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Homework Help: Tethebal| problem, radial acceleration, angle of ball orbit

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    This is a concept/procedure question. I am playing teth3rbalI with a 1 kilogran ball and it is tied to a meterlong string. When I hit the ball it circles the pole at 1.6 Hz. Find the anglethat the string makes with thepole.

    2. Relevant equations
    a[tex]_{r}[/tex]=v[tex]^{2}[/tex]/r
    a[tex]_{r}[/tex]=(4[tex]\pi[/tex][tex]^{2}[/tex]r)/T[tex]^{2}[/tex]

    T=1/f
    f[tex]_{r}[/tex]=ma[tex]_{r}[/tex]

    3. The attempt at a solution

    So I found the period for one cycle but that's basically it and I'm stuck without a radius or at least a velocity to go by. What am I overlooking?
     

    Attached Files:

  2. jcsd
  3. Nov 24, 2007 #2

    Shooting Star

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    The whirling string has to make an angle, say 'x', with the vertical in the downward direction. It lies on a cone, whose semi-vertical angle is 'x'. If 'T' is the tension in the string, then mg=T*cos(x). The centipetal force is T*sin(x). The mass m travels in a horizontal plane.

    Now you try for a while.
     
  4. Nov 24, 2007 #3
    hmmm

    k so wow, i' not getting very far at all on this.

    since Tcos(x) = mg then Tcos(x) = 9.8 N and since T sin(x) = centripedalforce then Tsin= 1kg((4[tex]\pi[/tex][tex]^{2}[/tex]r)/(.625[tex]^{2}[/tex]))

    I'm slightly nervous proceeding since my next move would be to do a pythagoras of 9.8[tex]^{2}[/tex] + ((4[tex]\pi[/tex][tex]^{2}[/tex]r)/TimePeriod[tex]^{2}[/tex])[tex]^{2}[/tex] = T[tex]^{2}[/tex] which doesn't seem right nor does it make me any more confident.
     
    Last edited: Nov 24, 2007
  5. Nov 24, 2007 #4
    kk think i got it but does the mass cancel out?
     
  6. Nov 25, 2007 #5

    Shooting Star

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    It'd be neater if you didn't write the values of g etc in every step. Use symbols and plug in the values later.

    Yes, the mass cancels out.

    The centripetal force is m*w^2*r= T*sin x.

    tan x = Tsin x/Tcos x = mw^2*r/mg =rw^2/g.

    You know the value of r, and w is given.
     
  7. Nov 25, 2007 #6

    cristo

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    If you look at Shooting Star's post this should become apparent.

    It would also help if you formatted your posts in a more readable way. For example [ tex] [ /tex] tags should be used for LaTeX set on its own, whereas you should use [ itex] [ /itex] tags for inline maths. Furthermore, it would help if you either did all your equations in tex, or none of them, since that would prevent strange mixed formatting.

    Just a few thoughts, anyway.
     
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