The setup for the experiment consisted of a meter stick that was pivoted at one end, or close to it.
The meter stick would be released from a horizontal position and swings down. When it reaches the bottom of its swing it collides inelastically with a piece of clay. This was achieved by wrapping the clay with tape and wrapping the bottom of the meter stick with tape.
The clay-stick combination continue to swing with each other to some final position. Below is the overall setup.
A camera was setup at the opposite end of the table to capture video for Logger Pro's video analysis. another meter stick was setup just behind the piece of clay to give Logger Pro a distance to reference.
The mass of the meter stick and the piece of clay were both measured using a balance.
Before the experiment began, the predictions were made. The motion of this experiment was divided up into three parts. Energy was used when the meter stick is released from a horizontal position to the moment right before it collides with the clay. Conservation of angular momentum was used during the inelastic collision with the stick and clay. And finally, Energy was used again when the clay-stick combination move together right after the collision to when they reach their highest point.
Part 1: Energy
For the first part, the meter stick started with gravitational potential energy and ended with kinetic energy as well as gravitational potential energy. GPE was set to equal zero at the point where the meter stick was horizontal. So, the initial GPE was zero. GPE was calculated from the center of mass which is at the 50 cm mark since we assumed a stick of uniform dimensions. This means the distance from the pivot to its center of mass was 49 cm (represented by "y" in the calculations) since the pivot was located at the 1 cm mark. The parallel axis theorem was used for the inertia of the stick since the pivot is neither at the center of mass nor directly at the end. Angular velocity was solved for so that it may be used for the next part.
Part 2: Angular Momentum
Now that the angular velocity before the collision is known, conservation of angular momentum could be used. This was used to calculate the angular velocity after the collision. The inertia of the system after the collision is the sum of the inertia of the stick and the clay. The inertia of the clay was treated as a point mass and calculated by mR^2, with R being the distance from the pivot to the end of the meter stick.
Part 3: Energy
Knowing the angular velocity after the collision allowed for the calculation of final height for the clay-stick combination. The clay and stick both started off with GPE and KE, and ended with GPE. Below were the final calculations needed for the height prediction.
A prediction of 0.3827 m was found after plugging in all numbers.
Now the experiment was run and the video was analyzed. The origin was set to zero where the piece of clay rest before the collision. The video was run and a data point was placed where the clay was at it highest. This gave an x and y-coordinate, but we were only interested in the y-coordinate. That y-coordinate was the final height we compared with the prediction.
