Group5_4_ch6

=__ **Law of Conservation of Energy Lab** __=

toc __Part A:__ Mike Poleway __Part B:__ Gabby Leibowitz __Part C:__ Maxx Grunfeld __Part D:__ Matt Ordover


 * __Objective:__** What is the relationship between changes in kinetic energy and changes in gravitational potential energy?
 * 1) If the cart starts at the top of the ramp, what is its speed at the position of the photogate?
 * 2) What is the speed of the ball when it leaves the launcher at short range?
 * 3) What is the speed of the pendulum at the bottom of its path, if released from h = 20 cm?
 * 4) What is the highest point the ball will reach when released from the top of the shorter incline?
 * 5) What is the speed of the ball when vertically launched at short range?
 * 6) What is the speed of the ball at the top of the loop?

This lab deals with the law of conservation of energy, which states that energy cannot be created nor destroyed but can change forms. As a result, it is expected that the initial energy of the object should equal the final energy of the object.
 * __Hypothesis:__**


 * __Methods and Materials:__**

__Station 1:__ Both the mass of the cart, by use of a scale, and the diameter of the top black area along the picket fence, by use of a meter stick, was measured. After measuring the initial height of the cart on the ramp with the meter stick, the cart and the plastic picket fence was released at the top of the ramp. The picket fence passed through the photogate providing a recordable time that could be used to calculate its velocity.



__Station 2:__ Both the mass of the ball, by use of a scale, and the height of the launcher, by use of a meter stick, was measured. Then, the meter stick was used to measure the diameter of the ball. The ball was placed into the horizontal launcher, which was launched at short range. The ball was shot and traveled through the photogates, providing a recordable time between the two gates. In order to then calculate the velocity of the ball, the distance between the photogates was measured by means of a meter stick.



__Station 3:__ Both the mass of the wooden cylinder, by use of a scale, and its diameter, by use of a meter stick, was measured. The cylinder was attached to a string that allowed it to swing through the photogate. The initial height of the cylinder above the photogate was measured by means of a meter stick. The wooden cylinder was released and swung through the photogate. By using the diameter of the cylinder and the time recorded by the photogate, velocity was able to be calculated.



__Station 4:__ Both the mass of the ball, by use of a scale, and the initial height of the curved ramp, by use of a meter stick, was measured. The metal ball was released down the first end of the ramp. The height of the point at which the ball reached on the other side of the ramp was then measured by means of the meter stick. This number was used as the final height.



__Station 5:__ Both the mass of the ball, by use of a scale, and its diameter, by use of a meter stick, was measured. The ball was placed into the vertical launcher and launched at short range. The time it took to pass through the gate was recorded by means of a photogate attached to the launcher. The initial height of the ball was recorded, in addition to its maximum height, which was used as the final height.



__Station 6:__ Both the mass of the ball, by use of a scale, and its diameter, by use of a metal stick, was measured. The initial height of the "roller coaster" was also measured by means of the meter stick. In addition, the final height was measured, which was located at the photogate. The ball was released at the top of the ramp and traveled through the roller coaster path. The photogate recorded the time the ball was in the gate, at the top of the loop.



__**Data and Observations:**__

__Our Group's Data:__



__Class Data:__


 * Station One:**
 * Station Two:**
 * Groups 1-4 were omitted as a result of faulty data

__Analysis:__
 * Station Three:**
 * Station Four:**
 * Station Five:**
 * Station Six:**


 * Sample Calculation for Average:** Average of Class Data- Station 6- Initial Height


 * Sample Calculation for Velocity:** Our Group's Data- Station 1- Final Velocity


 * Analysis of Station One**


 * Analysis of Station Two**




 * Analysis of Station Three**




 * Analysis of Station Four**




 * Analysis of Station Five**




 * Analysis of Station Six**

Our group's analysis led us to the conclusion that initial energy is equal to final energy, as predicted above. For this experiment, the accuracy of our results was tested using percent difference rather than percent error, as a result of the lack of a theoretical value that would be compared to our experimental values. In this case, since we were aiming for similar results between the initial and final energy, we were comparing two experimental results, making the percent difference equation perfect for this lab.

