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Dimensionless Science Challenge

 – Unlock the Genius –
STEP 1: What do you know?
?

ASK YOURSELF THE QUESTION

On a piece of paper write down the number of scientific constants the you know the value of.

If you don’t know any that’s fine as you soon will.

STEP 2: Overview.

We are going to learn the exact values for 4 key scientific constants:

MAGNETIC (PARTICLES)

ELECTRIC (WAVES)

m
Mass

The total energy of an object, inc. weight, kinetic, and thermal energy.

μ0
Magnetic Resistance

Slows down and limits the speed of a particle moving in space.

c
SPEED OF LIGHT

Speed of an Electromagnetic wave moving through the vacuum

ε0
Electrical Resistance

Absorbs the energy of an electron or EM wave as it moves through space

Notice that there are 2 types. Magnetic and Electric

CREATE

On 4 post-it notes draw the symbols for each constant, sun, magnet, and 2 lightening bolts.
Add the Zero (0) to the magnetic and electrical resistance cards.
Finally and the scientific symbol for each one and write the name down next to it.
You should now have 4 cards, one for each constant that looks like this…

Once you’re done, move on to the next step…

STEP 3: Meaning.

We can understand these constants easily by using a metaphor

IMAGINE

Can you remember what is like to swim underwater?

Now think about how this relates to our Magnetic and Electric constants

MAGNETIC

M = Mass – Body of the swimmer
µ0 = The body slows down over time

The larger the Mass, the more Energy needed to move

ELECTRIC

c = Light = MAX speed of swimmer 
  ε0 = the viscosity of the water

The fastest speed the swimmer can travel due to the density of the water.

The swimmer is like a particle (such as an electron) as it moves through space, (the water).

Once this is clear in your mind its time to move on…

STEP 4: Values.

Next we are now going to learn the values for each constant

Try to guess the value for each one before clicking the image to reveal the answer.

MAGNETIC

ELECTRIC

m
Mass
m
Mass
μ0
Magnetic Resistance
μ0
Magnetic Resistance
c
SPEED OF LIGHT
c
SPEED OF LIGHT
ε0
Electrical Resistance
ε0
Electrical Resistance
NOTE: The number ONE is a dimensionless quantity

CREATE

On the back of the 4 post-it notes write the value for each constant.
Again write out the scientific symbol for each one and write the name down next to it.
The back of your cards should now look like this…

Next we will need to add the circles…

STEP 6: Equations

Now that we have found values, for these scientific constants we are going to perform our first scientific calculation.

WHAT ARE EQUATIONS?

Scientific equations use multiplication and division to compare 3 or more qualities or quantities found in the universe.

Multiplying or Dividing one value by another defines the 3rd value.

All scientific equations are ratios

If the two bottom values (B and C) are multiplied the result is A.

If the top value (A) is divided by one of the bottom values the we get the result for  the other.

All scientific equations are based on this principle. This method of presentation will help you understand scientific concepts more easily.

TIP: By representing equation in this way makes it easy to understand science

Armed with this knowledge its time to take our 1st steps into science.

In a few moments time you will know how great scientists like Albert Einstein, and James Clerk Maxwell calculated the fixed speed of light.

The Speed of Light (c) is central to Einstein’s Theory of relativity

Maxwell discovered that all electromagnetic waves expand at the speed of light (c).

A4 Paper

We are going to perform our mathematics using our A4 paper.

Use 1 piece for each equation.

Follow these 3 step to solve each equation

Step 1

Draw

Create the template for the equation.

Step 2

Cards

Find the right cards and place them in the correct place.

STEP 3

Solve

Flip the cards and solve the equation. (Click to reveal)

STEP 3

Answer

How did you do? Did you find the right answer?

Keep hold of your equation templates as a learning tool for future use.

What did you just learn?

You have learnt why the speed of light is fixed!

The speed of light is fixed because light waves encounter electrical and magnetic resistance.

Throughout the universe the ‘Cosmic Microwave Background’, the energy found in the vacuum of space, exhibits electrical and magnetic resistance that prevents light traveling at an infinite speed.

Let’s examine this equation from another perspective

Division

Draw

Same equation only this time we are using division.

Cards

This time we are not including Mass in the equation

STEP 3

Solve

Flip the cards and solve the equation. (Click to reveal)

STEP 3

Answer

How did you do? Did you find the right answer?

Let’s put this relationship into a circle

CREATE

Draw a cricle and divide it in half

Divide one half again< into two equa parts./span>

Write ε0 in the larger section, and µ0 in the left lower section and c to the right.

You should have a card that looks like this…

 

Now that you have solved the equation that established the speed of light, you might feel the little Einstein awakening inside you.


But hold on what happened to Mass?

Well there is more to the story, which is what we will look in next.

Your doing really well.  Keep going!

STEP 6: Math

Now that we have the exact values, its time to put them to the test

A4 Paper

We are going to perform our mathematics using our A4 paper.

Use 1 piece for each equation.

