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Activities

Small Group Activity

30 min.

##### Name the experiment (changing entropy)
Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.
• Found in: Energy and Entropy course(s) Found in: Name the experiment sequence(s)

Problem

5 min.

##### Bottle in a Bottle

The internal energy of helium gas at temperature $T$ is to a very good approximation given by \begin{align} U &= \frac32 Nk_BT \end{align}

Consider a very irreversible process in which a small bottle of helium is placed inside a large bottle, which otherwise contains vacuum. The inner bottle contains a slow leak, so that the helium leaks into the outer bottle. The inner bottle contains one tenth the volume of the outer bottle, which is insulated. What is the change in temperature when this process is complete? How much of the helium will remain in the small bottle?

• Found in: Energy and Entropy course(s)

Small Group Activity

30 min.

##### Using $pV$ and $TS$ Plots
Students work out heat and work for rectangular paths on $pV$ and $TS$ plots. This gives with computing heat and work, applying the First Law, and recognizing that internal energy is a state function, which cannot change after a cyclic process.
• Found in: Energy and Entropy course(s)

Problem

5 min.

##### Inhomogeneous Linear ODEs with Constant Coefficients (First Example)

Inhomogeneous, linear ODEs with constant coefficients are among the most straigtforward to solve, although the algebra can get messy. This content should have been covered in your Differential Equations course (MTH 256 or equiv.). If you need a review, please see: The Method for Inhomogeneous Equations or your differential equations text.

The general solution of the homogeneous differential equation

$\ddot{x}-\dot{x}-6 x=0$

is

$x(t)=A\, e^{3t}+ B\, e^{-2t}$

where $A$ and $B$ are arbitrary constants that would be determined by the initial conditions of the problem.

1. Find a particular solution of the inhomogeneous differential equation $\ddot{x}-\dot{x}-6 x=-25\sin(4 t)$.

2. Find the general solution of $\ddot{x}-\dot{x}-6 x=-25\sin(4 t)$.

3. Some terms in your general solution have an undetermined coefficients, while some coefficients are fully determined. Explain what is different about these two cases.

4. Find a particular solution of $\ddot{x}-\dot{x}-6 x=12 e^{-3 t}$

5. Find the general solution of $\ddot{x}-\dot{x}-6 x=12 e^{-3 t}-25\sin(4 t)$

How is this general solution related to the particular solutions you found in the previous parts of this question?

Can you add these particular solutions together with arbitrary coefficients to get a new particular solution?

• Found in: Oscillations and Waves, None course(s)

Problem

##### Gauss's Law for a Rod inside a Cube
Consider a thin charged rod of length $L$ standing along the $z$-axis with the bottom end on the $x,y$-plane. The charge density $\lambda_0$ is constant. Find the total flux of the electric field through a closed cubical surface with sides of length $3L$ centered at the origin.
• Found in: AIMS Maxwell, Static Fields, Problem-Solving course(s)

Problem

##### Symmetry Arguments for Gauss's Law

Instructions for 2022: You will need to complete this assignment in a 15 minute appointment on Zoom or in person with one of the members of the teaching team between 1/21 and 10 pm on 1/26. Here is a link to a sign-up page.

You are required to watch a sample video for how to make symmetry arguments here. As demonstrated in the video you should bring with you to the meeting a cylinder, an observer, and a vector.

Use good symmetry arguments to find the possible direction for the electric field due to a charged wire. Also, use good symmetry arguments to find the possible functional dependence of the electric field due to a charged wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Problem

5 min.

##### Find Force Law: Logarithmic Spiral Orbit

(Use the equation for orbit shape.) Gain experience with unusual force laws.

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a $1/r^2$ force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

In class, we discussed how to calculate the shape of the orbit for an inverse square potential. More generally, the equation for the orbit of a mass $\mu$ under the influence of a central force $f(r)$ is given by: \begin{align} \frac{d^2 u}{d\phi^2} + u &=-\frac{\mu}{\ell^2}\frac{1}{u^2}f\left(\frac{1}{u}\right)\\ \Rightarrow f\left(\frac{1}{u}\right)&=-\frac{\ell^2}{\mu}u^2 \left(\frac{d^2 u}{d\phi^2} + u\right) \end{align} where $u=r^{-1}$.

Find the force law for a mass $\mu$, under the influence of a central-force field, that moves in a logarithmic spiral orbit given by $r = ke^{\alpha \phi}$, where $k$ and $\alpha$ are constants.

• Found in: Central Forces course(s)

Problem

5 min.

##### Line Sources Using Coulomb's Law
1. (4pts) Find the electric field around a finite, uniformly charged, straight rod, at a point a distance $s$ straight out from the midpoint, starting from Coulomb's Law.
2. (4pts) Find the electric field around an infinite, uniformly charged, straight rod, starting from the result for a finite rod.
• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Problem

##### Differential Form of Gauss's Law

For an infinitesimally thin cylindrical shell of radius $b$ with uniform surface charge density $\sigma$, the electric field is zero for $s<b$ and $\vec{E}= \frac{\sigma b}{\epsilon_0 s}\, \hat s$ for $s > b$. Use the differential form of Gauss' Law to find the charge density everywhere in space.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Small White Board Question

5 min.

##### Newton's 2nd Law SWBQ

Write Newton's 2nd Law for a single mass.

## Notes:

LG 2024: I added the Euler-Lagrange equation as an example of a generalized statement of Newton's 2nd Law. I'm planning on using a Lagrangian approach for the 2-body problem.

• Found in: Central Forces course(s)

Small Group Activity

60 min.