We hypothesized that the initial energy should equal the final energy given that no work was done. We did not take friction into account which explains why the final energy was often less than the initial energy. Our hypothesis was correct, but our results are a little off from the hypothesis because we did not take friction into account as work out. There are a few possible sources of error that account for some of the high percent differences that we got. One source of error for all the stations is possible measurement errors. Even the slightest mishap in measuring something could change the amount of initial or final energy. For stations 1,4, and 6 friction was a huge source of error. In our results and hypothesis we did not take work into account. However, at these stations friction would be considered work out. We did not take this into account, which would make the final energy significantly lower than the initial energy. Another possible source of error on station 2 was that only a portion of the projectile passed through the photogate. This would cause the diameter to be smaller, which would make the velocity higher. To help reduce error and improve our results, we could measure more accurately. In addition, we could take steps to try and reduce friction. Finally, we could film the projectile lab and make sure the entire projectile passed through the photogate, so we know that the velocity is correct. These situations are very applicable to everyday life. Roller coaster designers must take this into account at all times so they can figure out how big a drop must be to get up a certain size hill or how fast a cart must go in order to stay on the track. The law of conservation of energy is extremely important and virtually all types of engineers use it at some point.
 * __Conclusion:__**

=LCE for mass on a spring=

Part A: Matt Ordover Part B: Matt Ordover Part C: Maxx Grunfeld Part D: Mike Poleway (Gabby absent)


 * Objectives**
 * 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 spring oscillation


 * Hypothesis**
 * The spring constant for each spring will be equal to the slope on a force vs. displacement graph. This is true because of Hooke's Law.
 * The more flexible springs will have a smaller k value while the less flexible springs will have a larger k value.
 * The total amount of energy will be the same at min height, max height, and any point in between because of the law of conservation of energy.


 * Part A:**

media type="file" key="Movie on 2012-02-10 at 11.22
 * Procedure**


 * Data**
 * Red Spring**


 * White Spring**


 * Blue Spring**




 * Sample Calculations**

Sample Calculation for Force (Red Spring)

Percent Error for Spring Force Constants

Red:

White:

Blue:

We were able to use percent error for this part of the lab because we had both a theoretical and experimental value. Our theoretical was the value of the constant given on the spring, and we compared that value to the experimental results we obtained.


 * Percent Difference for Spring Force Constants**

Red:

White:

Blue: We also used percent difference to compare the results of our spring force constant with the results of the class.


 * Part B:**

A 500 gram mass was hung from the red spring. Then, we set up a motion detector directly underneath the mass to make a position vs. time graph as the mass bounces up and down. Next, we pulled the mass down and let it go as the data studio recorded its position and time. We used this data to calculate the total energy at min height, max height, and at equilibrium.
 * Procedure**


 * Data**


 * Sample Calculations**

Sample Energy Calculations: (in Joules)

Percent Difference for Equilibrium:

Percent Difference for Minimum Displacement:

Percent Difference for Maximum Displacement:
 * 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 for the displacement of the spring versus the applied force indicate that the data for the spring is constant. This is because our graph came out to be linear, implying that there is a constant value for the relationship between the displacement of the spring and the applied force. The constant is equivalent to the slope of the line in this situation.
 * 2) **How can you tell which spring is softer by merely looking at the graph?** By looking at the graph, the line with least steep slope is the softest spring. Our graph measured the displacement of the spring on the x-axis and the applied force on the y-axis. The more force that was applied, the more it was displaced (the more softer it was).
 * 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.** For part B of the experiment, the total energy should remain the same at all times after pulling the mass down and releasing it. This is due to the Law of Conservation of Energy. In the equilibrium stage, the mass has KE because it is in motion, GPE because it is above the 0 position, and EPE because the spring is compressed. At its minimum displacement, it has EPE because the spring is stretched and GPE because it is above the 0 position, and at maximum displacement, it only has GPE.



Conclusion: We hypothesized that the slope of our graphs would give us our constant 'k' value of each spring due to Hooke's law. In addition, we believed that the more flexible a spring, the less of a 'k' value it would have. Our hypothesis was correct, as the slope of our graphs were the 'k' constant. Our experimental values were almost identical to the given theoretical values when looking at the slope, proving this. According to Hooke's Law. K=F/X, which is how you find the slope in a force v distance graph. The most flexible spring was the red one, with the white spring being the least flexible. You can see this by looking at the changes in distance the springs go through. Like we hypothesized, the red spring ends up having the smallest constant at 24.37, while the white has the highest at 39.74. Furthermore, in part B, we believed that the total amount of energy would be the same at minimum height, max height, and any point in between. By finding the energy at several different points on the data studio graph, we learned that all of them were very similar. All the energies were within .05 J of each other, proving our hypothesis to be right. This is because of the law of conservation of energy, which states that energy cannot be created or destroyed, but transformed into another type. The amount of energy at the beginning needs to equal the amount of energy at the end, and this is shown through our calculations.

