Group4_4_ch6

toc Group 15 Members: Ryan Luo Tim Hwang Garrett Almeida

=__**Labs**__=

__**The Law of Conservation of Energy (2/4/12)**__
Garrett Almeida-C,D Ryan Luo-B Tim Hwang-A

__Objective:__ In this lab, our objective is to find the speed of the moving object in all of the experiments except for experiment #4, Galileo's ramp, which we were to find maximum height, and then confirm that the total initial energy and the total final energy are the same using the kinetic and potential energy equations we learned.

__Hypothesis__ Our hypothesis is that the sum of the initial kinetic energy and initial gravitational potential energy should equal the final kinetic energy and final gravitational potential energy. There may be variations in numbers during the six trials, however both parts of the equation should be equal for every trial.

__Methods, Materials, and Videos/Pictures of Each Experiment__ In this experiment, we weighed the cart, and then rolled the cart down from the top of the ramp. We used photogate to measure the time it took for the cart to reach the end of the ramp, and also measured with a meter stick the height where the cart was released and the height where the cart ended up. For the horizontal projectile experiment, the first thing our group did was to measure the height with a meter stick that the 10 g ball would pass the first photogate gate and the height where the ball would pass the second photogate gate. One person from our group would then launch the ball, and the time it takes to pass through the first gate and the second gate were recorded. In this experiment, our group would hold the pendulum 20 cm above the table, release the pendulum, and the photogate gate at the bottom of the pendulum swing records the time it takes the pendulum to reach the bottom of its trajectory. We would then measure the height of the photogate sensor to find the height at the lowest point of the pendulum's trajectory. The first thing we did in this experiment was to weight the ball and measure the height where we would release the ball down the ramp. Next, we released the ball down the shorter ramp and recorded the height where the ball would end up on the other ramp. For the vertical launch experiment, the first thing our group did was measure the height off the table the ball was being launched from. Next, we placed the yellow ball in the launcher and launched the ball straight up. We would put a meter stick next to the launcher as the ball was launched so we could record the height of the ball at its maximum height relative to the table. The time it took for the ball to be launched was recorded by the photogate sensor at the mouth of where the ball was being launched from. media type="file" key="Movie on 2012-02-03 at 11.13.mov" width="300" height="300" In the last experiment, our group measured out the height of where the ball would be released and the height of where the ball would end up and recorded it. Next, we used the photogate sensor to record the amount of time needed for the yellow ball to reach the bottom of the loop from where the ball was released.
 * Station 1: Cart on a Incline**
 * Station 2: Horizontal Projectile**
 * Station 3: Pendulum**
 * Station 4: Galileo's Ramp**
 * Station 5: Vertical Launch**
 * Station 6: Roller Coaster**

__Data__

Class Data:

//Station 1//

//Station 2// (first four groups omitted due to faulty data)

//Station 3//

//Station 4//

//Station 5//

//Station 6// The average column was based on the formula:

An example from station 1 (initial height):

__Excel Spreadsh____eet__

__Sample Calculations__ All calculations were done using the class data table.

//Station 1//
 * Calculations and Example of Percent Difference and Percent Energy Loss**

//Station 2//

//Station 3//

//Station 4//

Station 5 Station 6

Example of Percent Difference (shown in station 1)
 * Percent Difference and Percent Energy Lost Data**

Example of Percent Energy Lost (shown in station 1) Results for other trials:

__Conclusion__

At the start of the lab, our group's hypothesis was that the sum of the initial kinetic energy and initial gravitational potential energy should equal the final kinetic energy and final gravitational potential energy (KEi+GPEi=KEf+GPEf). Throughout the course of this lab, we have learned for this statement to be relatively accurate. Ideally, in an environment with no work (such as friction) then this formula would hold true. Our values calculated support our hypothesis.

In this lab, there many sources of error for the six stations. We know that there is error because ideally the percent energy lost and the percent difference would be zero given that our hypothesis is correct. Firstly, and as mentioned earlier, friction could have added work to the equation and tainted the results. This would have factored work into the equation. Aside from the friction, the measurements that we took could have provided us with the error. In stations one, four, and six, which ass use ramps or tracks, friction is more prominent in slowing down the ball. This should make the percent difference values larger than the others as the friction (work) will affect the accuracy of the result. At some points we had to measure two sections and add them together to get the lengths that we were looking for. If we did a bad job of adding or measuring up against our initial measurement, then this would have affected our final measurements and would have prevented the results from being accurate.

