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Write Vector Expression in n-t and x-y coordinates of Acceleration

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec2

    I have attached an image of the question.

    2. Relevant equations
    an = v2/r = rθ2 = vθ'

    at = v' = rθ'


    3. The attempt at a solution

    I've managed to calculate en and et correctly

    at = (4.2 ft)(4.475 rad/sec2) = 18.795 ft/sec2

    at = 18.795ft/sec2

    For an I calculated velocity first:

    v = rθ' = (4.2ft)(2.22 rad/sec)
    v = 9.324 ft/sec

    Hence an = (9.324 ft/sec)(2.22 rad/sec)
    an = 20.69928 ft/sec2

    Unfortunately, I'm now having difficulty with finding the velocity in terms of i and j.

    I had thought that I could use geometry to do it:

    atcos(90-66) = -17.77 i
    atsin(90-66) = 7.644 j

    But the system says it's wrong. Help is greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 2, 2013 #2
    Why don't you try to express en and et in terms of ex and ey ? Doing that, you can find the total acceleration, a = an + an , in terms of its projections on x and y axis.


    * e i is the unit vector in the direction of the subscript "i".
     
  4. Feb 2, 2013 #3

    SammyS

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    attachment.php?attachmentid=55292&d=1359837236.png

    Both n and t components contribute to each of the i and j components.
     
  5. Feb 2, 2013 #4
    @SammyS: You were right. To find the i component I did the following:

    -atcos(24) -ancos(66) = -25.589i

    For j:

    atsin(24) - ansin(66) = -11.265 j

    Thanks everyone.
     
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