Group3_4_ch6


 * Group 14: Robert Kwark, Max Llewellyn, Noah Pardes, Kosuke Seki**

toc =__LCE Lab (2/3/12)__= Part A - Kosuke Seki Part B - Robert Kwark Part C -Noah Pardes Part D - Max Llewelyn

Station 1: Cart on an Incline- Find the speed of the cart at the bottom of the incline. Station 2: Horizontal Projectile- Find the speed of the ball when it leaves the launcher. Station 3: Pendulum- Find the speed of the mass at the lowest point of the swing. Station 4: Galileo’s Ramp- Find the max height of a ball at the top of an incline. Station 5: Vertical Launch- Find the speed of the ball as it leaves the launcher. Station 6: Roller Coaster- Find the speed of the “roller coaster” at the top of the loop.
 * __Objectives:__** What is the relationship between changes in kinetic energy and changes in gravitational potential energy?

__**Hypothesis:**__ The sum of the kinetic energy and gravitational potential energy at the beginning should be the same as the sum of the kinetic energy and gravitational energy at the end. Either kinetic energy will increase and gravitational potential energy decrease to maintain equilibrium or vice versa.

//Station 5:// Put the launcher in lowest power and launch the ball. Measure the maximum height relative to the height of the photogate timer (max height-height of timer), and use the photogate timer (time in gate) to determine initial velocity.

//Station 6:// Measure the initial height using a metric ruler. Measure the height of the photogate timer, and subtract that from the initial height to find the initial height relative to the timer height. Then roll the ball down the roller coaster and use the timer to find final velocity/kinetic motion using the photogate.

//Station 1:// First, measure the top part of the pyramid on the transparent card to find what would be the diameter of a ball. That is the distance that is being measured by the photogate. Then push the cart down the ramp and take the final velocity, making sure to measure its initial and final height. Record the results.

//Station 2:// Measure the height of the launcher and both the photogate timers. Set the launcher to low power, and launch. Record the velocity of the ball as soon as it leaves the launcher and at the bottom of its trajectory.

//Station 3:// Pull the cork back a certain distance. Measure the height of the cork and of the photogate. Let go of the cork, making sure it goes through the photogate timer cleanly, and take the velocity.

//Station 4:// Measure the height of the ball at the top of the steeper side of the ramp. Release the ball, making sure not to push it or add spin to it, and record the height of the highest point it reached on the incline.

//Data Table: Our Results//
 * __Analysis__**

//Station 1://

//Station 2://

//Station 3://

//Station 4://

//Station 5://

//Station 6:// //Data Table: Percent Difference and Percent Energy Loss//


 * __Conclusion:__**

We believe that throughout all these experiments our hypothesis was supported by out experiments. In every station except station 2 (more on that in part 2) the difference in starting and ending energy was minimal and could easily have been due to friction. (aside from one outlier) Because, all out results were within 10.2% of the average, and we never lost more then 9.69% of the starting energy we believe it is reasonable to conclude that; A our data is accurate and was taken correctly, B the amount of energy lost is within the expected amount. We believe this data, and data verifying the data, supports our hypothesis.
 * __Part 1:__**

Looking at our % difference table is like looking through a chicken coop, seeing 5 white and brown grade A eggs and one cannon shell with a very confused chicken sitting on top looking very very sore. We had 5 very reasonable percent differences and 1 very not reasonable one. Starting with the eggs, baring the outlier of station 2, we never lost more then .47 J of energy, or 9.69% of the starting energy. One source of this error would be that the point where the sensor saw the ball weren't along a diameter. If they were along a chord of the sphere the velocity of the ball would have been over calculated if we assumed the sensor read along a diameter. We believe that accounting that small an energy loss due to friction and a misplaced sensor is very reasonable.
 * __Part 2:__**

Now on to the horizontal launch; we believe that the second photo gate detected only a chord of the sphere of the ball, not the full diameter of the ball.This means that it would take less time for the ball to pass through the gate, resulting in an increased velocity. This would explain both the decreased time between gates.