This lab offers many comparisons to everyday life. The pendulum at station 3 can be related to that of a swing. One can therefore calculate the amount of energy at different points. Station 6 is reminiscent of a roller coaster in that it shows there is a minimum speed before the ball falls out of the track. These energy rules have a huge influence for engineers, especially those creating roller coasters.

Law of Conservation of Energy Part 2 (2/10/12)
Garrett Almeida - A Timothy Hwang - B, D Ryan Luo - C

__** Objective: **__
 * Directly determine the spring constant 'k' of several springs by measuring the elongation of the spring for specific applied forces
 * Measure the elastic potential energy of the spring
 * Use a graph to find the work done in stretching the spring
 * Measure the gravitational potential and kinetic energy at 3 position during the red spring oscillation

__**Hypothesis:**__ -The spring constant for each spring will be the slope on a graph of their position vs. time. We know this because of Hooke's Law. -Softer springs will have a smaller k constant than harder springs because they will elongate more. -The total amount of energy will be the same at the min. height, the max. height, and at the equilibrium. We know this because of the Law of Conservation of Energy.

__**Methods and Materials:**__ Obtain all necessary materials. Take the springs and hook them up to the clamps on the ring stand. Next, use a meter stick to measure the distance from the table to each of the springs. Then, begin the five trials for each of the springs by placing different masses on each spring. Start off with just the 200g mass and keep on adding different masses for each trial. For part 2 of the lab, take a piece of cardboard and tape it to a 500g mass. Hook the mass on the red spring. Take a motion sensor and place it at the bottom of the spring to observe the graph for the three different positions of the spring when someone pulls it down. These are positions A, when the spring is elongated, B, when the spring is at equilibrium, and C when the spring is fully compressed.

__**Data:**__ Link to Excel Spreadsheet -


 * Part A Data Table**


 * Part A Graph for the Blue Spring**


 * Part A Graph for the Red Spring**


 * Part A Graph for the Green Spring**


 * Part B Data Table**

__**Data Studio Graph:**__

__**Class Data:**__

__**Calculations:**__ Percent Error (Red Spring): Percent Error= (theoretical - experimental)/theoretical*100 % Error= (25-24.628)/25*100= 1.49% Error

Percent Difference (Red Spring): Percent Difference= (average - independent experimental)/average*100 % Difference= (25.96-24.628)/25.96*100= 5.13% Difference

Law of Conservation of Energy: Total Energy A = Total Energy B = Total Energy C GPE a +EPE a +KE a =GPE b +EPE b +KE b =GPE c +EPE c +KE c

Lowest Point (A): GPE+EPE+KE mgh+(.5)kx 2 +(.5)mv 2 (.5)(9.8)(.217)+(.5)(24.628) 2 +(.5)(.5)(.045) 2 = Percent Difference (A): Percent Difference= (average - independent experimental)/average*100 % Difference= (

Equilibrium Point (B): GPE+EPE+KE mgh+(.5)kx 2 +(.5)mv 2 (.5)(9.8)(.280)+(.5)(24.628) 2 +(.5)(.5)(.430) 2 = Percent Difference (B): Percent Difference= (average - independent experimental)/average*100 % Difference= (

Highest Point (C): GPE+EPE+KE mgh+(.5)kx 2 +(.5)mv 2 (.5)(9.8)(.347)+(.5)(24.628) 2 +(.5)(.5)(.077) 2 = Percent Difference (C): Percent Difference= (average - independent experimental)/average*100 % Difference= (

__**Discussion Questions:**__ 1. Do the data for the displacement of the spring versus the applied force indicate that the data for the spring constant is indeed constant for this range of forces? Yes, the data indicates that the spring constant remains, as the name implies, constant. The linear trend in the graph shows how the value remains constant throughout the experiment.

2. How can you tell which spring is softer by merely looking at the graph? You can tell which spring is softer by looking at the slope of a point on the graph. The smaller the slope, the softer the spring is.