We found the percent error by comparing our results to the given theoretical value. Our red spring was 2.52%, our white spring was .63% and our blue spring was 1.56%. Our results were very good, as you always want a percent error as close to 0 as possible.The R^2 values for our graphs were all .99 which means they were all very accurate graphs as well. Our highest percent error was the red spring, and this spring also had a high percent difference at 6.33%. The other two results for our springs were very close to our peers, but we may have made some mistake with the red spring. For part B, our results were very similar, as we compared our individual energies with the average class energies found at certain points. Like always though, we can improve our results, as there were several possible sources of error. First, when measuring the distance the spring stretched, it was hard to get a definite answer because the spring would still be moving up and down. To fix this, we would have to wait until it stopped moving, which would sometimes take a while. In addition, we never actually weighed the weights, but instead just looked at the inscription saying how much they were. This is a rookie mistake, because it is possible that the weight could have been a few grams off. Next time we need to be smarter and simply weigh them. Finally, for part B, when using the motion detector, it was impossible to see if it was right under the weight. This could have hurt our results, and to fix this we could have used cardboard to give the detector something bigger to detect. Another group was using it though, and next time we need to be more careful not to make stupid mistakes so we can get better results.

=Roller Coaster Write-Up= Group Members: Maxx Grunfeld, Gabby Leibowitz, Matt Ordover, Mike Poleway


 * Top View:**


 * Side View:**

media type="file" key="IMG_0614.MOV" width="300" height="300"
 * Video:**


 * Drawings:**


 * Discussion:**


 * 1) Energy Conservation** - The law of conservation of energy states that energy may not be created or destroyed. However, since there is work out due to friction, the total energy will get smaller and smaller as the ball moves down the roller coaster. This can be seen in the equation Initial Energy + Work = Final Energy. Because the work goes opposite the direction of motion, it is negative and the final energy is therefore less than the initial energy. In addition, the energy starts out as gravitational potential energy at the top and is converted to kinetic energy by the time it gets to the bottom.


 * 2) Power** - Work is done when a force causes displacement and the equation is force times displacement. Power is the rate at which this work is done. This must be taken into account for the ball to reach the top of the coaster. Work is equal to GPE, and you make up a time for how long you want it to take your coaster to reach the top. Divide the GPE by the time and you will get the power you need from a motor to get your coaster to the top.


 * 3) Acceleration** - There are numerous ways to measure acceleration at various points throughout the roller coaster. You can use kinematics, newton's second law, or the law of conservation of energy. In order for our roller coaster to be considered safe we had to make sure our acceleration did not surpass 4 g's, which is the highest acceleration a human can withstand.


 * 4) Newton's Laws** - All motion that we know of follows Newton's three laws and our roller coaster is no exception. We can see his first law as the ball speeds up from the force of gravity and as our ball continues to roll on some of the flat parts of the coaster. In addition, it slows down at some points because of the normal force from the wall acts on the ball or the friction between the ball and the paper. The second law states that force equals mass times acceleration which is true at all points throughout our roller coaster. Acceleration changes at difference points throughout the roller coaster due to varying forces of gravity, friction, and normal force. Finally his third law can be seen as the ball slightly bounces off walls on the turns. This is because as the ball acts on the wall, the opposite reaction is the wall acting on the ball, so it bounces off.


 * 5) Gravitation and Apparent Weight** - Apparent weight is the normal force and it is how one feels when on the roller coaster. At the top of a hill there is no normal force, so you feel weightless. Also, their apparent weight is largest at the bottom of a hill. Therefore, when on a roller coaster you feel the heaviest at the bottom of the hill and the lightest at the top of a hill, even though your weight does not actually change. In addition, acceleration due to gravity is -9.8 m/s^2 at all times.


 * 6) Hooke's Law** - Since we created a theoretical spring system to stop the roller coaster, we could use Hooke's law to find the spring constant and the distance that the spring will compress. The Hooke's law equation is F=-kx. When creating the spring system, we had make sure that the coaster did not stop too abruptly, so it was safe. As a result we needed a spring constant that resulted in the acceleration being under 4 g's and safe for humans.


