 ## PROJECT DESCRIPTION

A year and a half in the making, this kinematic cube created by the 9th grade Strong/Swaaley team of High Tech High tells a story about a civilization that goes through the stages of the rise and fall of a civilization.  Each panel represents one of the four stages:

1. Coming together

2. Social Construction

3. The Dilemma

4. Social Dissolution

The Physics classes from the school years of 2014-2015 and 2015-2016, created, designed and built the cube.  In 2015-2016, Math class integrated into the team in order to learn math through the project.

## MATH INTEGRATION

Math class became integrated to help explore and model the equations that define the...

• gear ratios of both the winding mechanism

• the planetary gears on top of the cube

• angular acceleration of the cube

• angle and time between stops

• the number of rotations

• and more

Below are the equations we used to predict the movement of 800 pounds of wood and steel.

Long Now Equations 3

Long Now Equations 2

Long Now Equations 1

Long Now Equations 3

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## STUDENT WORK

Our students used the online graphing tool Desmos and isolated inputs and documented how the change in inputs affected or didn't affect the following our outputs.  Students applied their learning of functions to model inputs and outputs.

These were our inputs:

• Mass of weights

• Vertical travel of weights

• Compound pulley purchase

• Planetary Gearset Reduction

• Moment of Inertia

• Radius of Flying Pendulum Arm

• Length of Pendulum Rope

Students modeled how to achieve a particular output.  In the image below, our desired output was the number of rotations to equal 2.

The image below represents the function for the number of rotations when mass = 8 kg. The image below represents the function for the number of rotations when mass = 140 kg.

As students observed, the line didn't move off of 2 rotations.

They concluded that the mass of the weights did not affect the number of rotations. Students were also tasked to find out what inputs would yield specific outputs.  For example, if we wanted to time between stops to be 5 seconds instead of 2 seconds, students explored various inputs that would make that happen.

These were our 5 desired outputs.

1. Number of rotations

2. Angle and time between stops​

3. Final angular velocity of the cube

4. Tangential velocity of the ball

5. Horizontal deflection of the ball

Below you will see student results of the desired outputs and what values of the inputs could make that happen.

Rotations 3

Rotations 1

Horizontal Deflection 1

Rotations 3

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