11/21/16 - Conservation of Energy and Angular Momentum (Lab 19)

GROUP MEMBERS: Xavier L. and Billy J.

PURPOSE:
To predict how high a piece of clay and a meter stick will rise after an inelastic collision.

THEORY:
Consider a meter stick pivoted at one of its ends being held up horizontally. In this position, it has GPE. The meter stick is then released, allowing it to swing until it is nearly vertical. In this position, all of its GPE is turned into rotational KE. At the bottom of its swing, the meter stick collides with a piece of clay, which sticks to the end of the meter stick opposite the pivot. This is known as an inelastic collision, and therefore angular momentum is conserved, but energy is not conserved for the collision. Using this information, we can create an expression for the final position of the clay+meterstick system. The only difference is that our meterstick will not be directly at the end, so we will have to use parallel axis theorem in order to find the moment of inertia of the system after the collision.

APPARATUS:
This apparatus consists of two main parts: the clay blob and the meter stick. Everything else is meant to facilitate the placement of these materials as we attempt to swing the meter stick into the clay blob and allow them to rise together.

Apparatus Diagram

Apparatus fully assembled (just needs clay)

EXPERIMENTAL PROCEDURE:
We used a smartphone to video capture the collision, rise, and maximum angular displacement of the clay+meterstick system. After that, we used Logger Pro to measure the maximum height the system rose after the collision.

DATA/ GRAPHS:
mass of meter stick: 78.3 +/- 0.1 g
mass of clay: 22.9 +/- 0.1 g

length of meter stick: 1.0 m
pivot distance from end: 2.5 cm +/- 0.1 m

Position vs Time Graph (both x and y)

ANALYSIS:
We used conservation of energy to find the omega of the system at the bottom of the swing---before the collision. We then utilized the conservation of angular momentum in order to calculate the omega of the system after the collision. This enabled us to use conservation of energy once more to calculate the final height through which the system rose. The key is to recognize that in this section of the calculation, the rotational KE of the stick+clay system at the bottom of the swing is equal to the ΔGPEcm of the system. This means that we also had to find the cm of the system after the collision.

Final Height Calculations

Final Height Results

CONCLUSION:
Our predictions for this experiment were not as fruitful as we had hoped. After comparing our theoretical values to our experimental values, we discovered that there was about a 35.4% difference between them. There are many places this uncertainty could have arisen from. For example. in this experiment, we assumed that there is no friction at the pivot of the meterstick. Furthermore, our pivot had some leeway to move perpendicular to the axis of rotation so it is possible that some of the energy in the swing was lost to the wobbling of the pivot. Another possible source of error was friction between the clay blob and the paperclip holding it in place initially. On the other hand, at least our group can rule computational error as a minimal source of uncertainty. This is because we checked our work several times, including once with the professor to make sure that our methodology was sound.