A-level Topics

02 July

Phase Difference GeoGebra Apps

11 Wave Motion, 12 Superposition, GeoGebra 0 Comments

I created a series of GeoGebra apps for the JC topics of Waves and Superposition, mainly on the concept of Phase Difference. The sizes of these GeoGebra apps are optimised for embedding into SLS. When I have time, I will create detailed instructions on how to create such apps. Meanwhile, feel free to use them.

Instructions on how to embed the apps into SLS can be found in the SLS user guide.

Phase difference between two particles on a progressive wave. Move the particles along the wave to see the value.

Phase difference between two particles on a stationary wave. Move the particles along the wave to observe how their velocities are different or similar.

Observe velocity vectors of multiple particles on a progressive wave.

21 October

Idealized Stirling Cycle

09 First Law of Thermodynamics, GeoGebra 0 Comments

I created a new GeoGebra app based on an ideal Stirling Cycle (A. Romanelli Alternative thermodynamic cycle for the Stirling machine, American Journal of Physics 85, 926 (2017)) which includes two isothermal and two isochoric processes. The Stirling engine is a very good example to apply the First Law of Thermodynamics to, as the amount of gas is fixed so the macro-variables are only pressure, temperature and volume. Simplifying the cycle makes it even easier for first time learners to understand how the engine works.

For those who prefer to be impressed by an actual working model, it can be bought for less than S$30 on Lazada. All you need for it to run is a little hot water or some ice. Here’s a video of the one I bought:

The parts of the Stirling engine are labelled here:
How a Stirling Engine works

My simulation may not look identical to the engine shown but it does have the same power piston (to do work on the flywheel) and displacer piston (to shunt the air to and fro for more efficient heat exchange).

Geogebra link: https://www.geogebra.org/m/pbnw2yas

23 September

Geogebra App on Maximum Power Theorem

15 DC Circuits, GeoGebra 0 Comments

GeoGebra link: https://www.geogebra.org/m/hscshcj8

This simulation demonstrates the power dissipated in a variable resistor given that the battery has an internal resistance (made variable in this app as well).

Since the power dissipated by the resistor is given by

[latex]P=I^2R[/latex]

and the current is given by

[latex]I=E(R+r)[/latex],

[latex]P=E^2\times\dfrac{R}{(R+r)^2}=\dfrac{E^2}{\dfrac{r^2}{R}+R+2r}[/latex]

This power will be a maximum if the expression for the denominator [latex]\dfrac{r^2}{R}+R+2r[/latex] is a minimum.

Differentiating the expression with respect to R, we get
[latex]\dfrac{d(\dfrac{r^2}{R}+R+2r)}{dR}=-\dfrac{r^2}{R^2}+1[/latex]

When the denominator is a minimum,
[latex]-\dfrac{r^2}{R^2}+1=0[/latex]

Therefore,
[latex]r=R[/latex] when the power dissipated by the resistor is highest.

22 September

Geogebra Simulation of a Potentiometer

15 DC Circuits, GeoGebra, Simulations 0 Comments

Some of the more challenging problems in the topic of electricity in the A-level syllabus are those involving a potentiometer. The solution involves the concept of potential divider and the setup can be used to measure emf or potential difference across a variety of circuits components. Basically, students need to understand the rule – that the potential difference across a device is simply a fraction of the circuit’s emf, and that fraction is equal to the resistance of the device over the total resistance of the circuit.

[latex]V_{device}=\frac{R_{device}}{R_{total}}*emf[/latex]

The intention of this Geogebra app is for students to practise working on their calculations, as well as to reinforce their understanding of the principle by which the potentiometer works.

GeoGebra link: https://www.geogebra.org/m/pzy3qua8

24 August

Box on a Vertical Oscillating Spring – Geogebra App

10 Oscillations, GeoGebra, Simulations 0 Comments

GeoGebra link: https://www.geogebra.org/m/ev62ku7w

Students can explore how varying frequency and amplitude of the vertical oscillation of a platform could cause an object resting on it to temporarily leave the platform (i.e. when normal contact force is zero).