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.