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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

ELECTRIC

c
SPEED OF LIGHT

Speed of an Electromagnetic wave moving through the vacuum

μ0
Magnetic Resistance

Slows down and limits the speed of an electromagnetic wave.

e
Elementary Charge

The Energy of a single Electron. (Quantised Units)

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?

Space

To MOVE a DISTANCE (c) You use ENERGY (e)

Time

The water RESISTS your MOVEMENT (u0) Over TIME you lose ENERGY (e0)
Now think about how this relates to our Magnetic and Electric constants

MAGNETIC

C= MAX Speed of swimmer
u0 = resistance of water

We can only swim at a certain speed because of the resistance of the water

ELECTRIC

e = MAX energy of swimmer 
  e0 = stamina of the swimmer

We can only swim for a certain time before we run out of energy

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

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
What is different about the value for  Electrical Resistance

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…

The small ‘2’ found in the value for  Electrical Resistance squares the value which can also be written as 36

Next we will need to add the circles…

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 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

Cards

Place the cards for each equation on the paper in the correct place.

Step 2

Draw

Draw around each card and fill in the details for the equation.

STEP 3

Solve

Flip the cards to see the values and solve the equation.

As you discover a new constants, create a card for them!

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 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 to send communications from deep space satellites in the most efficient way.

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

CREATE

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

Energy (E)

Now solve these equations to find the exact value for Z0

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

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

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…

So far so good. Next up is geometry…

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!

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