09-June-2017: Lab 20: Physical Pendulum Lab

Lab 20: Physical Pendulum Lab

Author: Tian Cih Jiao

Lab Partner: Weisheng Zhang, Kitarou

Date: 6/9/2017

Purpose of the lab: Before we start carrying out experimental procedures, we need to derive expressions for the period of various physical pendulums. After that, we can verify our predicted values by comparing them with experimental values.

Theory/Introduction:

Part A: The pendulum is a ring of finite thickness (R outer, r inner) and a little notch cut out at the top, serving as a future suspension point. For this particular pendulum, we derive expressions for the moment of inertia and the period and hopefully the period figure matches the experimental values.

Here is my pre-lab calculation:

Part B: The pendulums are an isosceles triangle of height H and base B and a semicircular disk of radius R. For an isosceles triangle whose pivot is its apex and a semicircle whose pivot is at the top of the semicircle.

Apparatus/Experimental setup:

For this part, we measure everything we need to calculate the predict value of Time period. 

The calculation of predict and the error comparing with experimental value shown below:

Measured data:

Semicircle pendulum: T experimental = 0.665700s

 Isosceles-triangle pendulum: T experimental = 0.761826s

Analysis:

For the semicircle part, our error is only 0.415%, and the triangle part's error is 5.93%.

So our activity is very successful and error is very small.

Conclusion:

We get very close experimental result comparing with our prediction. Our errors are under 6%. However, there are still some errors that we can avoid. For example,  the pivots are not exactly at ends, so the distance from the center of mass to the pivot might be smaller than expected.

01-June-2017: Lab 19: Conservation of Energy/Conservation of angular momentum

Lab 19: Conservation of Energy/Conservation of angular momentum

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: May 31th, 2017

Purpose of the lab:

The purpose of this lab is to justify conservation of angular momentum, coming up with experimental values and compare them with our predictions. 

Theory/Introduction:

If there is no external torque acted upon, the conservation of angular momentum applies to the system. The equation is given as:
I initial * omega initial  = I final * omega final

Experimental procedure:
Before we start carrying out the experiment, we need to predict the maximum height where the system (clay and meter stick) will rise to by plugging in equations for conservation of energy/angular momentum.

Here is the calculation:

Lab picture:

First, we measured the mass of both meter stick and clay.
The apparatus is set up in such a way that the clay sticks to the meter stick when they come into a collision (by attaching nails at the other end of the meter stick, opposite to the pivot end).
We capture the video by Iphone 7 plus with 60 fps, then we use the software on macbook to trim the video. We analyze the video using LoggerPro by setting the length of the meter stick to 1 meter, then find the final position which is the highest point. By setting the lowest point close to zero, we can find out the height difference. Now that we have an experimental value and a predicted value, we can compare them and find the conservation of angular momentum in this lab.

Measured data:

mass of the clay = 0.035 kg

mass of the meter stick = 0.145 kg
measured change in height = 0.3115 m

Analysis:
From the lab, we can get that the height difference is 0.3115 m, and the predict value is 0.323327 m. They are very close.

Conclusion:
From the result of lab, we can see we did good job for measuring data and calculating so that the results are very close. However, there are still some reasonable errors such as air friction and friction at the pivot, the horizontal is not leveled.