A-level Topics

11 February

Graph Plotting App made with ChatGPT in 15 minutes

Seng Kwang Tan 21 Practical / Planning, AI, Student Learning Space 0 Comments

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.
16 September

Simulation of a Bouncing Ball

Seng Kwang Tan 03 Motion and Forces, GeoGebra, IP3 02 Kinematics 0 Comments

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:

28 March

Use of System Schema to Visualise Action-Reaction Pairs

Seng Kwang Tan 03 Motion and Forces, IP3 03 Dynamics 0 Comments

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.

21 February

Simple Harmonic Motion perspectives

Seng Kwang Tan 09 Oscillations, GeoGebra 0 Comments

This is a common example used in the JC1 topics of Oscillations, where if one were to look at an object moving in circles from the side view, it will appear to move in simple harmonic motion. This simple 3D animation allows users to rotate the view to see exactly that. Right click and drag to rotate the view. If you are using a mobile device, use two fingers to drag.

To access the animation in full screen, visit https://www.geogebra.org/m/tsz95u6p

08 February

Displacement-time graph with animation

Seng Kwang Tan 03 Motion and Forces, GeoGebra 0 Comments

This displacement-time graph is used in conjunction with an SLS package to help students learn how to describe motion of an object and to use gradient of a tangent to calculate the magnitude of velocity.

For a direct link to the app, go to https://www.geogebra.org/m/k3ja7bnm

I added a little spider to help students visualise the movement with time.

25 January

Vector Addition

Seng Kwang Tan 01 Quantities and Measurement, GeoGebra, IP3 01 Measurement 0 Comments

I made some refinement to an applet created last year to demonstrate how vector addition can be done either using vector triangle or parallelogram methods.

To access directly in Geogebra, the link is https://www.geogebra.org/m/p2yvdsvs