Abhisar
  • Abhisar
A particle moves in a potential region given by \(\sf U=8x^2-4x+400\) J. Its state of equilibrium will be
Physics
schrodinger
  • schrodinger
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Abhisar
  • Abhisar
Michele_Laino
  • Michele_Laino
we have to request that the subsequent condition holds: \[\Large \frac{{\partial U}}{{\partial x}} = 0\]
Abhisar
  • Abhisar
Oh, so you mean we have to solve the equation for u=0?

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Michele_Laino
  • Michele_Laino
not for U=0, its first derivative with respect to x has to be equal to zero, since, in a field of force coming from a potential, the relationship between force and potential energy is: \[\Large {\mathbf{F}} = - \nabla U\]
Abhisar
  • Abhisar
Oh, one min....
Abhisar
  • Abhisar
Ok, yes. Thanks a bunch c:
Michele_Laino
  • Michele_Laino
thus we get the subsequent condition: \[\Large {x_0} = \frac{1}{4}\] as equilibrium position
Michele_Laino
  • Michele_Laino
:)
Abhisar
  • Abhisar
Yes... c:
Michele_Laino
  • Michele_Laino
:)
UnkleRhaukus
  • UnkleRhaukus
now, the sign of the second derivative at this point, will determine whether this equilibrium point is stable or unstable
Abhisar
  • Abhisar
Oh I see, thanks for the info Felix c:

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