Day 14 - Help Session

Day 14 - Help Session#

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Announcements#

  • HW 4 is due today

    • We will work HW 4 Exercise 4 together + Q&A

    • Office Hours (14:00-16:00; 1248 BPS)

  • Midterm 1 is available now

    • We will talk about it Monday (come with questions)

    • There will be no office hours on Oct 3rd (DC traveling)

Exercise 4, Example of potential#

Consider a particle of mass \(m\) moving according to the potential:

\[ V(x,y,z)=A\exp\left\{-\frac{x^2+z^2}{2a^2}\right\}. \]

We can think of this potential as the energy landscape of a particle in three dimensions. That is, you can imagine a particle moving around this potential like a ball rolling around a landscape. That analogy is not perfect, but it is a good way to help us think about stability and equilibrium.

Exercise 4, Example of potential#

\[ V(x,y,z)=A\exp\left\{-\frac{x^2+z^2}{2a^2}\right\}. \]

  • 4a Plot this potential or sketch a plot of it. You can use perspective plots, contour plots or any other plot you find useful.

  • 4b What are some feature you notice with this potential? What happens when you change \(A\) and \(a\)?

Exercise 4, Example of potential#

\[ V(x,y,z)=A\exp\left\{-\frac{x^2+z^2}{2a^2}\right\}. \]

  • 4c Imagine a particle moving in this potential, what are some expected trajectories?

  • 4d Do there appear to be any equilibrium points? If so, are they stable or unstable?

  • 4a Is the resulting force conservative? Why?

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