Marissa+and+Ryan+Rolla+Costarific

=0Conservation of Energy on a Roller Coaster= Date of Publication (Date of Most Recent Edits)


 * Participants**: Ryan and Marissa
 * Purpose**: The purpose of this lab is to examine how mechanical energy (kinetic and potential energy) can be changed by outside forces.
 * Lab Documents**: [[file:Roller Coaster.doc]]

In this lab, Ryan and I had a lack of communication in the beginning. I was working with the rest of the class to collect the measurements of the cart’s movement while traveling on the roller coaster via a real track while Ryan was performing the same process on the logger pro program. We both preformed the same concept only we ultimately decided to use the results we found on logger pro due to the fact that we wanted to be more accurate in our results (less likely to have human error). We mainly made measurements of the height, speed, time, distance, and mass of the roller coaster cart. The speed was measured by marking points along the track on the video provided and this calculated the other measurements depicted in the graph below as well. In addition, the mass of the cart was measured on a scale. By using the computer program, we had an extra step. We were also able to calculate the Kinetic Energy, Potential Energy, and Total Energy and this can be seen on the graph that we plotted below.
 * Brief Description of Experiment**:


 * Data**: [[image:Roller_Coaster_graph_and_video.JPG width="802" height="500"]][[image:Roller_coaster_data.JPG width="802" height="557"]]


 * Sample Calculations:**


 * // Kinetic Energy Calculation // || KE = (1/2) (mass) (velocity)** ² **

The kinetic energy is calculated by multiplying one half by the mass of the cart (in kilograms) by the velocity of the cart squared, which is expressed as meters per second. In addition, the final result for the kinetic energy is expressed in joules. ||
 * // Potential Energy (gravity) Calculation // || PE = mass * 9.8 m/s ² * height

The potential energy is calculated by multiplying the mass of the cart (in kilograms) by 9.8m/s squared  which is the standard of gravity. This was then multiplied by the height in meters of the cart. The end product for potential energy is also expressed in joules. ||
 * // Mechanical Energy Calculation // || ME = KE + PE

The mechanical energy is calculated by adding the kinetic energy result to the potential energy result (both expressed in joules as stated above). ||
 * // Work // || work = force * distance

Work is calculated by multiplying the force by the distance applied or also known as the change within the kinetic energy. ||
 * //Total Velocity = Speed// || Speed = sqrt((Horizontal Speed m/s)*(Horizontal Speed m/s)+(Vertical Speed m/s)*(Vertical Speed m/s))

The Total Velocity is calculated by taking the square root of the squared horizontal speed plus the squared vertical speed. ||

This roller coaster lab was designed to observe how mechanical energy can be manipulated by outside forces. The lab was very useful in seeing changes in energy all throughtout the roller coaster cart’s course along the track. Not only does the track have different designed parts such a loop, dips, and a steep incline, but it has areas where friction is greater or lesser. These are all areas where the energy can change. In addition to this, t he energy of the roller coaster was measured by speed, time, and distance. As a result, were able to find the kinetic energy, potential energy, total energy, and work in the roller coaster. As soon as the kinetic energy, potential energy, and total energy are graphed, it is easy for one to see the differing areas of energy in relation to the roller coaster’s changing track design. Thus, the total energy was a sum of the potential energy and the kinetic energy.
 * Results:**

1. What external forces did you identify as removing energy from the roller coaster system? Into what form of energy do you think the mechanical energy was converted via these forces?  An external force such as gravity would remove energy from the roller coaster’s system. This is because of the simple function of gravity: what comes up must go down. In the case of the roller coaster, it obviously changes in energy when it latches on to the pulley device. If you pretend that the pulley device was not there to get the cart up to the top again, it would not make it up. The cart would ride along the track from the very top of the roller coaster track and when it hits that steep incline, it would keep going for a little longer but due to friction, it would gradually get slower and begin to fall back the way it came. This is due to a loss in energy because of gravity. Also, the cart would lose energy is in the loop because the gravity will naturally pull on the cart. The form of energy that the mechanical energy was converted into via these forces would have to be gravitational potential energy.
 * Lab Questions**

2. What external forces did you identify as adding energy to the roller coaster system? From what form of energy do you think the mechanical energy was converted via these forces?

As stated above, the pulley system changes the energy of the cart. While one may think it is losing energy, it is essentially having energy added because of its mechanical nature (again, as stated above, if the pulley was not there, it would lose energy—so that is a connection but not true for this situation since it has a pulley system).

3. Break the motion of the coaster into 4 pieces as described below. What fraction of the total mechanical energy from the top of the coaster was lost in: · The first big drop? 3/5 · The entrance to the loop? 0 · The exit of the loop? 1/10 · The back turn? 1/10 4. At what point in the motion of the roller coaster was mechanical energy being dissipated (lost from the system) most quickly with respect to distance traveled? How about with respect to time?

- In the beginning of the roller coaster the total energy (mechanical energy) was dissipated the most. This is because in the begining of the roller coaster there is a large drop that covers a large distance. During the drop, the Potential Energy of gravity is lost and never naturally gained again. The distance traveled was far in respect to time. The time of the drop was short in relation to the amount of energy lost. q:^D
 * Conclusion**:

- The purpose of this lab was to experiment the conservation of energy in a roller coaster. The Total Energy was conserved, and this was calculated by adding the Total Kinetic Energy and the Total Potential Energy. We felt like the experiment produced a valid reproducible result. We used Logger Pro application to analyze the video of the roller coaster. Thus there was minimum human error in our experiment. Our experimental results were very similar to our expeted results. As a class we discussed the conservation of energy and concluded that energy would moslty be conserved but since there were outside forces (like friction) working against the conservaton of energy, a significant amount of energy was lost. Analyzing the roller coaster video was not 100% acurate because it only captured the two dimensional view of the roller coaster. The video did not account for the depth of the roller coaster. In relation to our video, the depth would be when the cart travels around the loop and the last turn. A solution to this problem or error would be to shoot the cycle of the roller coaster at a few different angles. This way, we could have compared the data and selected the pieces that were the most accurate in order to create a data set that would depict better results.