3. Describe the changes in energy of the hanging mass, beginning with it starting at rest, you pulling the mass down and then releasing it, and then the mass cycling through one complete period. In theory, there should not be any changes in total energy due to the Law of Conservation of Energy. Although this is true, the different variables of the experiment do change, albeit changing so the sum of the variables is still equal the original total energy of the system. At rest, there is no kinetic energy, and the energies present are gravitational potential energy and elastic potential energy. As the spring is compressed and released, the gravitational potential energy decreases, while the spring gains kinetic energy equal to the amount of decreasing gravitational potential energy so the total energy of the system remains the same.

__**Conclusion:**__ Our hypothesis that the softer springs would have a smaller k value was proven to be correct. The softest spring, the red one, had the smallest spring constant k. Our hypothesis that the spring constant of a spring is equal to the slope of its position time graph was also proven to be correct, as you can see from our graph. Also, our hypothesis that the total amount of energy would be the same at the min. height, the max. height, and at the equilibrium was correct. This is why we set the total energy for the different heights equal to each other for the analysis. There were a few sources of error for this experiment. If the spring with the masses added was measured while the spring was still moving, we could have gotten an erroneous result. To fix this, we should wait until the spring stopped moving to measure it. Also, we could have measured the spring a few different times, and taken the average. For the second part of the lab, a source of error would be the motion detector and the fact that we did not use the cardboard. If the motion detector was not directly under the weight that we used, then the graph it produced would not have been accurate and since we did not use the cardboard because another group was using it at the time, there was a smaller area for the motion detector to detect. To fix this problem, make sure the motion detector is set directly underneath the weight and use the cardboard. Also, the motion sensor measures position in increments, and might not have actually recorded the actual min. height or max. height.

**Roller Coaster ("The Bombshell") Model Project**
Garrett Almeida- Set up, Data Table, and Sample Calculations Tim Hwang - Concepts section (all seven parts) Ryan Luo- Discussions on Safety and Error

__ Objectives: __ 1. Create a working model for a roller coaster to be used in a Six Flags Theme Park.

2. Develop a comprehensive analysis of information about the different parts of the ride. Information such as the height, speed, acceleration, number of g's, KE, and GPE need to be included. This part of the project can be used to determine the safety of one's ride.

__Materials__: In this project, we used tape to support our structure and paper to create the structure. We also used a compressed wood base to hold our structure. We used scissors to cut the paper to an optimal length and used rulers to measure the length and height (during the data analysis). In addition we used a photogate to measure the time it took for the ball to pass through the gate and a meter measuring tape to better measure the loops and distance for our data collection. A marble was used to test the course and thus simulated an actual roller coaster.

__Concepts__: For this project, we created a roller coaster, The Bombshell, made of paper to study how the Law of Conservation of Energy and many other things work. The Law of Conservation of Energy states that energy cannot be created or destroyed but it can change its form. The equation that we use to solve for energy conservation is KE + GPE + EPE + Win - Wout = KE + GPE + EPE. In general, the equation is just Work + Initial Energy = Final Energy. At the start of the initial hill, we have GPE. As it goes down and towards the top of the loop, GPE turns into KE and GPE. The total energy throughout the roller coaster should remain constant but because there is work due to friction, the final energy comes out to be less than the initial energy. As the marble moves down the roller coaster, it has an acceleration. This acceleration was needed to make it over many of the hills and loops. The initial height of the roller coaster is the highest, so the ball has enough velocity to make it through the entire coaster. The acceleration was solved by using one of the many techniques from kinematics, the law of conservation of energy, or Newton's second law. Newton's Laws of motion were taken into consideration while building this coaster or else it would not have been successful. The first law states that an object will stay in motion they are already in unless an unbalanced for causes change. Our coaster follows this law because initially the ball is at rest, but is acted upon gravity to begin motion at the start of the coaster. The second law of motion states that the net force is equal to the mass multiplied by the acceleration. This is also true for our roller coaster. The third law of motion states that actions have equal and opposite reaction which is show at the end of the coaster when the ball exerts a force on the wall, which would exert an equal and opposite force on the ball. Power is the rate at which work is being done. In order for the roller coaster to reach the top of the initial drop, we need to do work. This work is equal to the GPE at the top of the initial drop. To calculate power, one also needs the time over which the work is done. To ensure the safety of the people riding the roller coaster, a spring is needed at the end of the roller coaster. In order to calculate this Hooke's Law is needed. It states that the force of the spring is equal to the negative spring constant (k) times displacement of the compressed spring (x). Circular motion is when an object, the marble, rotates along a circular path. At the start of the roller coaster, the marble moves down the initial hill with kinetic energy and accelerates into the vertical loop. Since the law of conservation states that energy only changes its form, the kinetic energy is changed into gravitational potential energy and then changes throughout the coaster. If the diameters were larger for the vertical and horizontal loops, the ball might not have made it around. It is important to have enough velocity to make it around the loops.