 * 7) Circular Motion** - Circular motion is present in our roller coaster during the vertical and horizontal loops. You must make sure that the acceleration does not exceed 4 g's to ensure it is safe. To find acceleration in a loop we used the equation v^2/r. In addition, you must make sure that the velocity is large enough, so the ball makes it all the way around the loop.


 * 8) Safety** - Our roller coaster is safe at all points throughout. It stays under the maximum acceleration of 4 g's through the whole roller coaster. Also, the velocity of the ball in the vertical loop is greater than the minimum velocity of 0.626 m/s, so the riders would stay in their seats and the coaster stays on the track. Due to this, our roller coaster would be safe for humans to ride.


 * Data Tables:**
 * (slide mouse over to see rest) **
 * Sample Calculations:**




















 * Sources of Error**



After creating our roller coaster and testing it to find out analytical data, we came across a few possible sources of error. This is expected though, as not every experiment can be perfect, but there are some areas in which we can improve. The first possible error is the friction unaccounted for when the ball travels down our roller coaster. Like in all experiments, we ignore friction, but it definitely has a significant impact on the results. There's not way to fix this error though unless we put the roller coaster into a vacuum, which is impossible for us to do. In our situation, we just have to deal with the friction and hope it doesn't have too negative of an impact. Furthermore, our roller coaster was made out of paper, so when the metal ball went down the paper hills, it rattled the roller coaster. Since it was wobbly, its possible that our velocities could have been changing every trial. Also we would take the roller coaster apart and put it back together to analyze it better. While doing this, we could've made our roller coaster work a little differently. All in all, using paper to design our roller coaster could have possibly given us some unsteady results. If we had another chance to do this, my group probably would have made the roller coaster out of wood or a more sturdy material so every trial would be exactly the same and not effected by the stability of it. Finally, when measuring our velocities using the photo gates, it was hard to get it at the exact location. In addition, we also had to hold the photo gate with our hands, definitely effecting our data. To fix this problem, we would have to get a photo gate that actually stayed attached to the pole instead of using our hands to hold it. We would have to try our best to find the best location because it would be almost impossible to get it perfect, so there will almost always be some error in that area. In conclusion, I think we did a very good job in this project, but there were several possible sources of error that we could fix next time we do it.


 * Transporting the Roller Coaster**

Roller coaster hanging out the trunk of the car

Bringing it home...

Bringing it back...

=Elastic and Inelastic Collisions Lab= Maxx Grunfeld Gabby Leibowitz Mike Poleway Matt Ordover


 * 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** - The initial momentum of a system should equal the final momentum of the system as stated in the law of conservation of momentum. Elastic collisions conserve kinetic energy, while inelastic collisions do not. We can tell a collision is elastic if the final kinetic energy is only slightly different from the initial kinetic energy. However, if the final kinetic energy is significantly different from the initial kinetic energy than the collision is inelastic.


 * Methods and Materials** - We connected two motion detectors to two opposite sides of the dynamics track and plugged them into a computer. We then recorded the final and initial velocities for five different collisions using the motion detectors and two dynamics carts. We used various masses for different trials of each collision.

"Explosion" A in motion; B at rest (sticking)
 * Videos**
 * 1.** media type="file" key="1.mov" width="240" height="240"
 * 2.** media type="file" key="2.mov" width="240" height="240"

A in motion; B at rest (bouncing) A in motion; B in motion (bouncing)
 * 3.** media type="file" key="3.mov" width="240" height="240"
 * 4.** media type="file" key="4.mov" width="240" height="240"

A in motion; B in motion (sticking)
 * 5.** media type="file" key="5.mov" width="240" height="240"


 * Data**
 * Excel**


 * Sample Calculations**








 * Analysis**

Discussion Questions

1. Many of the collisions in this experiment were inelastic, which means that momentum was not conserved. The initial and final kinetic energies were not equal, proving that our momentum was indeed not conserved. In the sticking experiments, the carts had completely different kinetic energies, where the initial was .081 J and the final was .042 J.

2. If carts of unequal mass are pushed away from each other, then the cart with the smaller mass will have a larger velocity. This can be shown in the equation p=mv, where p is constant. This shows that if u have a higher mass, then you'd have a smaller velocity, but if u have a smaller mass, you'd have a larger velocity.

3.If carts of unequal masses are pushed away from each other, the momentum will still always be the same. If one mass is different, then the velocity will make up for it to get the same momentum. This is seen through the equation p=mv, and no matter the mass, the velocity will make up for it and keep the momentum the same.

