity force (downward) and the upward component of mv^2/r at that point. also v can be calculated from energy considerartion. Now treating it as a projectile problem the hitting of the peg can be understood. you can try this way. I have not done thew mathematics myself. So, i don't know how rigorous it is.
     
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