Citations: []

__Roller Coaster Diagrams and Photos:__ Diagrams and Picture of Side View:

Diagrams //The side diagrams show that the ball will go down an initial drop first before passing through a vertical loop, then a horizontal loop, two hills, and a back curve, before it stops. (in that order)//

Photo-

Diagrams and Picture of Top View:

Diagrams- //The diagrams show an aerial view of our roller coaster. The marble will start at the initial drop first before passing through a vertical loop, then a horizontal loop, two hills, and a back curve, before it stops. (in that order)//

Photo-



Video of Roller Coaster Simulation: media type="file" key="Roller Coaster Project (Garrett, Ryan, Timothy).mov" width="300" height="300"

__Data:__

Table-

Link to Excel Spread Sheet-

Sample Calculations-

Average Time (of Three Trials On the way down the initial drop) Actual Velocity (On the way down the initial drop)
 * T1, T2, T3 are all trial times**
 * v = velocity**
 * d = distance (diameter of ball)**
 * t = time (average time in gate)**

Acceleration on straight paths:(On the way down the initial drop)
 * a= acceleration**
 * d= distance**
 * vf= final velocity**
 * vi= initial velocity**

Acceleration for Marble on Vertical Loop:
 * a= Accerlation**
 * v= velocity**
 * r= radius**

Kinetic Energy (On the way down the initial drop)
 * m = mass of marble**
 * v = velocity**

Gravitational Potential Energy (Top of Initial Drop)
 * m = mass of marble**
 * g = acceleration due to gravity**
 * h = height**



Total Energy **(**On the way down the initial drop) Theoretical Speed (Top to mid initial drop)
 * KE= Kinetic Energy (already calculated)**
 * GPE= Gravitational Potential Energy (already calculated)**
 * m = mass of marble**
 * g = acceleration due to gravity**
 * h = height**
 * v = velocity**

Minimum Speed at the Top of the Loop Sketch of vertical Loop: Free Body Diagram of Marble on Top of Vertical Loop: Power If we plan on competing against the tallest roller coaster at 140 meters high, then we will build ours at a massive 150 meters high! We can assume that the coaster is around 750 kg and keep the same time of thirty seconds. The power calculation for this follows: Motor Choices - 40000w Isuzo Motor for $15,701.00 or 40000w General Motors for $10,000.00
 * Both Normal and weight forces point towards the center of the circle**
 * N=0**
 * N= Normal Force**
 * W= Weight**
 * m= mass of ball**
 * r= radius of loop**
 * v= velocity**
 * GPE= Gravitational Potential Energy**
 * t= time**

Energy Dissipated

Spring System Because the acceleration experience is below 4g's, humans can experience it without any injuries or difficulties. This makes the spring safe for us to stop on. On the real roller coaster that will be made to a larger size, these values may change.
 * KE value comes from the chart (bottom of the track velocity)**
 * d=x**

Our roller coaster is technically safe at all locations that were measured using the photogate. According to our photogate times, our vertical loop is actually safe to travel on, something that other groups cannot back with their data. Being that humans can only with stand around four g's, we needed to make a safe roller coaster that will prevent potential customers from suffering injuries and other problems. In order for the roller coaster to be considered safe, all parts must have less than 4g's experiences and judging by the data table I have created, the roller coaster is safe. No part of the roller coaster seems to exceed 3.5g's and this close proximity to 4g's means that it will likely impress riders with the thrill. This can influence other customers to ride on this coaster. Because this coaster does not have an acceleration above 39.2 meters per second squared or 4g's, it is safe for a human to travel on. One safety concern, however that needs to be pointed out, is that the loop is not always perfectly stable and can move or adjust its position when tape comes loose, however with stronger building materials in real life, this should not be a problem. Another is that the structure is not entirely stable, however using stronger materials should eliminate this problem. Overall, this seems that a great, safe roller coaster, when compared to the other projects my classmates have prepared.
 * Safety Discussion**