To improve the results of the 5 labs that yielded rational results we would take steps to reduce friction and to place the sensor so that it always read along the diameter of the balls passing through it. To improve the projectile lab we would first film the projectile in slow motion to track the arc it made, and find the proper place to put the sensor. We believe this would eliminate the vast majority of the error for that lab.
 * __Part 3:__**

This lab proved that when dealing with kinetic and gravitational energy what you start with is what you end with (there's no such thing as a free lunch in physics). The law of conservation of energy is important to high school students and roller coaster designers alike. It has applications in designing simple things like pitching machines, or playground slides for average weight children. However looking further; knowing that energy can not be created or destroyed is one of the most important things in Newtonian, Einsteinian, and (I'll edit this in when we know) physics. This is law important in every field from chemistry (eg: making batteries) to mechanical engineering (eg: measuring the inefficiencies in motor designs using a infrared camera to see heat) to electrical engineering (eg: calculating if a resistor on a board is going to overheat during operation) to nuclear engineering (eg: finding out the health of the reaction based on the electrical output and volume of waste energy). If energy didn't have to come from somewhere all these people would really have their work cut out for them.

=__Spring Constant Lab (2/10/12)__= Part A - Max Llewellyn Part B - Noah Pardes Part C - Kosuke Seki Part D - Robert Kwark

__Objective-__ Determine the following values:
 * The spring constant for several different springs
 * The EPE of each spring
 * The work done by each spring
 * The GPE and KE at 3 different points in the oscilation

__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.

__Procedure-__ For part A, the purpose was to find the spring constant coefficient in newton meters of several springs. To find this, we used different colored springs, red, yellow, and green. We began by measuring the distance of the spring to the tabletop with a meter stick. Then we began to add masses to the springs and found its displacement. Since weight is force and the displacement is displacement, the points go n the graph, and the slope is the spring constant. For part B, the purpose was to find velocities at different points on a period (the spring went up and down) and figure out whether energy has been conserved. A motion detector is at th tabletop, and a spring bounces up and down with a mass attached to it. Displacement is recorded in data studio, and a periodic graph is formed. We find certain values, and conclude whether energy has been conserved.

__Data-__ //Part A://
 * Percent Error and Percent Difference must be multiplied by 100 for above data.*

//Part B:// 1 //Class K Values://

//Excel Spreadsheet://

__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, it does. By looking at the graph, we can see that the relationship between force and the change in x is linear, telling us that it is constant.
 * 1) How can you tell which spring is softer by merely looking at the graph?
 * The ones with a lower slope are softer, having a lower k value. Therefore, the one that is the most flat is the softest.
 * 1) 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.
 * Theoretically, there shouldn't be any changes in total energy. However, the individual components do change. At the very bottom and top, there shouldn't be any kinetic energy, though we do because of the nature of the motion detector. There should just be elastic potential and gravitational potential. As it goes from the bottom toward the middle, it picks up speed, gaining kinetic energy and gravitational potential energy while losing elastic potential energy. As it goes from the top toward the middle, it gains kinetic energy and elastic potential energy while losing gravitational potential energy.

__Analysis__ (%Error and %Difference calculations were based on the white spring)

__Conclusion-__ Our hypotheses were all proven to be correct. The softer springs did have a smaller k constant than harder springs. The red spring, the softest one, had the lowest k value, while the green spring had the highest k value. We know this because the slopes of their position vs. time graphs is equal to their k constant. In addition, our hypothesis that the total amount of energy will be the same throughout the oscillation of a spring was proven to be true. For example, the total energy (Kinetic, gravitational potential, and elastic potential) at the top of the oscillation was essentially equal to the total energy at the bottom of the oscillation of the spring.

Our results for the k constants of the four springs were very accurate as well; our lowest percent error was 1.2%, and the highest was 4%. Considering that the box said anything within 10% of the actual k constant was good, our results were exceptional. When compared with the class, our results were still very good, ranging from 1.4% to 6% difference. For Part B of the lab, we also had very good results. At position A, the largest percent difference was .49%, and at position B, the largest percent difference was .758%. At C, all of our individual results were precisely at 1.186 J, so the percent difference was an incredible 0%.

