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. 

10/5/16: Work-Kinetic Energy Theorem

Title: Work-Kinetic Energy Theorem
Purpose:  The purpose of this experiment is to prove that the work-kinetic energy theorem is true. The work done is equal to the change in kinetic energy in a system.

Apparatus:

Theory:
The change in kinetic energy is equal to the amount of work we do as we move a mass from point v0 to vf.

Data:
N/A

Graphs:

Analysis:
The area under the force vs position graph is very close to the kinetic energy in  the same position in the kinetic energy vs position graph. This proves that the work-kinetic energy theorem is effective.

Conclusion:
The work done on the cart by the spring is very close, almost the same as the change in kinetic energy of the cart. Where uncertainty might have occurred may be that the track is not 100% frictionless, resulting in some of the energy being lost in friction.

9/28/16: Centripetal Force with a Motor

Title: Centripetal Force with a Motor
Purpose: The purpose of this lab is to find the relationship between the angle and angular speed.
Apparatus:

There is an electric motor mounted on a surveying tripod. A long shaft is going vertically up from the shaft. A horizontal rod is mounted on the vertical rod. A long string is tied to the end of the horizontal rod. A rubber stopper is tied to the end of the string. A ring stand is nearby with a horizontal piece of paper sticking out. 

Theory:

As seen from the picture, R, H, L, and h all can be measured. ϴ can be determined with these measures, as well as ω. 

We can determine values for ω hypothetically by collecting various values for h, and then the actual value of ω can be determined by measuring the time it takes to complete 10 rotations at various voltages. 

Data:

Graphs/Calculations:

Analysis:
From the percent error, we can see that all calculations were within 10%. Most were even within 5%, and only one was about 8% off. The reason for this is that the known values of H, h, R, and L all each have a certain amount of uncertainty to themselves, as well as the spin of the motor not being exactly constant at all times.

Conclusion:
From this experiment, we can see that the greater theta, the greater omega is. The faster the motor spins, the greater the angle is. The experimental results we obtained were all relatively accurate to the predicted numbers. 

9/26/16: Angular Acceleration

Title: Angular Acceleration
Purpose: The purpose of this experiment is to find a relationship between centripetal acceleration and angular speed.
Apparatus:

Theory: 

The theory of this experiment is that Force=mass*Radius*angular speed^2. If two variables are held constant and one is changing, the slope of the Force versus the changing variable should be a straight line, with the two variables multiplied being the slope. However, since omega slightly varied with each trial, we instead held one variable constant and had two variables changing. 

Data: 

Graphs: 

Force versus mass*omega^2

Force versus radius*omega^2

Force versus omega^2

Analysis: 

The slopes that the graphs are all relatively close to being linear, showing that such a relationship does exist. The slopes graphed are also pretty close to the experimental numbers, showing that the calculation and the experiment correspond with one another. 

Conclusion: 

The results turned out pretty good, proving that such relationship does exist, and is linear. The results obtained were all within 10%, and any sources of uncertainty might have came from calculations as well as the apparatus itself, which did not spin with constant omega.