During the creation of the roller coaster, it was apparent that there was plenty of room for error. Error can be found in the difference between total energy and final energy. The energy dissipated was a large value! These values do not equal one another mainly due to the force of friction and the lack of stability of the structure. Also, it is possible that the photogate measured a different section of the ball as opposed to the diameter and this would make the time recorded less than it actually is. The marble had a long path to travel on so it is possible that it was traveling diagonally for part of the project which could have affected the energy dissipation. Another thing to remember is that air resistance will affect the actual roller coaster and the marble. Because these forces were not accounted for, this could have affected the energy dissipation. One way to minimize this error would be to improve on structural support by adding more paper and tape to the structure. Also, giving the ball less room on the paths would eliminate some of that diagonal movement that was mentioned earlier.
 * Errors and Uncertainties**


 * All in all, this is a great model for a roller coaster when compared to those of my peers. With safety, thrill, and the possibility of being the largest roller coaster in the world, it is safety to say that this roller coaster, if created, would be a hit.**

Elastic and Inelastic Collisions Lab
Timothy Hwang - B Ryan Luo - A Garrett Almeida - C, D

Objective: What is the relationship between the initial momentum and final momentum of a system? Which collisions are elastic collisions and which ones are inelastic collisions?

Hypothesis: Because of the Law of Conservation of Momentum, we know that the initial momentum should equal the final momentum of a system. An elastic collision is a collision where kinetic energy is conserved, and an inelastic collision is a collision where kinetic energy is not conserved. Therefore, if there is a big difference between the total initial kinetic energy and the final kinetic energy then the collision would be an inelastic collision, but if there is a small difference between the total initial kinetic energy and the final kinetic energy, then the collision would be an elastic collision.

Methods and Materials: In the beginning of lab we collected the following materials: 2 carts (one normal cart and another with a spring), different masses, a dynamics track, 2 motion detectors, and 2 USB links. So to start off we connected the two motion detectors to either side of the dynamics track. We then recorded data for an explosion, one cart in motion and the other at rest (sticking), one in motion and the other at rest (bouncing), both in motion (sticking), and both in motion (bouncing). We did each scenario 3 times while changing the weight of one cart for the second and third trials of each run.

Data:

Data Studio Graphs-
 * All graphs are velocity vs. time graphs





Table- Excel Spreadsheet:

Pictures: This is a picture of one of our trials for when one cart is moving and the other is at rest. Once contact is made they stick together. This is a picture of one of our trials for when both carts are in motion and they bounce when they hit each other.

Sample Calculations


 * Total Momentum**
 * Total Kinetic Energy**
 * Percent Difference (Final Momentum)**

Analysis:

1. Is momentum conserved in this experiment? Explain, using actual data from the lab. Momentum is not conserved in this experiment. This is mainly because our collisions were predominantly inelastic meaning that kinetic energy is not conserved. We know this because the initial and final kinetic energies were not equal. Also, the initial and final momentum was not the same. Instead we got percent differences besides 0%, as it should if they were inelastic. In the example given above, in the percent difference is 1.2%, which is close but not exactly zero.

2. When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is. The cart with a larger mass has the lower velocity and the cart smaller mass has the higher velocity. This is because of the indirect relationship between the mass and velocity in the momentum equation. The equation p=mv (momentum equals mass times velocity) is the momentum equation. Given that p is constant, this statement would hold true.

3. When carts of unequal masses push away from each other, which cart has more momentum? The carts have the same momentum. Despite having unequal masses, the momentum remains the same. This is compensated because the velocities of the two masses are different. The smaller mass has the higher velocity and the greater mass has the lower velocity resulting in the same momentum. Essentially, the momentum remains the same.

4. Is the momentum dependent on which cart has its plunger cocked? Explain why or why. The momentum is not dependent on which cart has its plunger crooked. This is because the plunger should have equal effects on both carts during the collision. The fact that one cart has the plunger and the other does not is not important as only mass and velocity are factored into momentum.

