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I can't do space curvilinear motion

  1. Aug 15, 2011 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://a4.sphotos.ak.fbcdn.net/hphotos-ak-ash4/s720x720/300201_1919471514513_1473790586_31632884_1692676_n.jpg [Broken]

    2. Relevant equations

    aR = [itex]\ddot{R}[/itex] - R[itex]\dot{\phi}[/itex]2 - R[itex]\dot{\theta}[/itex]2cos2([itex]\phi[/itex])

    a[itex]\theta[/itex] = [itex]\frac{cos(\phi)}{R}[/itex][itex]\frac{d}{dt}[/itex](R2[itex]\dot{\theta}[/itex]) - 2R[itex]\dot{\theta}\dot{\phi}[/itex]sin[itex]\phi[/itex]

    a[itex]\phi[/itex] = [itex]\frac{1}{r}[/itex][itex]\frac{d}{dt}[/itex](R2[itex]\dot{\phi}[/itex]) + R[itex]\dot{\theta}[/itex]2sin[itex]\phi[/itex]cos[itex]\phi[/itex]


    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 16, 2011 #2
    You can calculate y,tt (the acceleration in the y direction) = v^2/r = 166*166/1200 = 23m/s^2 the acceleration in the y direction. With this you can find a_r and a_phi by some trig. You know at the instant of calculation that phi,t = 0, R,t = 0, and using some trig you can calculate theta,t.

    Does this help?
     
  4. Aug 16, 2011 #3
    i've already done that bit. I worked out the normal acceleration for the loop, [itex]\dot{\theta}[/itex] as 0.1437 rad/s, ar = 8.601 m/s2 and a[itex]\phi[/itex] as 21.49 m/s2 but the problem is when i try to input all this into working out the values of [itex]\ddot{R}[/itex] and [itex]\ddot{\phi}[/itex] that i seem to come out with something completely different.
     
  5. Aug 16, 2011 #4
    The units you have for a_phi and the units for a_phi in the answer are different. I think you are off by a factor of R?
     
  6. Aug 17, 2011 #5
    It's asking me to work out [itex]\ddot{\phi}[/itex] (rad/s2), which is a different quantity to a[itex]\phi[/itex], (m/s2). If i just divide 21.49/1077 that equals 0.0199 which is not the right answer. My problem is that i don't know whether the value i have for a[itex]\phi[/itex] is wrong, or whether i've done something wrong in the equation or what?
     
    Last edited: Aug 17, 2011
  7. Aug 17, 2011 #6
    Maybe I'm doing something wrong but I suspect the answer in the book. I got an acceleration in the y direction of about 23m/s^2 and R,tt should be a fraction of that number and not the 34.4m/s^2 in the book. I'm stumped, if you get an answer please let us know, if I'm doing something wring I would like to know.
     
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