the world in a different light
Here’s a quick video to demonstrate the movement of a ball initially moving in a circle before its centripetal force (contact force by the circular wall) is removed. The ball is observed to move in a tangent to the circle, in accordance with Newton’s 1st Law, since there is no longer a net force acting on it.
Using the GeoGebra app above, I intend to demonstrate the relationship between total energy, kinetic energy and gravitational potential energy in a rocket trying to escape a planet’s gravitational field.
By changing the total energy of the rocket, you will increase the initial kinetic energy, thus allowing it to fly further from the surface of the planet. The furthest point to which the rocket can fly can be observed by moving the slider for “distance”. You will notice that the furthest point is where kinetic energy would have depleted.
Gravitational potential energy of an object is taken as zero at an infinite distance away from the source of the gravitational field. This means gravitational potential energy anywhere else takes on a negative value of $\dfrac{-GMm}{r}$. Therefore, the total energy of the object may be negative, even after taking into account its positive kinetic energy as total energy = kinetic energy + gravitational potential energy.
The minimum total energy needed for the rocket to leave the planet’s gravitational field is zero, as that will mean that the minimum initial kinetic energy will be equal to the increase in gravitational potential energy needed, according to the equation $\Delta U = 0 – (-\dfrac{GMm}{R_P})$, where $R_P$ is the radius of the planet.
Since $\dfrac{1}{2}mv^2 = \dfrac{GMm}{R_P}$, escape velocity, $v = \sqrt{\dfrac{2GM}{R_P}}$.
After years of hosting my website on a traditional webhosting service that has seen multiple service disruption over the years, I have switched to Amazon Web Services, which is more reliable and scaleable. I want my students to be able to access new features in my website with faster loading speeds. AWS is much harder to set up as there is so much to learn and a lot of SSH commands to key in. The first key decision is to decide whether an EC2 or Lightsail instance is better suited to my needs. In the end, I decided to go with Lightsail as it seemed easier to update the necessary DNS records.
One of the first features I am experimenting with is a Udemy-style LMS plugin that allows me to create lessons and quizzes within a course structure and comes with a mobile-friendly user-interface. I wanted a platform in which my GeoGebra apps, as well as other online resources such as YouTube videos, can be stitched together for students to review or learn new topics at their own pace, as well as for classroom activities.
I initially wanted to use LearnPress, a fuss free and user-friendly plugin for this purpose, and even designed a course within it. However, I soon realise that it does not have a feature for analysis of students’ results. So now I have installed Tutor LMS and will be putting in content soon. Tutor LMS also comes with many more question types including ordering and fill-in-the-blank.
I experimented with Google OAuth in another Lightsail instance and will be implementing it here so my students can log in using their school gmail account.
The next necessary plugin was Mathjax for LaTex input. I needed to make some edits to the lesson sidebar in the Tutor LMS plugin in order to fix a bug that prevents the equations from rendering when navigating using the sidebar.
I have also updated some CSS to customise the Tutor LMS pages to fit the general style of my current website theme.
Further ideas for Home-based Learning. I’ve put a time bookmark from the point where it becomes relevant to Math and Science teachers, but you can always watch the video from the start.
Here is a template that I might use to generate questions for students’ self-assessment in future. Based on a query that one of the participants in a GeoGebra online tutorial asked about generating random questions for simple multiplication for lower primary students.
The online tutorial was conducted by some teachers in the Singapore MOE GeoGebra community to share how GeoGebra could be used to create resources for home-based learning.
An ex-colleague from HQ introduced me to Trinket: a useful web-based code editor that allows students to tinker with codes and showcase their work. Here’s an example of a BMI calculator that can be embedded via iframes.
As I am teaching programming to the lower sec IP students this term as part of their Skills and Knowledge curriculum, I was wondering if I should use this to ask my students to submit their work.