Conclusion: Our hypothesis was correct! The total initial and the total final momentum were equal to one another, just as we proposed using the Law of Conservation of Momentum. The elastic collisions would have small percent differences, although they should theoretically be zero, while the inelastic collisions would have larger percent differences. This was also proved to be right. We also correctly hypothesized that the explosions, sticking, and bouncing apart collisions would be inelastic. During the course of our experiment, we recorded relatively small percent differences. The explosion percent differences, however were relatively large. This can be explained because the carts started at rest when v=0, however both carts ended up moving at the end. Both carts had a p value. There were many sources of error for this experiment. One source of error could have been the track. The track could not have been level and this could have affected the data we got.The track was placed between two tables and this could have made the ramp uneven. We could have used a level or placed the track on one of the tables to make sure that the data was more accurate and that the track was level. Also, when we did the initial push on trials, it is possible that the motion sensors recorded something, such as our hand, that was not supposed to be used in our data. We could prevent this by being more careful around the sensors by removing our hand, or what ever was used to make the initial push, from the recording motion sensor quickly. The lab relates to many situations is real life. The prime real-life example could be car crashed. In order to make cars safe for drivers, companies use these physics concepts on collisions. This was mentioned in class when we spoke about bumpers and crush zones in the car where the metal would crumple. The bumper collisions are simulated using the bouncing apart collisions and the crushed bumper is related to the sticking together collisions.

__**Ballistic Pendulum Lab**__
Ryan Luo-A,B Tim Hwang-C Garrett Almeida-B,D

__**Objective:**__ What is the initial velocity of a ball fired into a ballistic pendulum?

__**Hypothesis:**__ The three initial velocity-measurements found through kinematics, the photogate, and LCE should be similar, if not the same. The LCE calculation should be the least reliable as energy is lost, while the photogate technique should produce the most accurate results.

__**Method and Materials:**__ During the course of this lab, we measured the initial velocity using three different techniques. These techniques were the photogate, kinematics, and the laws of conservation of energy and momentum. The first technique that we went about was the photogate. In order to do this technique we had to set up the photogate and attach the USB to the port on our computers. Then, we turned on the photogate, launched the ball, and recorded the time that it took the ball to pass through the device. We recorded these values on our data table. In addition, we recorded the diameter of the ball and plugged these values into the v= d/t equation. In the case of the kinematics technique, we clamped the launcher to the table, we launched the ball onto a sheet of carbon paper taped to the floor, and we recorded the vertical height as well as the horizontal distance to the dots marked by the carbon paper. We recorded this information and used projectile equations to get the initial velocity. Finally, we launched the ball into a pendulum and used the laws of conservation of energy and momentum to find the initial velocity. We shot the ball through the launcher and into a pendulum. We then recorded the angle that the pendulum moved. We massed the ball and the pendulum to find the mass of the system. We used this information to solve for our initial velocity. All three technique allowed us to calculate a velocity which was relatively similar.

__**Videos and Photos:**__

Photo of pendulum-

Video of ballistic pendulum- media type="file" key="Movie on 2012-03-16 at 11.42.mov" width="300" height="300"

Summary of ballistic pendulum-
 * We launched the ball and it moved the pendulum backward to create an angle. We recorded the angle in the table below and used it to find our height in our LCE equation.**

Photo of kinematics-

Video of ballistic pendulum- media type="file" key="Movie on 2012-03-16 at 11.48

Summary of the ballistic pendulum-
 * We shot the ball from the launcher onto the carbon paper one can see in the photo. We recorded the distances so that we could solve using kinematics.**

Picture of photogate- Summary of photogate-
 * We attached this device to the launcher just ahead of the release. This recorded the time it took the ball to pass through the photogate. The times are recorded in the table below.**

__**Data:**__ __**Excel Spreadsheet:**__

__**Sample Calculations:**__ Photogate:

Kinematics: y: d=V i t + (1/2)at 2 -.839= (1/2)(-9.8)t 2 t=.414
 * || x || y ||
 * V i || V i *cos0 = V i  || V i *sin0 = 0 ||
 * a || 0 || -9.8 ||
 * t || t = .414 || t = .414 ||
 * d || 1.331 || -.839 ||

x: d=V i t + (1/2)at 2 1.331=V i (.414) V i =3.21 m/s

Pendulum:

Laws of Conservation of Energy-

Laws of Conservation of Momentum-

Percent Difference: (photogate first trial)

