May 20th, 2015: Lab 19: Conservation of Energy and Angular Momentum

Purpose:

Given a clay+meter stick system, by releasing the meter stick to collide inelastically with the clay, show that there's conservation of energy and conservation of momentum in the system.

Experiment:

Data: M(stick+ clay) = 0.113 +/- 0.001 kg

m-meter stick = 0.080 +/- 0.001 kg

Coming up with predicted "h"
- Noticing that there's 3 parts to this lab to find "h",

• conservation of energy of meter stick before released to meter stick right before collision
• conservation of angular momentum of meter stick right before collision and the system right after collision
• conservation of energy of the system from right after inelastic collision to the maximum height reached.

* Energy and momentum approaches are more doable and kinematics wouldn't be possible because angular acceleration is not constant at all time.

- Note that at pivot on meter stick cannot be exactly at the edge. Using Parallel Axis Theorem gets us the pivot that, in our case, is 0.026 m away from the edge. So our "d" of shifting is 0.5-0.026= 0.474

- the three parts shown in calculation below,

- Note that GPE = 0 is set at the pivot for part 1 and 3. After finding cosθ, we can now find "h":

The experiment
- Take mass measurements of meter stick and clay(also with the paper clips and tape around it).
- Set up the apparatus. Place one farthest end of meter stick to the pivot point that's attached a standing rod.

camera seen attached to the bottom of chair

- Connect camera to Loggerpro for data collection. Place the camera such that the field of view show the collision and the system raised to maximum height.
- Test out the setup by releasing the meter stick, held horizontally, and make sure that it stays with the clay (after collision) all the way till they reach maximum height.
- For video capture setup, set scale and axis. Set scale by measuring the width of the whiteboard behind the setup. The axis should preferably be centered at where the clay is, for easier video analysis.

- Since the only data we mainly want from the experiment is the maximum height reached, when adding point series, we can just put two points, blue dots from the screenshot above.
- The lower dot won't be exactly at zero so we have to subtract between the two dots to find experimental value for "h".

Data Analysis:

- From the y-axis of point series data, we get h= 0.2419 - 0.007486 = 0.234414 m.

 - Comparing to predicted value and calculation of error and uncertainty:

- Experimental "h" should be smaller then predicted value due to other unaccounted error and certainty during calculation.

Conclusion

Our error and uncertainty include friction at pivot (we test it out with only meter stick released from one end doesn't travel to the same height at the other end), kinetic friction from the floor during the collision (from scraping of clay with the floor tends to slow system down), imperfect stability at the pivot point. The usual systematic error result from measurement equipments and poor video quality. Nonetheless, our experimental "h" is smaller than the predicted due to the errors and uncertainty described, and so it's safe to conclude that there's conservation of energy and conservation of angular momentum in the meter stick+ clay system.