This week's sets of classical pen and paper and computational exercises are again a continuation of the topics from the previous homework sets and the first midterm. We keep discussing conservation laws, conservative forces, energy, momentum and angular momentum. These conservation laws are central in Physics and understanding them properly lays the foundation for understanding and analyzing more complicated physics problems. The relevant reading background is
The numerical homework is based on what you did in homework 5 and/or the first midterm.
There are also two optional exercises, one is a simple survey after the midterm. We would love hearing back from you about how the course is progressing. The other exercise is an optional exercises on harmonic oscillations.
Compile a summary of the material covered in this class so far that covers the major topics (Newton’s Laws, conservative and nonconservative forces, and conservation of energy, momentum, and angular momentum and harmonic oscillations). This summary should not only contain a list of equations but should also include important concepts, numerical elements, and mathematical methods, and show the connections between different concepts. Make this summary as long as you need to throughly review all of the covered topics.
Which of the following force are conservative?
The Lennard-Jones potential is often used to describe the interaction between two atoms or ions or molecules. If you end up doing materals science and molecular dynamics calculations, it is very likely that you will encounter this potential model. The expression for the potential energy is of the molecule is:
$$ V(r) = V_0\left((\frac{a}{r})^{12}-(\frac{b}{r})^{6}\right), $$where \( V_0 \), \( a \) and \( b \) are constants and the potential depends only on the relative distance between two objects \( i \) and \( j \), that is \( r=\vert\boldsymbol{r}_i-\boldsymbol{r}_j\vert=\sqrt{(x_i-x_j)^2+(y_i-y_j)^2+(z_i-z_j)^2} \).
In the first midterm we looked at an object/particle moving in a potential which resulted in harmonic oscillations. The aim here is to summarize in more detail the material from harmonic oscillations.
Relevant reading here is Taylor chapter 5 and the lecture notes on oscillations.
We will consider a particle of mass \( m \) moving in a one-dimensional potential,
$$ V(x)=k\frac{x^2}{2}, $$where \( k \) is a parameter.
We will limit ourselves to a one-dimensional system. You will need to select values for the initial conditions and the various parameters \( k \), \( m \), \( b \), \( \omega \) and \( F_0 \) discussed here.
You don't need to do this exercise, but it gives you a bonus score of 10 points.
This time the additional bonus exercise is a simple survey. We are now moving into our second half of the semester and we would very much have your feedback on how things are functioning so that we can improve and correct.
The following gives you an opportunity to earn five extra credit points on each of the remaining homeworks and ten extra credit points on the midterms and finals. This assignment also covers an aspect of the scientific process that is not taught in most undergraduate programs: scientific writing. Writing scientific reports is how scientist communicate their results to the rest of the field. Knowing how to assemble a well written scientific report will greatly benefit you in you upper level classes, in graduate school, and in the work place.
The full information on extra credits is found at https://github.com/mhjensen/Physics321/blob/master/doc/Homeworks/ExtraCredits/. There you will also find examples on how to write a scientific article. Below you can also find a description on how to gain extra credits by attending scientific talks.
This assignment allows you to gain extra credit points by practicing your scientific writing. For each of the remaining homeworks you can submit the specified section of a scientific report (written about the numerical aspect of the homework) for five extra credit points on the assignment. For the two midterms and the final, submitting a full scientific report covering the numerical analysis problem will be worth ten extra points. For credit the grader must be able to tell that you put effort into the assignment (i.e. well written, well formatted, etc.). If you are unfamiliar with writing scientific reports, see the information here
The following table explains what aspect of a scientific report is due with which homework. You can submit the assignment in any format you like, in the same document as your homework, or in a different one. Remember to cite any external references you use and include a reference list. There are no length requirements, but make sure what you turn in is complete and through. If you have any questions, please contact Julie Butler at butler@frib.msu.edu.
| HW/Project | Due Date | Extra Credit Assignment |
|---|---|---|
| HW 3 | 2-8 | Abstract |
| HW 4 | 2-15 | Introduction |
| HW 5 | 2-22 | Methods |
| HW 6 | 3-1 | Results and Discussion |
| Midterm 1 | 3-12 | Full Written Report |
| HW 7 | 3-22 | Abstract |
| HW 8 | 3-29 | Introduction |
| HW 9 | 4-5 | Results and Discussion |
| Midterm 2 | _4-16_ | Full Written Report |
| HW 10 | 4-26 | Abstract |
| Final | 4-30 | Full Written Report |
You can also gain extra credits if you attend scientific talks. This is described here.
This opportunity will allow you to earn up to 5 extra credit points on a Homework per week. These points can push you above 100% or help make up for missed exercises. In order to earn all points you must:
Approved talks: Talks given by researchers through the following clubs:
All the material on extra credits is at https://github.com/mhjensen/Physics321/blob/master/doc/Homeworks/ExtraCredits/.