# Brazilian Jiu Jitsu and Physics

Torque is the main concept of physics that is used in Brazilian Jiu Jitsu as it a great method when causing an opponent to submit. This martial art uses leverage and force to apply joint locks and chokeholds on the competition. In this sport size is not a skill-determining factor as a smaller competitor can inflict pain on his/her larger competition due to the use of torque. Many of the moves involve exceeding the motion (or hyperextending) of a limb by putting pressure past what the fulcrum can handle.
Torque: a measure of how much the force acting on an object causes that object to rotate. The object rotates about an axis, which is called the pivot point or point of rotation.
Force: any interaction that will change the motion of an object.
Fulcrum: a pivot point around which a lever turns.
Lever: the perpendicular distance from the axis of rotation to the line along which the force acts.
Center of gravity: the point at which the system’s whole mass can be considered to be concentrated for the purpose of calculations.

Armbar

Kneebar

How does a Brazilian Jiu Jitsu practitioner’s understanding of physics (torque) make him or her more effective?

A competitor does not have to be very strong or large to win a competition when using torque effectively. This makes it so that everyone, no matter the size or strength, can successfully take an opponent down and win a match.

# Desmos Art Functions Card 2018

https://www.desmos.com/calculator/qhxd9blybp

This assignment was a lot more challenging than I thought it would be, however I know it greatly strengthened my understanding of the concepts taught in math 12 by applying what I know. I came across many challenges in completing this assignment but I am happy with how it turned out. The most difficult part of this card was definitely making an equation for the ribbon on the present. After many hours I was finally able to come up with the complicated polynomial function that I did. Then I just had to adjust and translate the other equations to piece it together. I was also having trouble figuring out a way to include a rational function in the card, as it was the last type that was required. This was when I thought about doing a star which turned out better than I thought. I am much more comfortable with transformations of functions and relations because of the applications and problem solving aspects of this project.

# Neuron Communication

## Neuron Structure

The function of a neuron is to process and transfer information. A neuron is composed of many structures to allow it to carry out these functions daily. The neuron consists of dendrites, a cell body, axon, myelin sheath, and terminal buttons. The functions of these structures is explained in the diagram below.

## Neuron Types

There are three types of neurons; the motor neuron, sensory neuron, and the interneuron.

#### Motor Neuron

Motor neurons are part of the central nervous system and connect to the muscles, glands, and organs in the body.

#### Sensory Neuron

Sensory neurons are activated by sensory input from the environment and send information to the brain when stimulated.

#### Interneuron

Interneurons consist of the neurons that connect sensory neurons to motor neurons and vice versa, assisting in the transfer of information.

## Action Potential

Action potential occurs when a neuron is stimulated. Prior to an action potential, a neuron is in resting potential where the axon is in a polarized state with a charge of -70 millivolts relative to the outside of the axon. During resting potential, the fluid inside the axon has more negatively charged ions than the fluid outside. Next, depolarization occurs when channels open in the membrane of the axon to allow sodium ions to enter, creating a balance of ions. Therefore, depolarizing the inside of the axon. This has a charge of about +30 millivolts. More channels then open to allow potassium ions to exit, repolarizing the axon (-70 to -80 millivolts). The recovery period involves the action potential continuing along the entire length of the axon from the cell body to the terminal buttons.

## Synapse Structure & Function

The synapse is a gap between the axon of one neuron (sending neuron) and the dendrite of another (receiving neuron). The terminal button of a neuron wants to release chemical messengers (neurotransmitters) from the axon to pass on information to another neuron. This is how neurons “communicate” with one another and can be visually demonstrated by the diagram below.

# Due to increasing concern regarding global climate change, Canada needs to consider using more nuclear power as a possible solution.

There is a lot of controversy on the subject of nuclear power due to the many pros and cons of the topic.

A positive outcome of nuclear power in Canada would be that there will be less air pollution compared to burning fossil fuels. We would also start producing fewer greenhouse gas emissions during the production of electricity compared to coal power plants. Overall it would make Canada a much more environmentally friendly country.

Another advantage of nuclear power is that it produces very inexpensive electricity. The cost of the element uranium, which is used as a fuel in this process, is low. Even though the expense of setting up nuclear power plants is moderately high, the expense of running them is quite low. The typical life of a nuclear reactor is anywhere from 40-60 years. These variables make the expense of delivering power low.

