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Rigid Body Problem

  1. Mar 8, 2007 #1
    1. The problem statement, all variables and given/known data

    Uniform disc, mass m, falls from position where theta 60 degrees. (P is a fixed point on rim of disc).

    Calculate the components of thrust along and perpendicular to GP on the smooth hinge at P when theta = 30degrees.

    see attatched image for diagram

    2. Relevant equations



    3. The attempt at a solution

    NB: theta with a dot is velocity (v), and theta with two dots is acceleration (r). Not sure if these are actually what the two of them mean, but thats what they'll be represented by.

    Transverse Equation:

    -ma(r)= mg sin theta - x
    x = mgsin theta + ma(r) (1)


    Radial Equation

    ma (v)^2= y - mgcos theta
    Y = ma (v)^2+ mgcos theta (2)

    Rotational equation about P

    I r= sum of moments
    2/3 m(a)^2 r= -mgasin theta

    2/3a r= -g sin theta

    a r= -(3/2) g sin theta (3)

    Integrating (3) gives

    a r= -3/2g cos theta + c

    c = 3/2g cos theta

    at theta = 60

    c = 3/2g cos 60
    therefore
    c = 3/4 g

    so

    a (v)^2= -3/2g cos theta + 3/4 g

    at theta = 30, (3) gives

    a r= -3/2g sin30
    = -3/4g

    (4) gives

    a (v)^2= -3/2g cos30 + 3/4g
    = -3/2 * root(3)/2g + 3/4g
    = -3root(3)/4g + 3/4g

    = (3-3root(3))/4 g


    From (3), at theta = 60

    -ma r= mgsin theta - x
    -m(-g/3) = mgsin60 - x
    1/3mg = root(3)/2mg - x
    1/3mg = root(3)/2mg - x
    2/6mg = 3root(3)/6mg - x
    x = 3root(3) - 2/6 mg

    which is wrong. So I won't even bother looking at my value for y...

    And i'm not sure where i've went wrong :/ seems every time i attempt this question I get a different answer.
     

    Attached Files:

  2. jcsd
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