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Tangential Speed

  1. May 12, 2008 #1
    [SOLVED] Tangential Speed

    A 4k ball is attached to a vertical rod with a cord 1.6 m long. As the ball rotates around the vertical rod in a circle of radius R = 0.8 m, what is the tangential speed of the ball?

    Any help is appreciated.
     
  2. jcsd
  3. May 12, 2008 #2
    You need more information. What was the speed when the radius was 1.6m?

    You need some kind of time information.
     
  4. May 12, 2008 #3
    Oh, forgot to add that the angle that the string makes with the rod is 30 degrees
     
  5. May 12, 2008 #4
    Picture the following force diagram. The string is the hypotenuse of a right triangle. The vertical side of the right triangle is equal to the weight of the ball [tex]mg[/tex] while the horizontal side is equal to the centripetal force [tex] F_{c}[/tex] acting on the ball [keeping the ball moving in a horizontal circle]. The angle between the vertical side of the triangle and the hypotenuse is 30 degrees as given. The forces are vectors and are therefore related through the tangent function:
    tan30=Fc/mg from which we can find the centripetal force
    Fc=mg*tan30=4*9.8*tan30
    Since centripetal force is equal to Fc=m*v^2/R all you need to know now is the radius of the circular path which is given....
    Finally, solve for v: v=sqrt[Fc*R/m]


    [tex]F_{c} = (mg)Tan\theta[/tex]


    [tex] V = \sqrt\frac{F_{c}(r)}{m}[/tex]
     
    Last edited: May 12, 2008
  6. May 12, 2008 #5
    Ok, that makes sense. Thx for your help.
     
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