## Spring Force Constant

• group A glass of water

group Small Group Activity

30 min.

##### A glass of water
Energy and Entropy 2021 (2 years)

Students generate a list of properties a glass of water might have. The class then discusses and categorizes those properties.
• group Applying the equipartition theorem

group Small Group Activity

30 min.

##### Applying the equipartition theorem
Contemporary Challenges 2022 (3 years)

Students count the quadratic degrees of freedom of a few toy molecules to predict their internal energy at temperature $T$.
• groups Pineapples and Pumpkins

groups Whole Class Activity

10 min.

##### Pineapples and Pumpkins
Static Fields 2022 (4 years)

Integration Sequence

There are two versions of this activity:

As a whole class activity, the instructor cuts a pumpkin in order to produce a small volume element $d\tau$, interspersing their work with a sequence of small whiteboard questions. This version of the activity is described here.

As a small group activity, students are given pineapple rounds and pumpkin wedges to explore area volume elements in cylindrical and spherical coordinate systems. In this version of the activity, the fruit is distribued to the students with appropriate children's pumpkin cutting equipment, as part of activities Vector Differential--Curvilinear, Scalar Surface and Volume Elements, or Vector Surface and Volume Elements.

• face Equipartition theorem

face Lecture

30 min.

##### Equipartition theorem
Contemporary Challenges 2022 (3 years)

This lecture introduces the equipartition theorem.
• group Going from Spin States to Wavefunctions

group Small Group Activity

60 min.

##### Going from Spin States to Wavefunctions
Quantum Fundamentals 2022

Arms Sequence for Complex Numbers and Quantum States

Students review using the Arms representation to represent states for discrete quantum systems and connecting the Arms representation to histogram and matrix representation. The student then extend the Arms representation to begin exploring the continuous position basis.
• keyboard Mean position

keyboard Computational Activity

120 min.

##### Mean position
Computational Physics Lab II 2022 (2 years)

Students compute probabilities and averages given a probability density in one dimension. This activity serves as a soft introduction to the particle in a box, introducing all the concepts that are needed.
• assignment Building the PDM: Instructions

assignment Homework

##### Building the PDM: Instructions
PDM Energy and Entropy 2021 (2 years) In your kits for the Portable Partial Derivative Machine should be the following:
• A 1ft by 1ft board with 5 holes and measuring tapes (the measuring tapes will be on the top side)
• 2 S-hooks
• A spring with 3 strings attached
• 2 small cloth bags
• 4 large ball bearings
• 8 small ball bearings
• 2 vertical clamp pulleys
• A ziploc bag containing
• 5 screws
• 5 hex nuts
• 5 washers
• 5 wing nuts
• 2 horizontal pulleys
To assemble the Portable PDM, start by placing the PDM on a table surface with the measuring tapes perpendicular to the table's edge and the board edge with 3 holes closest to you.
1. one screw should be put through each hole so that the threads stick out through the top side of the board. Next use a hex nut to secure each screw in place. It is not critical that they be screwed on any more than you can comfortably manage by hand.
2. After securing all 5 screws in place with a hex nut, put a washer on each screw.
3. Slide a horizontal pulley onto screws 1 and 2 (as labeled above).
4. On all 5 screws, add a wing nut to secure the other pieces. Again, it does not need to be tightened all the way as long as it is secure enough that nothing will fall off.
5. Using the middle wingnut/washer/screw (Screw 4), clamp the shortest of the strings tied to the spring.
6. Loop the remaining 2 looped-ends of string around the horizontal pulleys and along the measuring tape.
7. Using the string as a guide, clamp the vertical pulleys into place on the edge of the board.
8. Through the looped-end of each string, place 1 S-hook.
9. Put the other end of each s-hook through the hole in the small cloth bag.
Here is a poor photo of the final result, which doesn't show the two vertical pulleys. If you would like, you could view a video of the building process.
• assignment Curl

assignment Homework

##### Curl
Static Fields 2022 (4 years)

Shown above is a two-dimensional cross-section of a vector field. All the parallel cross-sections of this field look exactly the same. Determine the direction of the curl at points A, B, and C.

• group Scalar Surface and Volume Elements

group Small Group Activity

30 min.

##### Scalar Surface and Volume Elements
Static Fields 2022 (4 years)

Integration Sequence

Students use known algebraic expressions for length elements $d\ell$ to determine all simple scalar area $dA$ and volume elements $d\tau$ in cylindrical and spherical coordinates.

This activity is identical to Vector Surface and Volume Elements except uses a scalar approach to find surface, and volume elements.

• keyboard Position operator

keyboard Computational Activity

120 min.

##### Position operator
Computational Physics Lab II 2022 (2 years)

Students find matrix elements of the position operator $\hat x$ in a sinusoidal basis. This allows them to express this operator as a matrix, which they can then numerically diagonalize and visualize the eigenfunctions.
• Energy and Entropy 2021 (2 years) The spring constant $k$ for a one-dimensional spring is defined by: $F=k(x-x_0).$ Discuss briefly whether each of the variables in this equation is extensive or intensive.