# A-level Topics

## Analogue Meter Template

This GeoGebra applet (https://www.geogebra.org/m/watavkq8) can serve as a template for an analogue meter.

I added a check for the text input so that users have to key in the correct number of decimal places according to the precision of the instrument. For instance, a reading of 1 V should be recorded as 1.00 V and 1.5 V recorded as 1.50 V. Users need to read to half the smallest division, e.g. if the needle is between 2.4 and 2.5, they should input 2.45 V.

## Kinematics Graphs with Variable Initial Velocity and Acceleration

I used ChatGPT to create this simple interactive graph. Including the time taken to make 2 rounds of refinement using more prompts and the time it took to deploy it via Github, it took about 15 minutes from start to end.

The first prompt I used was :

Create a graph using chart.js with vertical axis being “displacement / m” and horizontal axis being “time / s”. There should be a slider for the initial velocity value ranging from 0 to 2 m/s, a slider for the acceleration value ranging from -2 m/s^2 to 2 m/s^2. The displacement will start from zero and will follow a function dependent on the initial velocity and acceleration values from the slider. Draw the line of the displacement on the graph. Update the graph whenever the sliders are moved.

The results of the first attempt is shown above. It is already functional, with the initial velocity and acceleration sliders working together to change the shape of the graph.

The function it used to calculate displacement is based on the kinematics equation $s = ut + \dfrac{1}{2}at^2$, written as

    displacement.push(0.5 * acceleration * t * t + initialVelocity * t);

After the first successful attempt, I gave some refinement prompts like:

Show the values of the velocity and acceleration, along with the units.

Use drop-down list to change the vertical axis to velocity or acceleration, updating the axis each time and the curve as well.

So the second attempt looked like this

ChatGPT got 1 out of 2 requests correct. The values of the velocity and acceleration were intended to be displayed next to the sliders. It must have been because I was not clear enough. Hence, the last refinement I asked for was :

Give the codes to show the values of velocity and acceleration next to the sliders. Just those codes.

I didn’t want to get ChatGPT to generate the entire page of html and javascript again so I targetted the specific codes that I needed to change.

It was helpful in telling me where to update these codes. So at the end of the day, this is what was obtained after I made some manual tweaks to change the way the unit is displayed (e.g. m s-2 instead of m/s2):

It was good enough for my purpose now. The web app can be sent to students as a link (https://physicstjc.github.io/sls/kinematics-graph) or embedded into SLS as a standalone app. For use in SLS, do note the following:

1. The html file must be named index.html
2. The chart.js file must be copied and saved in the same zipped file at the same level as the index.html file. Change the path of the Chart JS from <script src=”https://cdnjs.cloudflare.com/ajax/libs/Chart.js/3.7.0/chart.min.js”></script> to <script src=”chart.min.js”></script>.
3. For reference, this is what it looks like when zipped.

## Delight – a web-based board game on electricity

I had previously shared about this physical board game that I designed to teach electricity concepts. Now, with ChatGPT’s help, I have managed to produce a simple implementation of the board game so that there is no need to print and cut out the pieces anymore.

However, the game is still unable to detect if the light bulb will light up and automatically change the image colour or add the scores. That will require further complex programming due to the many possible outcomes for this game.

https://physicstjc.github.io/sls/delight/index.html

The rules of the game are as such:

1. Players will take turns to connect their own bulbs to the terminals while trying to sabotage their opponent’s bulbs.
2. Players will take turns to place one piece on the 4-by-4 game board by clicking to select the electrical component and clicking on the square on the board to place it.
3. Upon placing the piece, the player can also turn that piece in any orientation (by clicking on it) within the same turn.
4. Players can choose to use up to two turns at any point in the game to rotate any piece that had been placed by any player.
5. In other words, each player has 9 turns: 7 placement turns and 2 rotation turns.

At lower levels, students can compete to see who has the most lit bulbs. However, they will need to be able to identify which light bulbs are lit. Do watch out for short-circuits.

At higher levels, students can compete to see whose light bulbs has the most total electrical power, with some calculations involved.

## Graph Plotting App made with ChatGPT in 15 minutes

As evidence of the prowess of generative AI, this graph plotting app was created in about 15 minutes with simple prompts and a text editor. It was tested with an existing set of data and uploaded immediately to the repository.