Unlike solar and wind energy, nuclear reactors are not dependent on weather conditions and can run without disruption in any climatic condition. It is also much more proficient than fossil fuels. Their energy densities are extremely high compared to fossil fuels and the energy released by nuclear fission is about 10 million times greater than the amount of energy being released by fossil fuels. Canada currently has 19 CANDU nuclear reactors (in Ontario and in New Brunswick). None of them have experienced any incidents like the one in Chernobyl in 1986.

Overall, it isn’t a bad idea to consider using nuclear power in Canada because it does not pollute the atmosphere, it is not very costly, it is reliable, and it is much more proficient than fossil fuels.

A negative affect of nuclear power is the amount of radioactive waste that comes with 20 metric tons of nuclear fuel per year created by a single nuclear power plant. When considering each nuclear power plant on Earth, the amount of nuclear fuel produced is 2,000 metric tons. It is difficult to dispose of nuclear waste as the half life of uranium is 70 million years. Another downside is that although it is not an air pollutant, nuclear waste is a water pollutant. A nuclear power plant takes about 5-10 years to build. Also, uranium is finite and there is only enough of it for the next 70-80 years as well as only a few countries have uranium.

There have been accidents regarding nuclear power plants. When discussing nuclear power, the incident in Chernobyl often comes up. On April 26th, 1986, in Pripyat, Ukraine, an explosion and fire in a reactor sent radioactivity into the atmosphere. This had harmful effects on humans and ecology that can still be seen today.

Nuclear weapons were used at the end of World War II in the form of atomic bombs. These bombs were dropped in Hiroshima and Nagasaki, Japan. They created mass destruction and impacted human health (both physical and neurological birth defects) for years to come.

Due to all these pros and cons, I can see both sides of this issue and understand why it is a controversial topic that is being considered to be put in place in Canada.

# The Magic of Light

Refraction is the bending of light waves and occurs when a wave passes from one medium to another. In this case, the penny is originally in the bottom of the cup without any water and is not visible to the camera. As water is added, the light is refracted and the penny is “magically” brought into view without the camera being moved. The penny we see at the end is a virtual image as the penny (object) is in the same spot it started.

Every transparent medium has its own index of refraction. At first, there is no bending of light as there is only one medium and that is air. The greater the index of refraction, the greater the change in direction of light. Water has a greater index of refraction than air. Therefore, once water is added to the cup, the penny will come into view because the light is now bending as it passes through a different medium. The penny appears to keep moving as the water level rises because as the depth of the water increases, the angle of refraction increases. The angle of incidence remained the same as the camera did not move. Only the angle of refraction increased as the water depth rose.

# Wave Interference Activity: Constructive and Destructive Interference

### Constructive Interference

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Constructive interference is when a crest from one source meets a crest from another source, the energies combine to displace the medium (the energies are additive). In other words, when the two crests meet, they produce a single amplitude equal to the sum of the two individual amplitudes. The same thing occurs when trough meets trough. When the crests of the waves line up, there is constructive interference. Often, this is described by saying the waves are “in-phase”. In the first video, we put the slinky on the ground and flicked the same way to represent the crest meeting the other crest. The same thing occurred in the second video except we flicked the other way to represent the trough meeting another trough.

### Destructive Interference

IMG_6781-1s5818s

Destructive interference is when a crest and trough meet the energies combine to work against each other- they tend to cancel out. The sum of two waves can be less than either wave and can even be zero. When the crests of the wave in one wave match up with the troughs of the wave in the other, the waves are said to be “out-of-phase”. In this video, the slinky is flicked 2 separate ways to represent a crest and a trough. When they meet, they

# Exploring Waves Lab

### Pulse Wave

IMG_6674-u81gvt

A pulse wave is a single disturbance that is non-repeating and has one major crest. It often refers to some type of one-time disturbance. A pulse has a velocity and an amplitude but since there is only one crest, there is no frequency or true wavelength, although the width of the pulse relates to its wavelength. To measure a pulse wave’s speed, we use v=d/t.

### Periodic Wave

IMG_6675-128gvwp

This type of wave repeats at regular intervals and requires regularly recurring disturbances. Periodic waves are usually characterized by their amplitude, frequency, and wavelength. A wave whose displacement has a periodic variation with time or distance or both.

