GR0177 #92



Alternate Solutions 
uhurulol 20141021 21:55:52  Process of elimination solution:
Hamiltonian , a minus in front of the potential would indicate a Lagrangian. Eliminate (A) (C) and (D).
Spring potential energy and kinetic energy are both proportional to , not or , eliminate (B).
All that's left is (E). Hooray.  

Comments 
uhurulol 20141021 21:55:52  Process of elimination solution:
Hamiltonian , a minus in front of the potential would indicate a Lagrangian. Eliminate (A) (C) and (D).
Spring potential energy and kinetic energy are both proportional to , not or , eliminate (B).
All that's left is (E). Hooray.   Barney 20121107 09:18:00  The TestTakers Solution:
The Hamiltonian is the Energy E of the system  pick choice (E).
(Funny to see that ETS people seem to like little eastereggs. This is not the only case where you can observe such "accidental" matching.)   jmason86 20090705 20:04:03  If you didn't know the potential energy of the spring, you could derive it from Hooke's law.
In general, , so
What I don't get is that the negative in Hooke's law doesn't just disappear because you integrate.. so why is potential energy stored in a spring defined to be positive? This would lead to the incorrect answer of (D).
jmg810 20090708 14:19:25 
If a force is derivable from a position dependent potential then = (), and hence .

jmg810 20090709 09:20:29 
Typo fix:

jmason86 20090723 17:36:11 
Thanks!

  neutrino 20071031 03:34:57  I don't understand the signs. If the string is ``fully stretched", , but is max. I would guess answer D in this case.
What is my error?
hot_dark_matter 20080523 15:00:49 
If the spring is fully stretched, it doesn't mean that the kinetic energy is zero. Presumably, the directions of and indicate the system can have translational and rotational energy.
As for the signs, kinetic energy is always positive and so is the potential energy stored by a spring. This eliminates all choices but (B) and (E). Given that there is only one spring, the answer must be (E).

 

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