05-31-2017: Lab 19: Conservation of Energy/ Conservation of Angular Momentum

Lab 19: Conservation of Energy/ Conservation of Angular Momentum

Kevin Nguyen

Lab Partners: Kevin Tran, Jose Rodriguez

Date of Lab Performed: 05-31-2017

Purpose: The purpose of this lab is to use the concept of angular momentum of the meter stick and clay and conservation of energy and conservation of angular momentum to find how high the meter stick and clay has risen. 

Theory:

Picture of the apparatus

In this experiment, we used the conservation of energy/ conservation of momentum to solve for the final height the clay has risen after the meter stick hits it.

We used conservation of energy first to find the angular velocity right before the meter stick collides with the clay

Then use the concept of angular momentum to find the angular velocity of the system right after the collision.

Then use the conservation of energy in order to find the maximum height the meter stick plus clay rises.

Summary:

Picture of the apparatus

First, we measured the mass of the clay (and the 3 metal pieces that acted as a stand for the clay) and meter stick since they were useful for our predicted height calculations. We set up the apparatus like above. Note that the axis of rotation is at the 10 cm mark, so the moment arm is 90cm long. 

Then record a high speed video of the ruler swinging, colliding with the clay, and rising to its maximum height. After that, put the video on logger pro, set the origin at the clay, which we considered as a point mass, and set the distance between the axis of rotation and the clay to be 0.9 m. 

Ignore the blue dots

After that, jump to the point of the video where the ruler is at its maximum height. Then, using the video tool, measure the distance between the x-axis and the maximum height the ruler and clay went. 

The experimental result was 0.276 m

Then compare the experimental results to the calculated results

Data Table

Calculated result

The height calculated was 0.253 m

The percent difference between the two values is 8.696%

Conclusion

There is a relatively large difference between the calculated result (.253m) and the experimental result (.276m). There are several reasons for the relatively large difference between the two values.

First, since we did not take into account the air resistance on the meter stick, the angular velocity may have been slower than what it should have been. A slower angular momentum would have resulted in a lower height.

Second, the friction on the axis causes the ruler to rotate slower and therefore have a slower angular velocity, causing the ruler to travel less than what it should have traveled.