4. Mass and velocity are the only two factors that momentum depends on, and the cocked plunger doesn't have any effect. It should actually have the same effect on both carts. In the end, nothing except for the mass and velocity determined the momentum of the carts.

This lab proves our original hypothesis true, that the total initial momentum is equal to the total final momentum. Our group stated that elastic collisions conserve kinetic energy while inelastic collisions do not. Therefore, you can see from our results that the trials having a large difference between their initial and final momentums were elastic collisions, while the trials that had barely any different were inelastic collisions. Analyzing the percent differences also leads you to this conclusion, for the trials with a higher percent error can be concluded to be elastic collisions while the trials with a lower percent error can be concluded to be inelastic collisions. Although there does exist some higher numbers of percent error, the mostly low percent error (such as1.739% and 1.695%) that exists within our experiment provides accuracy to our results. However, like all experiments, there were many sources of error that could have existed and ways to limit this error from occurring in the future. Firstly, we assumed that the only motion that was being calculated by the motion sensor was the movement of the carts. However, it is very likely that one of the group members accidentally provided an additional force to the carts, such as a push, which was picked up by the motion detector and therefore, tampered with the results. Furthermore, the absence of an extra force was not the only thing inaccurately assumed by our group. After placing and removing multiple masses on the cart, we continued to assume that the original mass of the system remained the same. However, it would have ensured greater accuracy if our group remeasured the total mass each time. In the future, in order to limit the number of sources of error that occurred, there would have to be some sort of motor device that mechanically released the carts, therefore, eliminating the source of human error that could have gotten in the way of 100% accurate results. But, considering these materials were inaccessible for a physics classroom lab, performing even more trials and re-massing the system each trial would provide our group with a realistic way to lower our error. This lab relates to every day life in many ways, the most comparable event being car accidents. Performing this experiment gives one perspective on the relative momentum of different car accidents, after just seeing it demonstrated small-scale.
 * Conclusion**

= Ballistic Pendulum = __Part A:__ Mike Poleway __Part B__: Gabby Leibowitz __Part C:__ Matt Ordover __Part D:__ Gabby Leibowitz (Maxx Grunfeld- Absent)


 * Objective -** What is the initial speed of a ball fired into a ballistic pendulum?


 * Hypothesis** - Our group hypothesized that the three methods of measuring initial velocity- through using a photogate, through kinematics, and through the law of conservation of energy- will each produce similar results. The photogate method will produce the most accurate results since it requires the fewest calculations and is mostly based on values given by a computer.


 * Methods and Materials** - There are three ways to solve for velocity. For each method, the ball is loaded into the launcher, which is clamped to the table, and shot at medium range. The first method measures velocity using a photogate. The USB link attached to the photogate is connected to a computer and the recordable timer provides a reading of the time in gate values. The photogate is placed right outside the launcher and the time it took for the ball to travel through the photogate is recorded. After measuring the diameter of the ball by means of a meter stick, the velocity can be found by using the equation v=d/t. After performing this 5 times, the average velocity is recorded. The next method measures velocity using kinematics. A meter stick is used to find the vertical distance from the launcher to the ground and the horizontal distance from the launcher to a piece of carbon paper which is placed on the floor. (After shooting the ball once for a "test try", the position of the carbon paper can be estimated). After launching the ball 5 times, the exact horizontal distance of where the ball hit can be found by using a meter stick to measure where the ball left a mark on the carbon paper. Knowing this value allows one to complete an x-y-component chart, and eventually, solve for average velocity. The last method measures velocity using the law of conservation of energy. The ball is launched into a pendulum that swings up to the measured angle (theta). The mass of the ball and pendulum with the ball is measured. The ball is then shot into the pendulum while pushing the angle indicator. This provides one with the angle and allows the height of the pendulum to be calculated using the equation L-Lcos(theta). After this is found, the velocity can be found using LCE methods.

Video of Method One (Photogate): media type="file" key="photogate video.mov" width="300" height="300"

Video of Method Two (Kinematics): media type="file" key="kinematics video.mov" width="300" height="300"

Video of Method Three (LCE): media type="file" key="LCE video.mov" width="300" height="300"


 * Data**
 * Sample Calculations**

Photogate Kinematics Y-Axis

X-Axis

LCE (Velocity after collision)

LCM

Percent Difference


 * Analysis- Discussion Questions-**

1) In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy? Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? Generally, energy is conserved in elastic collisions, and it is not conserved in inelastic collisions. Maximum loss of kinetic energy occurs in a fully inelastic collision like a car crashing into a wall.

