11/9: Angular Acceleration

Title: Angular Acceleration
Purpose: The purpose of this experiment is to see what factors affect angular acceleration (Part 1), and determine the moments of inertia theoretically compared to experimentally (Part 2).
Apparatus:

The rotational sensor has two disks stacked on top of each other with another pulley to which a string is wrapped around and hung over with a hanging mass. Air is directed so that the disks can be (mostly) frictionless.
Theory:
The idea of this lab is to measure the angular acceleration of the hanging mass with varying hanging masses, size of the torque pulley, and the different disks. The ratio of the change in angular acceleration should be proportional to how much the variables differs from each other. For part 2, it we use the equation derived from the lab instructions and compare it to the theoretical inertia which is (1/2)MR^2.
Data:

    

Graphs/Calculations: 

Sample graph of how to obtain angular acceleration

Ratio of experiments 1, 2, and 3

Ratio of experiments 1 and 4

Ratio of experiments 4, 5, and 6

Ratio of experiments 2 and 4

Part 2 Calculations

Analysis: 

From the different ratios between all the experiments, we can see that a correlation appears. From experiments 1, 2, and 3, it appears that with twice the amount of hanging mass, the angular acceleration also increases by two. With three times the amount of hanging mass, the angular acceleration increases by three. From experiments 1 and 4, it can be seen that when the radius of the torque pulley increases, the speed also increases by almost the same amount. With experiments 4, 5, and 6, it can be seen that with the different masses of the steel and aluminum disks, the angular acceleration also varies by about the same amount. And from experiments 2 and 4, it can be seen that by changing the radius of the pulley as well as changing the amount of mass hanging produces about the same ratio. From the calculations of part 2, it can be seen that the theoretical inertias and experimental inertias are not that far away from each other.

Conclusion:
Sources of uncertainty and error may be from measuring the angular acceleration as we rotated the disks, as it is not completely frictionless. Our track in particular seemed to be especially rough, as the graphs proved to be a bit too jagged. Other sources of uncertainty may be from calculations and rounding off significant figures. 

10/12/16: Magnetic Potential Energy

Title: Magnetic Potential Energy
Purpose: The purpose of this experiment is to hypothesize an equation for magnetic potential energy and use it to verify that the conservation of energy applies to the system.

Apparatus:
The apparatus would be to place a glider on an air track to serve as a cart on a frictionless surface.

Theory:
When the glider is at its closest to the magnet at the end of the track, the KE is zero and all the energy is magnetic potential energy. The cart then rebounds and the magnetic potential energy is converted back to KE. In order to find the magnetic PE, we need to raise the air track so that the cart reaches an equilibrium point where the magnetic repulsion force between the magnets is equal to the gravitational force component on the cart parallel to the track. After that, we can integrate that force equation as a hypothesis of the magnetic PE equation. From such equation, we can verify that energy is conserved in this system.

Data:

Graphs/Calculations:

Analysis:
From the graph, it can be seen that the model that we came up with held true. The equation that we derived for the magnetic PE works, as the KE and MPE graphs do satisfy each other.

Conclusion:
The model works, and it seem that energy is mostly conserved. There is a slight bump, which can be due to the uncertainty in the force equation we arrived at in the force vs distance graph as well as a slight chance of still some friction on the air track.

10/13/16: Ballistic Pendulum

Title: Ballistic Pendulum
Purpose:
The purpose of this lab is to determine the firing speed of a ball from a spring-loaded gun.

Apparatus:

Theory: 

When the gun shoots the ball into the block, it should be an inelastic collision. We can write a conservation of momentum equation for the speed of the system immediately after the collision. After the collision, the system rises a certain height, going from KE to GPE. At the max height, KE will be zero. A conservation of energy equation can be written to relate the max height of the system to the initial speed of the block. 

Data: 

Calculation: 

10/26/16: Collisions in Two Dimensions

Title: Collisions in Two Dimensions
Purpose:
The purpose of this lab is to look at a two-dimensional collision and determine if momentum and energy are conserved.

Apparatus:

We will set a clear ball on the leveled glass table. We will aim and roll one marble and one steel ball at the stationary ball. We will capture this will a phone in slow motion and then use video analysis to capture the position and velocities of the ball.

Theory:
The idea behind this lab is that momentum should be conserved from before and after the collision. However, since it is difficult to whether momentum is conserved in two dimensions, with the x and y directions, the center of mass is used as a system between the two balls.

Data:
Position of Collision between Metal and Clear Ball

Position of Collision between Marble and Clear Ball

Velocity of Collision between Metal and Clear Ball

Velocity of Collision between Marble and Clear Ball

Graphs/Calculations:
Xcm and Ycm vs Time between Clear and Metal Ball

Xcm and Ycm vs Time between Marble and Clear Ball

Vcm vs Time between Metal and Clear Ball

Vcm vs Time between Marble and Clear Ball

Energy vs Time between Metal and Clear Ball

Energy vs Time between Marble and Clear Ball

Momentum vs Time between Metal and Clear Ball

Momentum vs Time between Marble and Clear Ball

Analysis:
From the graphs, it can be seen that by looking at the x and y components, the position and velocity seem to be all over the place. However, when looking at the center of mass, the positions are almost linear, and the velocities do correspond with each other. The energies and momentum look almost conserved, and it is more obvious between the marble and clear ball than the metal and clear ball.

Conclusion:
Momentum and energy do not look to be perfectly conserved by the graphs, and reasonings behind this may be that the surface that we conducted this experiment on is not perfectly frictionless, meaning that some kinetic energy was changed to friction heat. Another source of error is that when drawing the dots in video capture, the dots were not perfect dots.

10/5/16: Conservation of Energy System

Title: Conservation of Energy System
Purpose:
The purpose of this experiment is to show the conservation of energy with a mass-spring system.
Apparatus:

With the motion sensor on the ground and a spring hanging on top of it, we will place a mass of 250g on the spring and then measure the position and velocity graphs.

Theory:

Data:

This is the prediction graph we came up with for the position, velocity, KE, GPE and EPE versus time graph. 

Graph: 

Position vs Time and Velocity vs Time

KE vs Time, GPE vs Time, and EPE vs Time

KE vs Position, KE vs Velocity, and GPE vs Position

GPE vs Velocity, EPE vs Velocity, EPE vs Position

Esum vs Position and Esum vs Time

Analysis: 

These graphs make sense because they match how the system was delivered. With kinetic energy vs time, the first pull of the spring is the greatest, so the first wave is greater than others. With GPE, the spring bounces back to approximately the same position, but gradually decreasing with time. For EPE, the same reasoning applies as to the GPE, as the spring is gradually decreasing with time. With the position graphs, it can be seen that it all gradually decreases, which makes sense as the spring is slowly stopping. The oscillating shape is also correct, as the spring has an oscillating movement. 

Conclusion: 

The graphs match pretty well with my predictions, and it shows that energy is mostly conserved, as our systems are not perfect, as well as the fact that our lab conditions are not perfect either. However, the results obtained do enough justification that energy is conserved given if the circumstances are just right.