The user will begin by uploading a set of data from an experiment, with the column header being the labels for the axes, in the form of a CSV file. The app immediately calculates and displays the best-fit straight line using linear regression, providing users with insights into the relationships between the variables in the dataset. This allows for easy analysis of trends, patterns, and relationships within the data. Students can use the app to quickly visualize and analyze data. The screenshot button enables them to save the graph in picture form for submission to their teachers.

It has also been made compatible with the Student Learning Space. The screenshots saved by students can be uploaded as an attachment for a free-response question. This is especially useful when students are doing lab work and the teacher does not want the students to bother too much with configuring the graph. The ZIP file for use in the SLS can be downloaded here.

Prompts used are:

1. Create a website using html and javascript for users to plot a graph using data from a csv file.
2. The user can upload a csv file with the first column being the horizontal axis and the second column being the vertical axis.
3. The column headers, which is the first set of values in the csv file, will form the labels for the axes of the graph.
4. Plot the points with the data in the csv file and use linear regression to obtain the best-fit straight line of the data.
5. The best fit line should be a line joining two red dots.
6. Indicate the gradient and intercept of the best-fit line.
7. Add a button at the bottom for users to take a screenshot of the graph.
8. Put all the codes in one html file.

## Simulation of a Bouncing Ball

While I have shared a simulation of a bouncing ball made using Glowscript before, I felt that one made using GeoGebra is necessary for a more comprehensive library.

It took a while due to the need to adjust the equations used based on the position of the graphs, but here it is: https://www.geogebra.org/m/dfb53dps

The kinematics of a bouncing ball can be explained by considering the dynamics and forces involved in its motion. In this simulation, air resistance is assumed negligible. When a ball is dropped from a certain height and bounces off the ground, several key principles of physics come into play. Let’s break down the process step by step:

Free Fall: When the ball is released, it enters a state of free fall. During free fall, the only force acting on the ball is gravity. This force is directed downward and can be described by W = mg

W is the gravitational force.
m is the mass of the ball.
g is the acceleration due to gravity (approximately 9.81 m/s² near the surface of the Earth).

Impact with the Ground and Bounce: When the ball reaches the ground, it experiences a force due to the collision with the surface. This force is an example of a contact force and much larger than the gravitational force. This force depends on the elasticity of the ball and the surface it bounces off.

During the collision with the ground, the ball’s momentum changes rapidly. If the ball and the ground are both ideal elastic materials, the ball will bounce back with the same speed it had just before impact. In reality, some energy is lost during the collision, causing the bounce to be less than perfectly elastic. This simulation assumes elastic collisions.

Post-Bounce Motion: After the bounce, the ball starts moving upward. Gravity acts on it as it ascends, decelerating its motion until it reaches its peak height.

Second Descent: The ball then starts descending again, experiencing the force of gravity pulling it back down towards the ground.

This process continues with each bounce. In practice, with each bounce, some energy is lost due to the non-ideal nature of the collision and other dissipative forces like air resistance. As a result, each bounce is typically lower than the previous one until the ball eventually comes to rest. However, for simplicity, the simulation assumes no energy is lost during the collision and to dissipative forces.

An animated gif file is included here for use in powerpoint slides:

## Use of System Schema to Visualise Action-Reaction Pairs

It is a common misconception for students to assume that when a book is placed on a table, its weight and the normal contact force acting on it are action-reaction pairs because they are equal in magnitude and opposite in direction.

While we can emphasise the other requirements for action-reaction pairs – that they must act on two different bodies and be of the same type of force – I have tried a different approach to prevent this misconception from taking root. After reading this article on the use of the system schema representational tool to promote understanding of Newton’s third law, I tried it out with my IP3 students.

The system schema identifies the bodies in a question and represents them with shapes detached from each other to give space to draw the connecting arrows between them. The arrows must be labelled with the type of force, either by coding them (e.g. r for reaction force, g for gravitational force) or in full.

Every force will be drawn as a double-headed arrow between two bodies to represent that they are action-reaction pairs. It is important for students to understand that every force in the universe comes in such a pair, and the system schema can help them visualise that. If there is a force without a partner, it just means the system is not in the frame yet.

The next step to using the system schema is for students to isolate the object in question and draw its free-body diagram. Each force vector in the diagram should be accompanied by a name that includes: 1. the type of force and 2. the subject which exerts that force on the object.

The effectiveness of this method of instruction is clearly presented in the paper mentioned above, as performance on the force concept inventory’s questions on the third law saw an improved average from 2.8 ± 1.2 to 3.7 ± 0.8.