10 September

LOL Diagram Template using GeoGebra

Seng Kwang Tan GeoGebra, IP3 06 Work, Energy and Power 0 Comments

Direct link: https://www.geogebra.org/m/u2m3gnzj

The above is a GeoGebra applet that can be customised for any energy problem. Simply make a copy of it and change the values or labels as needed. This can be integrated into either GeoGebra Classroom or Google Classroom (as a GeoGebra assignment) and the teacher can then monitor every student’s attempt at interpreting the energy changes in the problem. The teacher can also choose different extents of scaffolding, e.g. provide the initial or final states and ask students to fill in the rest.

What is an LOL Diagram?

An LOL diagram is a tool used to visualize and analyze the conservation of energy in physical systems. “LOL” does not stand for anything meaningful. Rather, they just form the shapes of the two sets of axes and the circle in between. They help clarify which objects or components are included in the energy system being considered and how energy is transferred or transformed within that system.

In LOL diagrams:

  • An energy system is defined as an object or a collection of objects whose energies are being tracked.
  • LOL diagrams consist of three parts: a L-shaped bar-chart representing the initial state, an O representing the object (or system) of interest and another L-shaped bar-chart representing the final state.
  • There can also be energy transferred into the system or out of the system if the system is not closed or isolated. These are represented using horizontal bars below the L axes, with arrows indicating if they are energy transferred in or out.

When performing calculations involving the initial and final energy states, the energy transferred into the system is added to the initial energy state while the energy transferred out of the system is added to the final energy state. The sums must be equal. In other words,

Initial energy stores + Energy transferred into system = Final energy stores + Energy transferred out of system

How do I use an LOL diagram?

Here’s a breakdown of how LOL diagrams are used, using an example of a falling mass:

  1. System Definition (O):
    • Choose what is part of the energy system (objects whose energies are being tracked) and what isn’t.
    • For example, in the case of a falling mass, the mass itself and the Earth are part of the energy system.
  2. Initial State (L):
    • Represent the initial energy configuration of the system.
    • Identify the types of energy present in the system at the beginning. In this example, we begin with some gravitational potential energy.
  3. Transition:
    • Show how energy changes as the system evolves. In the falling mass example, the gravitational potential energy decreases, and kinetic energy increases.
  4. Final State (L):
    • Represent the energy distribution in the system at the end of the process.
    • In the falling mass example, at the point just before it hits the ground, kinetic energy is maximized, and gravitational potential energy is minimized.

LOL diagrams illustrate that energy within the system is conserved, meaning the total energy in the system remains constant.

External work (work done by forces outside the defined system) may impact the system’s energy, but internal work (work done within the defined system) does not change the total energy of the system.

The mathematical representation of the above problem will then simply be:

GPE = KE

$mgh = \dfrac{1}{2}mv^2$

This problem seems a bit trivial. Since LOL diagrams are a visual tool to help students and scientists analyze energy transformations and conservation, they can be used for making it easier to set up and solve conservation of energy equations in problems of greater complexity.

LOL Diagram of an Electrical Circuit

It is also important to note that the choice of the object (or system) of interest will result in different LOL diagrams for the same phenomenon.

For example, consider a filament bulb in a circuit with a battery. The system at room temperature also has some energy in the internal store (or internal energy, which consists of the kinetic and potential energies of the particles in the system).

When considering the filament as the object of interest, when energy is transferred electrically from the battery, part of it is transferred by light from the bulb to the surroundings and another part is added to the internal store, as it heats up the filament light.

On the other hand, when considering the circuit as the whole, the chemical potential store of the battery is included in the initial energy state of the system. Hence, there is no additional energy transfer into the system but the energy transfer output is still the same.

How do I modify the GeoGebra applet to make my own LOL Diagram?

Here’s a video that demonstrates how the editing process is done, in a little more than one minute!

The final product is here.

25 July

Snell’s Law Self-Assessment

Seng Kwang Tan GeoGebra, IP3 07 Light 0 Comments

My third applet today is a self-assessment tool for students to practise calculations with Snell’s Law, i.e. $n_1 \sin{\theta_1} = n_2 \sin{\theta_2}$.

The direct link to the applet is https://www.geogebra.org/m/fhmmuhbg

Snell’s law, also known as the law of refraction, describes how light waves change direction as they pass from one medium to another with different refractive indices. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. This law is fundamental in understanding the bending of light when it moves between materials of different optical densities, such as when light passes from air to water, resulting in phenomena like the bending of a pencil in a glass of water.

When light travels from a medium with higher optical density to a medium with lower optical density,

  1. The light ray bends away from the normal: The “normal” is an imaginary line perpendicular to the interface (boundary) between the two media. As light enters the medium with lower optical density, it slows down, causing it to bend away from the normal.
  2. The angle of refraction is larger than the angle of incidence: The angle of incidence is the angle between the incident ray and the normal, while the angle of refraction is the angle between the refracted ray and the normal. In this scenario, the angle of refraction will be larger than the angle of incidence.

When light travels from a medium with lower optical density to a medium with higher optical density,

  1. The light ray bends towards the normal: As the light enters the medium with higher optical density, it slows down, causing it to bend towards the normal, which is an imaginary line perpendicular to the interface (boundary) between the two media.
  2. The angle of refraction is smaller than the angle of incidence: The angle of incidence is the angle between the incident ray and the normal, while the angle of refraction is the angle between the refracted ray and the normal. In this situation, the angle of refraction will be smaller than the angle of incidence.

When light travels from a medium with a higher refractive index to a medium with a lower refractive index and strikes the interface at an angle of incidence greater than the critical angle, total internal reflection occurs. At this critical angle, the light is entirely reflected back into the higher refractive index medium, with no refraction into the second medium, resulting in the complete internal reflection of the light. This phenomenon is crucial in various applications, such as optical fiber communications and the brilliance of gemstones like diamonds.

Update on 27 Jul 2023: I improved on the rather unpolished applet to adjust the calculations for the object when it is below the boundary between the two media. Also added was an indication for when total internal reflection takes place.

25 July

Where is the Fish? A Refraction Simulation

Seng Kwang Tan GeoGebra, IP3 07 Light 0 Comments

I have seen a few simulations for apparent depth but was not satisfied with them. So I created this from scratch for use in tomorrow’s lesson. The positions of the eye and image of the fish are adjustable. It is more challenging to design for the actual fish to be draggable, so I only could allow the image to be dragged and hence, use it to shift the position of the actual fish.

Direct link to the applet: https://www.geogebra.org/m/kdszgpfg

13 June

How Nuclear Fusion can be achieved

Seng Kwang Tan Blog 0 Comments

Helion Energy is currently aiming to produce nuclear fusion energy commercially by 2028. The idea behind how it intends to do so is well-described in the video above.

Imagine one glass of D20 generating 9 GWh of electrical energy – enough power for a home for 865 years, at a cost of 1 cent per kWh. If successful, it will be a significant source of green energy in the next 10-20 years.

More importantly, nuclear fusion energy could potentially address the fears of many with regards to nuclear fission energy, such as the possibility of catastrophic meltdowns, weaponisation of raw material and environmental impact of mining and disposing of nuclear waste. This is because nuclear fusion reactions are self-limiting in that the reactors will shut down automatically if the optimal conditions are not maintained.

I can’t wait to see this happen, if it happens. Other than solving much of the world’s energy problems, it will also open up new opportunities in the energy sector for scientists and engineering. In fact, Helion itself is recruiting quite aggressively now.