Follow these 3 step to solve each equation

Step 1

Draw

Create the template for the equation.

Step 2

Cards

Find the right cards and place them in the correct place.

STEP 3

Solve

Flip the cards and solve the equation. (Click to reveal)

STEP 3

Answer

How did you do? Did you find the right answer?

Keep hold of your equation templates as a learning tool for future use.

Try this simple equation

Try this simple equation

Try this simple equation

Try this simple equation

We are going to find the dimensionless values for mass (m) and energy (E).

Einstein’s famous equation defines the relationship between mass (m), energy (E), and the speed of light (c).

Can you solve the equation?

Find your ‘c’ card and 2 new cards, marked ‘m’ for mass and ‘E’ for energy.

Draw out the equation. Can you guess which card goes where?

Click to reveal

If you did it right your cards should now look like this…

Onto the next step

Now let’s see how we might solve this equation.

Flip the cards. We have missing values for both Mass (m) and Energy (E)

If we set mass (m) to ONE, can you work out the value of energy (E)?

Click to reveal the answer

Did you get it?

Congratulations, you now know the dimensionless values for six constants!

CREATE

Now that you know the exact dimensionless values for mass and energy, let’s make 2 new card to represent them.

Mass (m)

Mass is the total energy of an object. This is made up of 3 things:

 

WeightTemperature Motion

 

We can use an image of a weight radiating heat as it moves through space to represent this.
Create a card with this symbol, add the letter m and write the number 1 on the back like this… .

 

Energy (E)

When a particle moves in space it loses Energy (E) in proportion to is mass.
Represent this as a dot and an arrow surrounded by a set of circles. Create a card with the letter E and write the number 9 on the back like this…

 

You now know the exact ‘dimensionless values’ for 6 scientific constants. Way to go!

Now that you have solved the ‘mass energy equivalence’ equation, you might feel the little Einstein awakening inside you.


If so, are you up for a more challenging equation?.

Still good?  Then its time to go deeper into science…

STEP 5: The Circle

The values we have defined are not yet complete.

The next step is to add the ‘geometric constant’ pi (π) into the equation.

WHAT IS π?

π is not a ‘number’, its a RATIO!

π is the relationship of a circles circumference to its diameter.

If the Diameter of a circle is ONE, the Circumference will be π.

As any circle can have a diameter of ONE ascribed to it, the size of the circle is not important.

Adding π to the constants

Click on the cards to see which constants have pi in them.

MAGNETIC

ELECTRIC

c
SPEED OF LIGHT
c
SPEED OF LIGHT
μ0
Magnetic Resistance
μ0
MAGNETIC RESISTANCE
e
Elementary Charge
e
ELEMENTARY CHARGE
ε0
Electrical Resistance
ε0
Electrical Resistance
Did you spot the odd one out?

CREATE

Add the value for π to the numbers you wrote down previously each constant.
The back of your cards should now look like this…

So far so good. Next up is some simple math…

STEP 6: Division

We are now at the last step that will define the exact values for our constants.

But before we do we need to understand what fractions are.

WHAT ARE FRACTIONS?

Fractions are RATIOS!

Scientific equations use multiplication and division to compare 3 or more qualities or quantities found in the universe. Dividing one value by another expresses a ratio between various phenomena. Energy (E) is made up of mass (m), which is held in ratio by the square of the speed of light (c2).

It is this nature of the universe that allows science to make accurate predictions before any experiment is conducted, which produces evidence for a hypothesis.

BONUS: With a mass of 1 what will be the value of energy according to your speed of light card?

Whole numbers and fractions

Two of our constants are whole numbers, and two are made up of a Fraction. Can you guess which ones?

Click on the cards, starting from the left to reveal the final values for our constants.

MAGNETIC

ELECTRIC

c
SPEED OF LIGHT
c
WHOLE
μ0
Magnetic Resistance
μ0
WHOLE
e
Elementary Charge
e
FRACTION
ε0
Electrical Resistance
ε0
FRACTION
Looking at these final values, can you see the numbers 1 to 6?

CREATE

Add the fractional values to the electrical constants
The back of your cards should now look like this…

Congratulations!

You have just learnt the exact ‘dimensionless values’ for 4 important scientific constants.

Impressive stuff. Next up, everyone’s favorite; Mathematics

STEP 8: Science

We are going to discover the value for another important scientific constant.

Z0

Z0 = ‘Impedance of the Vacuum’

Impedance is similar to resistance except that it varies with frequency.

Just like a spring that is oscillating at a certain vibrational frequency.

When the vibration changes so does the value of resistance.

Solve for Z0 and become as intelligent as a NASA scientist or a telecommunications engineer

NASA Scientists use Z0 for efficient deep space communications

Telecommunications experts use Z0 as a foundation for tuning transmitters.

CREATE

Take a new card and draw a spring on one side. At the bottom write Z0 = vacuum impedance.
You should have a card the looks like this…

Now solve these equations to find the exact value for Z0

Find Z0 with the Magnetic Constant (µ0) and the Speed of Light (c)

Draw out the equation and add the cards in the right place

Click to reveal

Your card should look like this.