### Transverse Wave

IMG_6673-1xnrpll

This type of wave occurs when the spring is pulled sideways. It’s a moving wave that consists of oscillations in which the direction of displacement is perpendicular to the direction of propagation. Transverse waves may occur on a string, on the surface of a liquid, and throughout a solid. Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

### Longitudinal Wave

IMG_6676-1hvn6pp

A longitudinal wave is one in which the direction of displacement is the same as (parallel) the direction of propagation. It involves a wave consisting of a periodic disturbance or vibration that takes place in the same direction as the advance of the wave.

# Archimedes Challenge

## History of the Arch Bridge

An arch bridge is a semicircular structure that distributes its weight by dispersing it outwards through arches onto its two abutments, rather than straight down a column or pillar. Arch bridges have been around for about 3,000 years. The oldest arch bridges can be found in Mycenaean Greece but it was the Romans who were to fully realize the potential of arches for bridge construction. An arch bridge built of stone does not require mortar. This may be one of the reasons why arch bridges were invented as there was no mortar until it was invented later on. Also, there were no advanced materials such as steel and building arch bridges out of stone was common.

The implications of arch bridges being built was the ability to create aqueducts that could bring water to cities and to create roads and bridges that could be used to transport goods and people more easily. The Romans built many arch bridges throughout Europe, Asia, and North Africa which greatly benefited them in creating and maintaining their empire.

## Physics Involved

The abutments prevent the footers from pushing outwards. The keystone sides must be sloped to allow the keystone to slide down, pushing outward. The force of gravity is distributed from the key stone throughout the bridge, locking everything together.

If we assume that the mass of a bridge is 200kg we can find the force of gravity acting on that bridge.

Fg=mg

Fg=(200)(9.81)

Fg=1.96x 10^3N

In Newtons Third Law we learned that for each action there is an equal and opposite reaction. In this case with the bridge, the force of gravity (Fg) is pushing down from the key stone to the abutments. The ground pushes back on the abutments creating normal force (Fn) which is equal and opposite to the force of gravity. This creates a resistance which is passed from stone to stone. It eventually pushes on the key stone which is supporting the load. Arch bridges are always under compression. In physics 11 we haven’t covered much compression or tension but basically the force of compression is pushed outwards from the key stone along the curve of the arch to the abutments. The curve of the arch and its ability to dissipate the force outward reduces the effects of tension underneath the arch. The greater the degree of curvature (the larger the semicircle of the arch), the greater the effects of tension on the underside.

If a horse and carriage were to cross such a bridge, they would exert their force of gravity through the bridge (key stone down to the abutments) and the normal force would push back, holding the bridge together. This makes the bridge secure and efficient for crossing bodies of water, valleys, etc.

## Design and Building Process

On day one we started out with 4 orange tubs of play do, 1 blue tub, and a container of toothpicks. We spent the class making “bricks/stones” as that is what shape was common for creating arch bridges. A difficulty we encountered was trying to make them all the same size and shape as one another.

Thursday we continued molding our play do into bricks. Friday we made our first attempt at building the bridge with the amount we had and we realized it was quite difficult to stack the play do bricks. We ended up using the toothpicks, placing 5 play do bricks on each toothpick and then tried making the bridge again. We didn’t have enough however to make much of the bridge other than the abutments so we planned to buy more play do and toothpicks over the weekend.

Over the weekend we got 3 more tubs of orange play do and 2 more tubs of blue play do. We made some more bricks and flattened out the blue play do to make “water” underneath the bridge. We used the fresh play do for the abutments so they would stick better and be a sturdier base and started stacking the dried out play do on top. I thought of rolling up a piece of paper as the frame of the arch while we tried to balance the bricks and put a key stone in but it was quite difficult. We tried many times to stack, balance, and place the bricks the way these bridges were made but I believe we chose a poor material to make the bridge out of and that this affected our construction of the project. We ended up laying the bricks across the opposite way to make the “arch” and it looked like more of a doorway shape than an arch.

If I were to re create this project I may have used stones, wood, or another material to make the finished product more accurate to what arch bridges look like. Also, we should have prepared better by researching the history of the arch bridge first to get a better understanding of how they were constructed and the key steps to creating one. Nevertheless, I now have a better understanding of this invention and why they were efficient/stable ways of transport. I also gained knowledge of the physics involved in the arch bridge, although it took a lot of research, I now realize that it relates back to previous concepts in this course. This project helped me apply my learning to a real life invention involving physics and reminded me that physics is everywhere, you just have to think about it!

## Resources

https://science.howstuffworks.com/engineering/civil/bridge5.htm

https://www.britannica.com/technology/bridge-engineering/Roman-arch-bridges