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Posted by on Friday, June 15, 2012 at 11:49am.

A ball having a mass of 5 kg is attached to a string 1 m long and is whirled in a vertical circle at a constant speed of 13 m/s.

(a) Determine the tension in the string when the ball is at the top of the circle.
(b) Determine the tension in the string when the ball is at the bottom of the circle.

The answers are supposed to be
a) 796 N
b) 894 N

How do I get these answers? Thank you in advance.

  • Physics - , Friday, June 15, 2012 at 3:26pm

    T(top ) = m(v²/R – g ) =796 N
    T(bottom ) = m(v²/R + g) = 894 N

  • Physics - , Friday, June 15, 2012 at 3:49pm

    When I use the first equation I get -90.8 N. What am I doing wrong?

    I'm putting this is my calculator:

    5(169/(.5-9.81)) = -90.76262084 N

  • Physics - , Friday, June 15, 2012 at 3:58pm

    T(top)= 5•(13²/1-9.8)=5•(169-9.8)=
    =5•159.2=796 N.
    T(bottom) = 5•(13²/1+9.8)=5•(169+9.8)=
    =5•178.8=894 N

  • Physics - , Friday, June 15, 2012 at 4:00pm

    I see what I was doing wrong now. I was putting the parenthesis in the wrong places. Thank you!

  • Physics - , Friday, June 15, 2012 at 4:04pm

    Why does the force done by gravity change from positive to negative?

  • Physics - , Friday, June 15, 2012 at 5:13pm

    Really we have (according to Newton’s 2 law)
    (positive direction of y-axis - downwards)
    for the top point:
    ma =T+mg => mv²/2=T+mg,
    T= mv²/2 - mg
    for the bottom point:
    - ma = - T+mg => - mv²/2= -T+mg ,
    T= mv²/2 + mg

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