In part A, the fact that we didn't get 0% error showed that there were some errors in our procedure. One of these errors might have been from the fact that the weights were lopsided when we measured the change in distance. For example, it was somewhat difficult to discern whether the spring dropped to 28.8 cm or 29 cm because one side of the weight was at 28.8 cm and the other side was at 29 cm. In order to fix this, we can either add the weights evenly so that it won't be lopsided, or we can measure the center of the weight. Another source of error could have been that we did not add enough weight to make the spring stretch; for example, we used a starting weight of 200g weights on the green spring, but we kept getting skewed results. We realized that the 200g was not making the spring stretch at all. When we put a starting weight of 300g on the spring, we finally got accurate results. In order to fix this, make sure to add enough initial weight to make the spring stretch a bit. In part B, one source of error could have been the motion detector. If the motion director was not directly under the weight, then the motion director would measure the distance to something other than the weight on the spring, resulting in a bad graph. One way to remedy this was to add a weight with a large surface area so that it would be easier for the motion detector to sense distance to the weight. One real life application of this is bungee jumping. The cord would have to have a k constant for the appropriate weight so that the cord would not snap, and also so that the person would not stretch too far (or else they would hit the surface at the bottom). On the other hand, the k constant can't so large that the person would barely bounce up and down.

=__**Roller Coaster Write-Up**__= __//Video://__ We propose to construct a roller coaster ("Need for Speed 1.0") for Six Flags to put in their park. Our working model and analysis should convince you that our roller coaster, with a bit of tweaking, would provide many exhilarating thrills and attract more customers than ever before!

media type="file" key="Group 14 Rollor Coaster.mov" width="300" height="300"

Picture of roller coaster (side view):



Photo of roller coaster (top view):

Procedure of taking velocity at a point: media type="file" key="Movie on 2012-03-02 at 15.17.mov" width="300" height="300"

Successful Roller-coaster Runs (3 for 3)

__//Excel Sheet://__

//__Data:__//

//__Equations:__// (All referring to the descent down the first hill unless otherwise notified)


 * Average Time:**


 * Actual Velocity:**


 * Potential Energy (On the way down 1st hill):**


 * Kinetic Energy (On the way down 1st hill):**


 * Theoretical Kinetic Energy:**


 * Total Energy (Initial Drop)**


 * Energy Lost (On the way down 1st hill):**


 * Acceleration on Vertical Loop:**


 * Acceleration on straightaways:**


 * G's (On the Way down 1st hill):**

-The roller coaster would have a much larger mass, meaning that a lot more power will be needed to move it up the hill. -If the initial height was 100m, and the mass of the coaster is 1000 kg, you would need a 28,000 wattage motor or greater to move the roller coaster up to the top of the hill.
 * 5b. Power:**


 * 5c. Minimum Speed (Vertical Loop):**

1.75 cm above the top of the loop is the required minimum height of the roller coaster.
 * 5d. Minimum Height Requirement:**


 * 5e. Energy Dissipated:**


 * Spring Displacement:**

-First we found the distances needed to stop the marble with 2g's of force. 2g's is well under the maximum limit of 4g's, and should be comfortable enough for passengers to bear. Then when used that distance to find k, the spring constant. Of course, on a real roller coaster, the constant and distance would be much larger because both the distance and mass would be significantly larger.

Since height, mass, and acceleration due to gravity wouldn't change, just finding the percent error of the KE would provide a good way to evaluate our deviations and errors.
 * Percent Error (on the way down 1st hill):**

//__Write-Up:__// 1. Energy Conservation The Law of Conservation of Energy states that energy cannot be created or destroyed, only change form. In a contained system, the total energy remains constant, though the type of energy may change. The general equation for this is: Initial Energy + Work= Final Energy. The more in-depth equation is: KE+GPE+EPE+W = KE+GPE+EPE. The energy was maintained throughout the roller coaster. The GPE was converted into KE, with friction taking away a considerable amount of energy as well. That friction would be classified as negative work, as it was working against, or slowing down, the marble. In addition to friction, an incredible amount of energy was lost because parts of the roller coaster were not stable. This occurred especially in the turns and loops. This normal force that the paper exerts at these bends would be classified as another form of negative work.

