1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Circuler motion angle

  1. Feb 5, 2010 #1
    hi,
    can some one please tell me where am i wrong?

    A mass of 9.50 kg is suspended from a 1.19 m long string. It revolves in a horizontal circle.
    The tangential speed of the mass is 2.28 m/s. Calculate the angle between the string and the vertical.

    so what i need is the ratio between radius and string length. to find the radius i use v and the fact it equals wr. w is the square of ration between g and l.

    thanks
     
  2. jcsd
  3. Feb 5, 2010 #2
    Let the angle between the string and the vertical be [itex]\theta[/itex]

    [itex]Tcos\theta=mg[/itex] ------ (1)

    [itex]Tsin\theta=\frac{mv^2}{r}[/itex] ------ (2)

    Dividing (1) by (2),

    [itex]tan\theta=\frac{v^2}{rg}[/itex]

    [itex]r=lsin\theta[/itex]

    So,

    [itex]tan\theta=\frac{v^2}{lsin\theta g}[/itex]

    [itex]\frac{sin^2\theta}{cos\theta}=\frac{(2.28)^2}{1.19*9.8}=0.45[/itex]

    [itex]1-cos^2\theta=0.45cos\theta[/itex]

    [itex]cos^2\theta+0.45cos\theta-1=0[/itex]

    [itex]cos\theta=\frac{-0.45\pm\sqrt{(0.45)^2+4}}{2}[/itex]

    [itex]cos\theta=\frac{-0.45\pm2.05}{2}[/itex]

    [itex]cos\theta=0.8[/itex] or [itex]cos\theta=-1.25[/itex]

    Rejecting [itex]cos\theta=-1.25[/itex], we get

    [itex]cos\theta=0.8[/itex]

    [itex]\theta=36.87^0[/itex]
     
  4. Feb 5, 2010 #3

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I respectfully ask in the future that you do not post full solutions to problems. Provide help and guidance only, per Forum rules. Thanks.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook