I can't do space curvilinear motion

  • #1

Homework Statement



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

Homework 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]


The Attempt at a Solution

 
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Answers and Replies

  • #2
Spinnor
Gold Member
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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?
 
  • #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.
 
  • #4
Spinnor
Gold Member
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364
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?
 
  • #5
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?
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:
  • #6
Spinnor
Gold Member
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364
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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