Proof by contradiction

 Proof by contradiction, also known as indirect proof or reductio ad absurdum, is a method of proof in which a claim is shown to be true by showing that the opposite of the claim leads to a contradiction or absurdity.

Experimenting with spintronics

 

Time to play and experiment with spintonics from @UpperStoryCo and write some lesson plans for it. Discovering it is not only good for electronics but its quite good for mechanics and problem solving as well.

Resistivity

The resistance of a wire is directly proportional to its length. This means that as the length of a wire increases, its resistance also increases. This relationship can be described by the equation:

R = ρL / A

where R is the resistance of the wire, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

The reason for this relationship is that as the length of a wire increases, the number of collisions between the electrons and the atoms of the wire also increases. These collisions cause resistance and make it more difficult for the electrons to flow through the wire. As a result, the resistance of the wire increases as its length increases.

It's important to note that this relationship holds true only for a given material and cross-sectional area. If the material or cross-sectional area of the wire is changed, the relationship between length and resistance will also change.

Resistivity is a measure of the resistance of a material to the flow of electric current. It is typically denoted by the symbol ρ and is expressed in units of ohm-meters (Ω*m).

In general, materials that are good conductors of electricity have low resistivity, while materials that are poor conductors have high resistivity. For example, metals such as copper and aluminium have low resistivity and are commonly used in electrical wiring because they allow an electric current to flow easily. On the other hand, materials such as rubber and glass have high resistivity and are often used as insulation because they resist the flow of electric current.

The resistivity of a material is related to its electrical conductivity, which measures how easily a material allows electric current to flow. The relationship between resistivity and conductivity is given by the equation:

conductivity = 1 / resistivity

This means that materials with high resistivity have low conductivity and vice versa.

 

Ball drop

To record the motion of a ping pong ball being dropped against a black background in a totally dark room using a camera and flash gun set at 15 Hz (15 flashes per second), you will need to follow these steps:

1. Set up your camera on a tripod or other stable surface, making sure it is pointed at the area where you will be dropping the ping pong ball.

2. Set the camera to manual mode, and adjust the exposure settings to ensure that the image is well-exposed when the flash fires. You may need to experiment with different settings to get the right balance.

3. Set up the flash gun on a separate stand or tripod, making sure it is pointed at the area where you will be dropping the ping pong ball.

4. Set the flash gun to strobe mode, and adjust the flash frequency to 15 Hz (15 flashes per second).

5. Turn off any other light sources in the room, so that the room is completely dark.

6. Drop the ping pong ball from a height above the camera and flash, making sure that it falls within the field of view of the camera.

7. Start the camera's continuous shooting mode, and let it run for a few seconds as the ping pong ball falls.

8. Review the images on the camera's display or on a computer to see the motion of the ping pong ball as it falls.

By using a flash set to strobe at a high frequency and shooting in a completely dark room, you will be able to capture the motion of the ping pong ball as it falls, showing the effects of gravity on its motion.

Making Crystals

 One of my most enjoyable experiments is making crystals from solutions. Sometimes we manage to produce some large, well-formed crystals when the students make copper sulfate. Even the small ones look good under the microscope.

Microtome

Dissections mean opportunities to create slides of what the students are looking at and learn how to slice very thinly so we can see what is going on at the cellular level using a Microtome. A microtome is a scientific instrument used to cut very thin slices of material, known as sections. These sections can then be mounted on a microscope slide and viewed under a microscope for further analysis.

Microtomes are commonly used in a variety of scientific fields, including biology, pathology, and materials science. In biology, microtomes are often used to prepare sections of plant or animal tissue for microscopy. In pathology, microtomes are used to cut sections of human or animal tissue for histological examination. In materials science, microtomes are used to cut sections of materials for microscopic examination to study their structure and properties.

There are several types of microtomes, including manual microtomes, motorized microtomes, and cryomicrotomes. Mine is really basic. Manual microtomes use a hand crank to advance the material through a blade, while motorized microtomes use an electric motor to do the same. Cryomicrotomes are used to cut frozen sections of material, such as tissue that has been preserved in cryogenic fluids.

 

Calculating Vectors with Pasco Capstone

 Using the ball launcher on the @Pascoscientific smart cart and then analysing the video footage and putting in the vectors to show that the x and y vectors are independent and a classic quadratic graph for the flight of the ball.