Nov-21-2016: Lab 19 - Conservation of Energy and Angular Momentum

LAB 19 - Conservation of Energy and Angular Momentum

Tony Wu, Michell Kuang

November 21, 2016

Lab Goal: To understand and observe the conservation of energy and angular momentum through an inelastic collision of a meter stick and a piece of clay.

Theory/Introduction: If a system does not interact with its environment in any way, then certain mechanical properties of the system cannot change. These quantities are said to be conserved. In mechanics, examples of conserved quantities are energy, momentum, and angular momentum.  In the case of our inelastic collision, the kinetic energy and angular momentum of the meter stick are partially transferred to the clay.  The energy and momentum of the entire system is conserved.

Apparatus:

The meter stick is pivoted about its 10 cm mark.  The clay is wrapped in masking tape to get it to stick to the meter stick.

Experimental Procedure: We release the meter stick from a 90 degree from the horizontal.  We take a slow motion video capture of the stick.  We use Logger Pro to determine the speed of the meter stick as it travels towards the clay and the speed of the meter stick + clay combination after the inelastic collision.  We now have all we need to calculate the expected maximum height that the meter stick travels.

Data and Calculations: 

We use the parallel axis theorem to calculate the moment of inertia of the meter stick about its 10 cm mark.
We then use the moment of inertia to solve for omega, the angular speed, before and after the collision.
After we have the angular speeds, we use the conservation of energy and angular momentum in order to solve
for theta, the angle which the meter stick makes at its highest point after the collision.
With theta found, we calculate the highest height, h, that the meter stick travels.

Conclusions: Our values for the expected and experimental maximum heights were not as close as it could have been.  We had an expected value of 0.196 meters and an experimental value of 0.2106 meters.  An error of 6.93%.  

Sources of Error:
Collision not being entirely inelastic
Some energy being transferred as heat in the collision
The pivot that the meter stick is on has some friction
The angular speeds of the meter stick are inaccurate because it requires that the user input dots accurately