Flip them over and solve for Z0

Once you have solved the equation, click here to check your answer

Did you get the right answer?

TIP: try making the calculation without π first, then add the π to symbol next the total afterwards.

CREATE

Write the value for Z0 on the other side of the card. Again write Z0 = vacuum impedance at the bottom.
You card should look like this…

Congratulations you now know the Value for 7 scientific constants.

Next let’s look at another way Z0 can be found.

Find Z0 with the Electric Constant (ε0) and the Speed of Light (c)

Draw out the equation. What card goes above ε0?

Click to reveal

Its the MASS card. Flip the cards.

Can you simplify the equation?

Click here to view the simplified equation

When combined with mass the 1’s cancel out!

Thank about what this means…

TIP: What happens to a fraction when it is divided by ONE?

Before we move on let’s break down the math.

The value for ε0 is already a fraction.
Mass over ε0 cancels out the ones.
ε0 with mass becomes 6²π or 36π

Let’s put what we have learnt into an order

This help us understand and remember


Place your µ0 card on the left and your m/ε0 card on the right.
What card goes in the middle that will value multiply µ0 to make it m/ε0?

µ0

Click

Energy

m/ε0

TIP: You can replace the π symbol for a circle for a cleaner look.

Let’s recap

What is Energy?

E = Energy

E = C x C

Energy is a combination of two equal quantities of light speed for every unit of mass 1.

We can view this relationships in a circle.

The outer circle represent a unit of mass.

With this in mind answer this question.

 

What card goes between ‘c’ and ‘c’ as µ0 is transformed into m/ε0?

µ0

c

Click

Impedance

c

m/ε0

Take a moment to play with the cards, until you fully understand the relatiopnship of these key scientific constants.

Once you are clear then move onto the next step

Still good?  Then its time to go deeper into science…

STEP 8: Science

We are going to discover the value for another important scientific constant.

Solve for Z0 and become as intelligent as a NASA scientist or a telecommunications engineer

STEP 6: Geometry.

Now that we have the exact values, its time to put them into a framework of geometry.

Geometry expands from a dot (0D) into higher dimensional space.

1D

Line

A line represents a circles:

r = Radius – the distance from the center to the circumference

D = Diameter – the distance across the circle

2D

Circle

A circle is composed of:

C = Circumference – The distance around the outside of the circle

A = Area – the space contained inside a circle

3D

Sphere

A sphere has a:

S = Surface – The space that encompasses the sphere

V = Volume – the space contained inside a sphere

If you need to, make a note of these 6 geometric aspects, r, D, C, A, S and V.

GEOMETRIC CONSTANTS

Each constant can be represented as an aspect of a sphere.

Click the card to see the equation

MAGNETIC

ELECTRIC

c
SPEED OF LIGHT
c
RADIUS
μ0
Magnetic Resistance
μ0
SURFACE
e
Elementary Charge
e
DIAMETER
ε0
Electrical Resistance
ε0
AREA

CREATE

Let’s make a 2nd set of cards

On one side write the exact values our constants like before…

On the back draw the symbol for each constant.
Note down which aspect of the sphere each represents

Take a moment to play with your cards. Mix them up, and then arrange them in order.

Looking great. Now its time to do some science…

Click

Impedance

c

m/ε0

Einstein’s famous equation defines the relationship between mass (m), energy (E), and the speed of light (c).

Can you solve the equation?

Draw out the equation. Can you guess which card goes where?

Click to reveal

If you did it right your cards should now look like this…

Onto the next step

Draw out the equation. Can you guess which card goes where?

Click to reveal

If you did it right your cards should now look like this…

Onto the next step

So far so good. Next up is geometry…

Find Z0 with the Electric Constant (ε0) and the Magnetic Constant (µ0)

Draw out the equation. Can you guess which card goes where?

Click to reveal

If you did it right your cards should now look like this…

Onto the next step

Draw out the equation. Can you guess which card goes where?

Click to reveal

If you did it right your cards should now look like this…

Onto the next step

FRACTIONS : A matter of perspective

We can view the same length as being multiplied or divided depending on the scale we use:

TOP : We count the distance in units of one and travel two unit lengths. = 2/1

BOTTOM: We count the total distance as one and divide it into smaller parts = 2/1

It all depends on what we call ONE!

CREATE

Create a second ‘Speed of light’ Card. Now line up the card in order like this…

To make thing clearer we can replace π with a circle.
Can you see how we can multiply the numbers 4 x 3 to get 12 and the by 3 again to get 36. We the two ‘c’ cards are multiplied we get 9, the value for energy. The M card reminds us that Mass is found in conjunction with Electrical resistance. Take a few minutes to thing about this relationship. Once you are clear move onto the next step.
Next we can create 5 new cards and place one beneath our existing cards. Label the cards R, I, E, I , and W, like this…

R = Resistance
Try to guess the value for each one before clicking the image to reveal the answer.