Day 15 - Potential Energy and Stability

Mexican Hat/Sombrero Potential

Mexican Hat Potential

Announcements

  • HW 4 is due today
  • Midterm 1 is available today (Due Feb 24th)

Seminars this week

MONDAY, February 17, 2025

  • QuIC Seminar, 12:30 pm, 1400 BPS, Dr. Michael Hilke, The history of quantum computing
  • High Energy Physics Seminar, 1:30pm, BPS 1400 BPS, Joshua Isaacson, Event Generation for Next-Gen HEP Experiments
  • Condensed Matter Seminar 4:10 pm, 1400 BPS, Lisa Lapidus, The Physics of Biomolecular Condensation

Seminars this week

TUESDAY, February 18, 2025

  • Theory Seminar, 11:00am., FRIB 1200 lab, Ibrahim Abdurahman, Investigating Fission Dynamics within Time-Dependent Density Functional Theory Extended to Superfluid Systems

Seminars this week

WEDNESDAY, February 19, 2025

  • Astronomy Seminar, 1:30 pm, 1400 BPS, Aaron Bello-Arufa, The atmospheres of small exoplanets with JWST
  • PER Seminar, 3:00 pm., BPS 1400, Anthony Escuardo, OPTYCS: A Community of Practice Supporting Teaching and Scholarship at Two-Year College
  • FRIB Nuclear Science Seminar, 3:30pm., FRIB 1300 Auditorium, Elise Novitski, A new approach to measuring neutrino mass

Seminars this week

THURSDAY, February 20, 2025

  • High Energy Physics Seminar, 1:30pm, BPS 1400 BPS, Ben Assi, Precision QCD and EFT for Next-Generation Collider Studies
  • Physics and Astronomy sColloquium, 3:30 pm, 1415 BPS, Eric Hudson, Laser spectroscopy of a nucleus

This Week's Goals

  • Understand the concept of potential energy
  • Determine the equilibrium points of a system using potential energy
  • Analyze the stability of equilibrium points
  • Define and begin to apply conservation of linear and angular momentum

Reminders: Conservative Forces

  • Conservative forces are those with zero curl

  • The work done by a conservative force is path-independent; on a closed path, the work done is zero

  • The force can be written as the gradient of a scalar potential energy function

Clicker Question 15-1

Here's the graph of the potential energy function for a pendulum.

What can you say about the equilibrium points? There is/are:

  1. One stable point
  2. Two stable points
  3. One stable and one unstable point
  4. Two unstable and one stable point

Clicker Question 15-2

Here's a potential energy function for a pendulum:

  1. Find the equilibrium points () of the pendulum by setting:

  1. Characterize the stability of the equilibrium points () by examining the second derivative:

Click when done.

Clicker Question 15-3

A double-well potential energy function is given by

We assume we have scaled the potential energy so that all the units are consistent.

How many equilibrium points does this system have?

  1. 1
  2. 2
  3. 3
  4. 4

Clicker Question 15-4

A double-well potential energy function is given by

  1. Find the equilibrium points () of the pendulum by setting:

  1. Characterize the stability of the equilibrium points () by examining the second derivative:

Click when done.

Clicker Question 15-5

Here's a graph of the potential energy function for a double-well potential.

Describe the motion of a particle with the total energy,

  1. , barrier height
  2. , barrier height
  3. , barrier height

Click when done.