__**Analysis:**__ > > >> **79% is nowhere near 1.8% and it seems as though there is a huge discrepancy. Theoretically, these ratios should be the same, however these numbers are very, very different.** >> __**Conclusion:**__ In this lab, our hypothesis was correct in determining that the values we got through kinematics, the photogate, and the laws of conservation of energy and momentum were similar. When using kinematics to solve for average velocity, we got 3.26 m/s. As for the pendulum trials, our average velocity was 3.37. The photogate provided the highest average velocity with 3.44 m/s. We witnessed the least percent difference in the pendulum and the most in the photogate. This does not coincide with what we hypothesized in that the LCE trials would be the least reliable and that the photogate trials would be the most accurate. Instead, it proved the opposite; the LCE trials had a smaller percent difference than the photogate trials. Being that the percent difference was not zero for all trials, it was apparent that there was some error in the lab. One fault is that the launchers are not always consistent in shooting with the same power every time and marking the same horizontal distance. Instead, we had many different distances and times in the photogate. We can use a more accurate launcher that launches the balls with the same power each time to eliminate this error. Also, the photogate was not placed exactly near the opening of the launcher where the ball is released. We could have placed it closer to the mouth of the launcher to eliminate this source of error. In addition, the photogate may not have measured the time it took for the diameter of the ball to pass, but another (smaller) part of the ball. This would minimize the time and yield a greater error. To do this we could have set the photogate lower or higher to better attain a measure of its diameter. Also, it is possible that our kinematics measurements were not accurate. A second opinion from a lab partner could have helped. We then could have averaged the two values to yield a smaller error. The lab showed us an example of an inelastic collision, in which kinetic energy is not conserved. These inelastic collisions can be found in our modern day world. One example that we spoke about in class was that of car crashes. As for projectiles, throwing a ball off a cliff serves as a prime example.
 * 1) In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?
 * An elastic collision would conserve energy and an inelastic collision would not conserve energy. An inelastic collision, such as a car crashing into a tree, would cause kinetic energy to be lost completely therefore kinetic energy would not be conserved
 * 1) Consider the collision between the ball and pendulum.
 * Is it elastic or inelastic?
 * It is inelastic.
 * Is energy conserved?
 * Energy is not conserved.
 * Is momentum conserved?
 * Energy may not be conserved but momentum is conserved because of the consideration of mass. Velocity lost in one cart is gained by the other.
 * 1) Consider the swing and rise of the pendulum and embedded ball.
 * Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height?
 * Energy is not conserved because it is inelastic. The ball sticks to the catcher so velocity is lost and therefore energy KE is lost.
 * How about momentum?
 * Momentum is conserved.
 * 1) It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum.
 * Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum.
 * Percent loss
 * According to your calculations, would it be valid to assume that energy was conserved in that collision? **No, the collision is inellastic. We know this because there is .018% energy loss after the collision. Our results, however are very close to zero.**
 * Calculate the ratio M/(m+M). Compare this ratio with the ratio calculated in part (b). Theoretically, these two ratios should be the same. State the level of agreement for these two quantities for your data.
 * 1) Go to [] Select “Ballistic Pendulum” from the column on the left. What is the effect of increasing the mass of the ball? What is the effect of increasing the pendulum mass? Try it. (NOTE: You have to read “Student Notes” first before you can run the simulation.)
 * Increasing the mass of the ball increases final height of the pendulum as well as theta between the original and final positions of the pendulum. Increasing the mass of the pendulum, however, decreases the final height of the pendulum as well as theta between the original and final positions of the pendulum. The larger the mass of the ball the higher the pendulum goes, but the larger the mass of the pendulum the lower the pendulum goes.
 * 1) Is there a significant difference between the three calculated values of velocity? What factors would increase the difference between these results? How would you build a ballistic pendulum so that momentum method gave better results?
 * There is not a significance between the three calculated velocities as we can observe by looking at the percent differences. The largest percent difference was 2.91% which is not very high. Of these techniques, the photogate would be the most accurate because it precisely measures the velocity right after launching the projectile. Of the experiments, we found the kinematics one to be the most different from the actual velocity, which is strange considering that there should not be a tremendous loss in energy that we observed from our calculations. We can conclude that inaccurate measurements may have been the factor reasonable for slightly skewing our results. As we know, the spring for these launchers are not the most consistent, which could have also led to minute difference between these velocities. Being that air resistance does effect the results and it wasn't taken into account while doing the calculations, it could have been another factor that increased the difference between results. If we were to build a ballistic pendulum we would have tried to use a projectile with minimum air resistance so we could at least rule one factor out that could be effecting our results in any way.