##### The Wire
Students compute a vector line integral, then investigate whether this integral is path independent.
• Found in: Vector Calculus II, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Workshop Presentations 2023 sequence(s)

Small Group Activity

30 min.

##### Grey space capsule
In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.
• Found in: Contemporary Challenges course(s)

Small Group Activity

60 min.

##### Electrostatic Potential Due to a Pair of Charges (with Series)
Students work in small groups to use the superposition principle $V(\vec{r}) = \frac{1}{4\pi\epsilon_0}\sum_i \frac{q_i}{\vert\vec{r}-\vec{r}_i\vert}$ to find the electrostatic potential $V$ everywhere in space due to a pair of charges (either identical charges or a dipole). Different groups are assigned different arrangements of charges and different regions of space to consider: either on the axis of the charges or in the plane equidistant from the two charges, for either small or large values of the relevant geometric variable. Each group is asked to find a power series expansion for the electrostatic potential, valid in their group's assigned region of space. The whole class wrap-up discussion then compares and contrasts the results and discuss the symmetries of the two cases.
• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Lecture

5 min.

##### Wavelength of peak intensity
This very short lecture introduces Wein's displacement law.
• Found in: Contemporary Challenges course(s)

Small Group Activity

30 min.

##### Changes in Internal Energy
Students consider the change in internal energy during three different processes involving a container of water vapor on a stove. Using the 1st Law of Thermodynamics, students reason about how the internal energy would change and then compare this prediction with data from NIST presented as a contour plot.
• Found in: Warm-Up sequence(s)

Small Group Activity

120 min.

##### Projectile with Linear Drag
Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.
• Found in: Theoretical Mechanics course(s) Found in: Drag Force Sequence, Separable ODE's Sequence sequence(s)

Small Group Activity

30 min.

##### Electric Field Due to a Ring of Charge

Students work in small groups to use Coulomb's Law $\vec{E}(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})\left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}$ to find an integral expression for the electric field, $\vec{E}(\vec{r})$, everywhere in space, due to a ring of charge.

In an optional extension, students find a series expansion for $\vec{E}(\vec{r})$ either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Small Group Activity

30 min.

##### Magnetic Field Due to a Spinning Ring of Charge

Students work in small groups to use the Biot-Savart law $\vec{B}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})\times \left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}$ to find an integral expression for the magnetic field, $\vec{B}(\vec{r})$, due to a spinning ring of charge.

In an optional extension, students find a series expansion for $\vec{B}(\vec{r})$ either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Lecture

120 min.

##### Gibbs entropy approach
These lecture notes for the first week of https://paradigms.oregonstate.edu/courses/ph441 include a couple of small group activities in which students work with the Gibbs formulation of the entropy.
• Found in: Thermal and Statistical Physics course(s)

Small Group Activity

60 min.

##### The Park

This is the first activity relating the surfaces to the corresponding contour diagrams, thus emphasizing the use of multiple representations.

Students work in small groups to interpret level curves representing different concentrations of lead.

• Found in: Vector Calculus I, Surfaces/Bridge Workshop, Problem-Solving course(s)

Small Group Activity

30 min.

##### Wavefunctions on a Quantum Ring
This activity lets students explore translating a wavefunction that isn't obviously made up of eigenstates at first glance into ket and matrix form. Then students explore wave functions, probabilities in a region, expectation values, and what wavefunctions can tell you about measurements of $L_z$.
• Found in: Central Forces course(s)

Small Group Activity

5 min.

##### Events on Spacetime Diagrams
Students practice identifying whether events on spacetime diagrams are simultaneous, colocated, or neither for different observers. Then students decide which of two events occurs first in two different reference frames.
• Found in: Theoretical Mechanics course(s)

Small Group Activity

120 min.

##### Equipotential Surfaces
Students are prompted to consider the scalar superposition of the electric potential due to multiple point charges. First a single point charge is discussed, then four positive charges, then an electric quadrupole. Students draw the equipotential curves in the plane of the charges, while also considering the 3D nature of equipotentials.

Computational Activity

120 min.

##### Electrostatic potential of spherical shell
Students solve numerically for the potential due to a spherical shell of charge. Although this potential is straightforward to compute using Gauss's Law, it serves as a nice example for numerically integrating in spherical coordinates because the correct answer is easy to recognize.
• Found in: Computational Physics Lab II course(s) Found in: Computational integrating charge distributions sequence(s)

Small Group Activity

10 min.

##### Thermal radiation at twice the temperature
This small group activity has students reasoning about how the Planck distribution shifts when the temperature is doubled. This leads to a qualitative argument for the Stefan-Boltzmann law.
• Found in: Contemporary Challenges course(s)

Lecture

5 min.

##### Energy and Entropy review
This very quick lecture reviews the content taught in https://paradigms.oregonstate.edu/courses/ph423, and is the first content in https://paradigms.oregonstate.edu/courses/ph441.
• Found in: Energy and Entropy, Thermal and Statistical Physics course(s)

Small Group Activity

60 min.

##### Establish Classroom Norms
In this hour-long activity, students establish classroom norms for being respectful when working in small groups. This is particularly helpful in the first course a cohort of students encounters.
• Found in: Theoretical Mechanics course(s)

Whole Class Activity

10 min.

##### Curvilinear Coordinates Introduction
First, students are shown diagrams of cylindrical and spherical coordinates. Common notation systems are discussed, especially that physicists and mathematicians use opposite conventions for the angles $\theta$ and $\phi$. Then students are asked to check their understanding by sketching several coordinate equals constant surfaces on their small whiteboards.
• Found in: Static Fields, Central Forces, AIMS Maxwell, Vector Calculus I, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Curvilinear Coordinate Sequence sequence(s)