2) Consider the collision between the ball and pendulum.

a) Is it elastic or inelastic? Inelastic

b) Is energy conserved? Not perfectly conserved.

c) Is momentum conserved? Momentum is conserved as stated in the Law of Conservation of Momentum.

3) Consider the swing and rise of the pendulum and embedded ball. a) Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? Some energy is lost as this is an inelastic collision, but most of it is just converted to gravitational potential energy.

b) How about momentum? Yes momentum is always conserved because of the Law of Conservation of Momentum.

4) It would greatly simplify the calculations if kinetic energy were conserved in thebetween ball and pendulum. a) Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum. b) What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy. c) According to your calculations, would it be valid to assume that energy was conserved in that collision? No energy is not conserved, which is seen through our percent loss of 78.98%.

d) 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. 5) 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.) Due to the Law of Conservation of Momentum, increasing the mass of the ball will increase the height of the pendulum and theta. On the contrary, increasing the mass of the pendulum will decrease the height and theta.

6) 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? The velocities calculated using the photogate and kinematics were very similar. However, the velocity calculated using LCM was significantly higher. This could be due to inconsistencies with the launcher, the photogate only getting a chord of the ball, or poor measurements. If I built a ballistic pendulum, I would add a digital reading of the angle and I would make sure that there was not any drag on the pendulum, so there would be no friction. This would produce more accurate results.

Our hypothesis was accurate, for all the velocities measured using the three different methods produced similar results. For the first method we used a photogate to measure the velocity, in which we recorded an average value of 3.21 m/s. For the second method we used basic kinematics and an x-y-component chart to first find distance, and then velocity, in which we measured an average value of 3.41 m/s. For the last method, we used the law of conservation of energy to find theta, the height, and then eventually velocity, which gave us a value of 4.49 m/s. All these methods yielded similar results and our percent difference values prove the accuracy of this experiment. The photogate had a maximum percent difference of 2.00% and a minimum percent difference of .592%. The kinematic calculations had a maximum percent difference of 1.55% and a minimum percent difference of .56%. Finally, the law of conservation of energy method had a maximum percent difference of 1.27% and a minimum percent difference of .85%. These prove extremely accurate results that prove our hypothesis. However, there are many sources of error that could have occurred to contribute to the percent difference values. One source of error that affected all the trials was the fact that the launchers were not consistent, and regardless of the fact that they were clamped to the table and launched at medium range each time, they still did not launch the ball the same distance each trial. If we were to fix this experiment, purchasing new launchers or new springs to ensure that they are not weak or rusted from multiple trials performed by other physics students. A possible source of error for the photogate part of the lab could be that the photogate was not perfectly lined up so that the ball passes through the center of the gate, therefore, recording a smaller time and a larger velocity. In this case, human error got in the way of perfect results and in order to limit this in the future, we would need to somehow attach the photogate to the launcher perfectly centered at its desired position. In addition, a possible source of error for the kinematics method was that human error got in the way of measuring exact distances of where the ball landed on the carbon paper. Both rounding the dimensions or misreading the measurement could lead to slightly flawed data. In order to reduce this error, there would need to be some machine that could record the exact distance after the ball was launched, limiting any human error to take place. However, since this material is unrealistic of acquire during a physics lab, having multiple group members measure the distance would make the data more reliable. Finally, a source of error from the LCE method could have come from the friction that existed between the angle indicator and the surface. The presence of friction would have given us a smaller angle, and therefore, a larger velocity. Once again, to limit this source of error a machine would have to be used to mechanically measure the angle void of friction. But since buying this material is unrealistic, measuring the angle by hand with a protractor and then averaging the two values together would give the data a little more accuracy.
 * Conclusion-**

After analyzing our data, the photogate method definitely provided the most accurate results, as we hypothesized. Since it required our group to perform the fewest calculations, the amount of human error that could have gotten in the way was limited. It was mostly based on computerized data which is more accurate than hand calculations which involves estimation. This lab relates to one's life in many ways. Projectiles are very common and are seen in every day life. Simply throwing a ball off a hill while having a catch with a friend demonstrates a projectile. It is essential to know the works of projectiles for all athletes who should have a good idea of where a ball will land after it is thrown (especially in that of football). In addition, the fact that this lab was an example of an inelastic collision also relates to our lives. Knowing the physics behind inelastic collisions helps a mechanist develop better and safer cars.