2. Step 1: Conservation of Energy  (1/2)*k*x 2 = (1/2)*m*v 2 + (1/2)* I *ω 2  The mechanism is initiated by the potential energy of the spring, which, when released by a small pin, transfers its elastic potential energy into rotational and linear kinetic energy.

3. Step 2: Conservation of energy  (1/2)*m*v o 2 + (1/2)* I *ω o 2 + m*g*h = (1/2)*m*v f 2 + (1/2)* I *ω f 2  marble rolls into p.v.c. pipe, and continues downward. The kinetic energy of the marble is now combined with gravitational potential energy, as the datum of this step is located at the end of the pipe. The kinetic energies of the marble are then maximized.

4. Step 3: Linear Momentum/Center of Mass  m 1 v 1 + m 2 v 2 = m 1 v 1 ′ + m 2 v 2 ′  In this case, the subscript ‘1’ represents the marble, and the subscript ‘2’ represents the ball. After the collision, the marble remains stationary while the larger ball is given just enough momentum to knock its center of mass (balanced slightly over the edge of the board) off, causing it to fall.

5. Step 4: Translation of Energy  m*g*h = (1/2)* I *ω 2  When the ball falls to the bottom of the circle, (when the string is completely tense between the ball and the nail) it reaches its highest angular velocity.

6. Step 5: Angular Momentum  I 1 ω 1 + I 2 ω 2 = I 1 ω 1 ′ + I 2 ω 2 ′  When the ball reaches the bottom of its circle, it strikes a board directly at its center of mass, causing it to obtain angular momentum and fall.

7. Step 6: Angular Momentum… Again  I 1 ω 1 + I 2 ω 2 = I 1 ω 1 ′ + I 2 ω 2 ′  The board falls and strikes a block, rotating about a metal rod with its axis perpendicular. This pulls a string, causing the banner to fall and triggering the next group’s mechanism.