7-June-2017: Physical Pendulum Lab

Physical Pendulum Lab
May Soe Moe
Lab Partners: Steven Castro, Stephanie Flores
Date: 7-June-2017

Objective: To derive expressions for the period of various physical pendulums and to verify the predicted periods by experiment

Introduction:

We did the pre-lab questions for this lab, in which we derived expressions for the moment of inertia of the semicircle rotating around its midpoint, its rim, the moment of inertia of the isosceles triangle rotating around its apex, and its midpoint. Once we get our expressions for moment of inertia of theseshapes, we derived our angular frequencies by using torque equation: T=Iα. Then, we used our previous derived equation in class, which is α=ω^2θ. We first use the torque equation and find α and put it into "α=ω^2θ" form. Whatever constant in that form is our ω^2. And we will find its square root and put into period equation: T=2π/ω. Then, we will conduct an experiment of a semicircle rotating around its midpoint, and an isosceles triangle rotating around its apex, and figure out their period by using motion sensor and Logger Pro. After that, we will compare the theoretical value and our experimental value.

Experimental Procedure:

(1) We set up to conduct the experiment as below:

Semi-circle Oscillating around its Midpoint

Isosceles Triangle Oscillating around its Apex

PhotoGate will determine the period of the triangle as the triangle oscillates.

(2) We chose our physical pendulums to be a semicircle and an isosceles triangle.

(3) Semicircle rotates and oscillates around its midpoint, and the triangle rotates around its apex.

(4) We sticked a piece of paper at the bottom of the pendulums to make sure PhotoGate can sense their motions correctly.

(5) We connected PhotoGate to our laptop and Logger Pro.

(6) After all the set up, we gave a push to the pendulums to make them start oscillating, and started to collect data in Logger Pro.

Experimental Data and Measurements:

Measurements of the Semi-circle and Triangle Pendulums

Experimental value of Period of A Semi-circle rotating around its midpoint collected by the PhotoGate

Experimental value of Period of A Triangle rotating around its Apex collected by the PhotoGate

Theoretical Calculation:

Calculating the moment of inertia of a semi-circle rotating around its midpoint

Calculating Angular Frequency 

Calculating the Moment of Inertia of an Isosceles Triangle around its Apex

Calculating Angular Frequency of the Triangle around its Apex

Calculating the period by using the derivation from above

Comparing the results

Conclusion:
Theoretical calculation part of this lab was done by finding moment of inertia around the midpoint of the semi-circle, moment of inertia around the apex of the triangle, and by using torque equation to find the angular frequencies of the oscillating semi-circle, and the triangle. Once we have the angular frequencies of the pendulums, we could calculate the period. The experimental part was done by using PhotoGate to figure out pendulums' periods. Now, when we compare the results of theoretical period and experimental period, we found that they are less than 3% error, which is really close and within acceptable range. Therefore, this lab was successful and it also proved that our derived equations of the period of oscillating triangle and semi-circle were correct.

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

Lab 19: Conservation of Energy/Conservation of Angular Momentum
May Soe Moe
Lab Partners: Ben Chen, Steven Castro, Stephanie Flores
Date: 31-May-2017

Objective: To determine how high the clay-stick combination rises after the collision, and compare the experimental results with theoretical results

Introduction: 
In this lab, we will theoretically figure out how high the clay and the stick rises up after the meter stick collides with the clay by using the conservation of angular momentum and the conservation of energy. We will use the conservation of energy first to find out the angular velocity of the stick right after the collision. Once we get the initial angular velocity, we will use the conservation of the angular momentum to find out the final angular momentum. After that, we will use the conservation of energy again to get the maximum height the clay and the meter stick reach after the collision. Experimentally, after setting up the apparatus, we will shoot a slow-motion video with an iPhone of the meter stick colliding with the clay and reaching up to the maximum height. After that, we will use Logger Pro to set up the initial point and final height of the clay and the meter stick. Logger Pro will give us the maximum height the clay and the stick reach together. We will compare what Logger Pro gives us with the theoretical calculation we did.

Experimental Procedure:
(1) We set up our apparatus as below:

Our apparatus set up

After the clay collides with the stick

(2) The pivot is at 10 cm mark, and we will consider the pivot is at 0 cm mark, the center of mass is at 40 cm mark, and the clay is at 90 cm mark.

(3) After setting up, we aim where to put the clay, so that the stick collides with the clay.

(4) We put the pins into the clay so that it would stand. The clay only sticks to the meter stick if it is standing on the pins.

(5) Once we got our aim, we set up a ring stand where the phone could capture the whole process of the stick colliding to the clay and the clay sticking to the stick.

(6) We made sure that we could see the maximum height the clay and the stick reached in the video.

(7) After recording the whole process, we inserted the video into Logger Pro.

(8) We define our x and y- axes and marked where the initial and final position of the stick. Logger Pro automatically determined the maximum height the clay and the stick reached.

What we did in Logger Pro to get the maximum height

Experimental Data: 

We got the maximum height as 0.3743, experimentally.

One thing to note in this screenshot is that our actual maximum height is -0.3743, not 0.6104. We set our x and y- coordinates wrong, therefore, it is switched. 

Theoretical Calculations:

Calculating the angular velocity at the bottom to find the angular velocity at maximum height

Calculating angular velocity at maximum height and using it to find the maximum height

Conclusion:
When we compared it to our theoretical maximum height (0.394m) and experimental maximum height (0.3743m), it has 5% difference and 5% percentage error. This is within acceptable range. The source of uncertainties might be that when we marked the clay to determine the maximum height in Logger Pro, it might not have been the same exact location on the clay, which could be a difference from the video. Overall, the lab was successful that our theoretical and experimental maximum height of the clay and the meter stick are close to each other. Therefore, we can also see that this experiment confirms the conservation of angular momentum and the conservation of energy.