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GR9677 #68
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Alternate Solutions |
jmason86
2009-10-04 15:04:26 | MOE:
As Yosun said: PE = mgscos . Eliminate (B) and (C)
Also as Yosun said: Translational KE = 1/2m . Eliminate (D)
Only (A) and (E) remain.
Rotational KE = something... another term. (A) is only the Translational KE and the PE; it lacks a Rotational KE term. Eliminate (A).
(E) Remains. |  |
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Comments |
jmason86
2009-10-04 15:04:26 | MOE:
As Yosun said: PE = mgscos. Eliminate (B) and (C)
Also as Yosun said: Translational KE = 1/2m. Eliminate (D)
Only (A) and (E) remain.
Rotational KE = something... another term. (A) is only the Translational KE and the PE; it lacks a Rotational KE term. Eliminate (A).
(E) Remains. | | f4hy
2009-04-03 18:28:36 | LIMITS!
I first eliminated C since the wrong sign and then B because no theta dependance.
From there I thought what would happen if  . Well then it should be like a free falling particle so D is out. The spinning must give some kinetic energy so there goes A. E is the only one left. |  | r10101
2007-10-30 19:13:43 | After eliminating (B) and (C) by the potential term, use variable dependency: T = T) for sure, so (A) and (D) are both out as well.
p3ace
2008-04-11 10:25:59 |
This is a great observation, but if there were other choices with  dependence in the middle term, one would have to solve more exactly.
I would use the expression for  in spherical coordinates which should be memorized, and in cylindrical coord.'s as well.
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p3ace
2008-04-11 10:44:23 |
I hit post prematurely. Sorry.rnAs I was saying, the expressions for velocity in the other coordinates are very handy for problems like this one because one can simply dot r vector with itself to get v^2 for kinetic energy. rnIn this case, The spherical symmetry lends itself perfectly to the problem because s is just r, and is  '. Also, is fixed, so ' is zero. Then dot the velocity with itself and multiply by (1/2)m and Wah-Lah. You have it.rnI would type in the origianl expression for velocity in spherical coordinates but I'm not used to Latex and would rather be studying. I got it from Mechanics by Symon, and I've used it to solve numersous problems with cylindrical or spherical symmetry.
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