Monday, May 30, 2016

Dance of the Changes: ∆p vs. ∆K

Once momentum p and kinetic energy K were derived and the connection between them was established, our task as a class was to find any connections, if any, between ∆p & ∆K. The derivations shown below were conducted in class with the participation of everyone using what I call "Stand/Sit Participation Method". This ensures that every student is active in the derivation process from beginning to end with emphasis on understanding all along.

Students were asked to compare and contrast the two relationships that were derived and only then did the following slide show up.

This, my friends, led to the Free Body Diagrams (FBD) challenges activity that eventually  led to the formulation of Newton's 2nd Law of Motion (N2L.)

A simple harmonic oscillator (SHO) attached to a force probe with a motion detector set below the mass that is attached to the spring provided the conformation of N2L.

The above derivation is aimed at achieving three goals.

1) To help students realize that Physix concepts are not disconnected islands, rather they are individual cells within the organism of Physix knowledge.

2) To establish the emergence of acceleration as a quintessential aspect of any changes in the state of motion of particles.

3) To overemphasize the complementarity between between space and time that relativity asserted and Heisenberg's Uncertainty Principle alluded to in Quantum Mechanics.

Thank you for reading this post and I look forward reading your valuable comments.   

Dedicated to the memory of my beloved father (RA).

Derivation of classical Kinetic Energy formula from STR

This year, thanks to NMC's media folks, I was able to use a lightboard (click here to read an article that describes how to build one) to put together two videos about Special Theory of Relativity (STR).

The first video (see the link shown below), goes through the process of deriving the classical formula of kinetic energy (K) from its relativistic sibling. The student were sent the link shown below and were asked to view it, take notes on it, record the said notes onto their IONs (Input/Output Notebooks), and then write a reflection paper on the subject matter as well as the video itself.

Kinetic Energy in STR Video (12:52 min):

The second video contrasts the two relativity relationships as understood by Galileo on one hand and the one formulated by Einstein on the other hand. The latter is also used to assist students in their understanding of how light speed remains constant in all inertial frames of reference.

Galilean vs. Einsteinean Relativity (6:21 min):

Once the students' reflections papers were collected, I challenged the students to justify the reasoning behind the Physicists insistence on inventing yet another relationship (that of K) that depends on the same physical quantities, mass and velocity.

Once satisfactory responses were obtained, I stated, "Now that we established connections between momentum p and kinetic energy K, would there be any relationship between ∆p & ∆K?" This led to the changes presentation, which I shall address in the following post.

After watching the two videos listed above, please, share your thoughts, reflections, and ideas about how you might use them in your own curriculum. Thank you

Dedicated to the memory of my beloved father (RA).

Physix Curriculum Map a la Mr. Le Nadj!

Students love Modern Physics topics. Unfortunately, most introductory Physics courses eschew Special Theory of Relativity (STR), General Theory of Relativity (GTR), and Quantum Mechanics (QM) because of their perceived difficulty.

For the past four years, I have been introducing more and more of STR early on in the year/semester. But, this year I used STR as a means of introducing classical Physics concepts such as kinetic energy. The mind map below summarizes the gist of this approach. It is important to mention that the Modeling Approach serves as the backbone and the glue that holds this teaching method together. Thus, the use of many abbreviations that only modelers would know.

Physix a la Mr. Le Nadj! Curriculum Map

In future posts, I shall address each of the branches. I shall also give samples of presentations material, examples of students reactions/reflections, and typical artifacts that assist in making the case for such a pedagogical approach.

Please, feel free to share your thoughts in the comments area so that readers like you would benefit from them personally or their students indirectly. Thank you

Dedicated to the memory of my beloved father (RA).