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Homework Help: Swinging, pendulum like mass

  1. Aug 21, 2008 #1
    how can i express tension in this case, using alpha, alpha max,g, m, and L ??

    a case of a mass of m hanging from a ceiling on a cord with a length of L swinging at a maximum angle of "alpha max" on either side, and at any given moment and an angle of alpha(changes all the time)

    how can i express T, the strings tension, using the parameters m,g,alpha,alpha max,and L??

    what i did was say:
    according to circular movement, looking at the radial acceleration ar
    F=ma
    T-mg*cos(alpha)=mar=m*v^2/L
    T=m(v^2/L+g*cos(alpha))

    now how can i express v using the parameters, what i think i need to do is look at the maximum angle, and say V=0 so mar=0 so T(point of max)=mgcos(alpha max) but i dont see how that cann further me at all,
    again, in the end i need an expression T=???????? using only m,g,L,alph, alpha max

    ***no friction at all, mass will reach alpha max every time, no loss of energy
     
  2. jcsd
  3. Aug 21, 2008 #2
    T-mg*cos(alpha)=(m/L)*v^2

    V^2=(L/m)(T-mgcos(alpha))

    from here using energy,
    E(max point)=mgh=const
    my point of reference for potential energy being the ceiling

    h=cos(alpha)*L

    E=0.5mv^2+mgh=-mgcos(alpha max)*L
    v^2=(L/m)(T-mgcos(alpha))

    0.5(m)(L/m)(T-mgcos(alpha))-mgcos(alpha)*L=-mgcos(alpha)*L

    0.5(T-mgcos(alpha))-mgcos(alpha)=-mgcos(alpha)
    T-mgcos(alpha)-2mgcos(alpha)=-2mgcos(alpha)

    T=3mgcos(alpha)-2mgcos(alpha max)

    is this correct??
    the question asked me to use L in the expression, do i need it??
     
  4. Aug 21, 2008 #3
    I would start by determining the period of the pendulum which will be a function of length and gravity. You then have your alpha max which will determine your displacement. Period and displacement you can then equate to velocity.

    EDIT: Bit of a time lapse with post #2, wasn't able to read it before this post. What happened to this L?

     
  5. Aug 21, 2008 #4
    i divided the whole equation by L
     
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