2. Power Power is the rate at which work is done. In order to make the roller coaster reach the top of the first hill (or its starting point), we need to do work. This work is equal to the GPE at the top (if we disregard friction or any other kind of work). In order to calculate power, you also need the time over which that work is done. And since we did not want the passengers to wait too long to experience the thrill of the roller coaster, we made the time 6 seconds.

3. Acceleration In order to have enough speed to make it through the various loops and hills that our roller coaster offers, height was essential. That, and the angle of the ramp, was the only way that we could convert the gravitational potential energy into kinetic energy, or motion, without adding work to the ball. Acceleration, however, is relatively simple to solve. We can either use kinematics, the law of conservation of energy, or we can use Newton’s second law of motion. We used kinematics, finding acceleration using distance.

4. Newton’s Laws and Circular Motion Newton’s three laws govern all motion that we know of today. Our roller coaster, however, not only follows the laws but also is a prime example of many. The first states that an object in motion will stay in motion, or than an object in rest will stay in rest unless acted upon by an unbalanced force. This is evident in the beginning of the ride, where the ball, originally at rest, starts to move due to the force of gravity. The second law of motion states that the net force is equal to the mass multiplied by the acceleration, and this is true as well in our coaster. the third law states that all actions have an equal and opposite reaction - and, no surprise, our roller coaster illustrates this beautifully. At the end of the coaster, we have a wall that stops the ball. The bearing hits it with a considerable force, but the wall acts on the ball itself as well, making it move backwards. That is an example of the third law. Circular motion is also present in our roller coaster through the loops. The acceleration in the loop would be equal to v^2/r. At the top of the loop, the coaster would have both weight and Normal forces pointing towards the center of the circle, which would mean they are both positive. Using that, we were able to find the theoretical minimum velocity at the top of the loop, .586 m/s.

5. Gravitation/Apparent weight The force of gravity is equal to -9.8 m/s^2. However, when accelerating, the force of gravity on a person may be too much; the limit that a human can survive is 4 g's, or 39.2 m/s^2. Apparent weight is when the normal force acting on an object is equal to zero, thus feeling “weightless.” Unfortunately, people can't change their actual mass without exercise and a good diet, so the weight of an individual will not change unless they go to another planet, which has a different gravitational force. The apparent weight is most significant when the ball is at the top of the hill, because the normal force is nearly nonexistent. This lack of normal force creates the feeling of weightlessness on roller coasters.

6. Hooke’s Law Hooke’s Law states that the extension of a spring is in direct proportion with the load applied to it. In equation form, this means that F=-kx, where F means force applied to the spring, k is the spring constant, and x is the amount of displacement of the spring. This would relate to the elastic potential energy in the roller coaster. The theoretical spring we created at the end of the roller coaster would have a spring constant of 2.01 N/m because that would be the spring constant needed for the passengers to feel 2 G's <span style="font-family: 'Times New Roman',Times,serif; font-size: 125%;"> of acceleration, which is quite bearable (instead of making them jerk suddenly at the end). The distance the spring would move is 1.784 cm.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 16px; text-decoration: none; vertical-align: baseline;">Safety Discussion: <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 16px; text-decoration: none; vertical-align: baseline;">Our roller coaster is safe at all locations except the vertical loop. After finding the minimum velocity needed for the roller coaster (ball) to make it all the way around, we realized that the coaster did not have enough velocity. The result was that the ball made it most of the way around, then dropped. This is shown in our data; the minimum speed at the top of the loop is at least 0.586 m/s, but our coaster was traveling at 0.078 m/s at the top. There are two major explanations for this; one is that when we were measuring the velocity, the sensor only recorded the time it took for a chord or even a curve of the ball to pass through the sensor. The other is that the vertical loop was not entirely stabilized; a lot of the speed was lost because the paper absorbed a lot of the force and speed. A way we could fix this to make it safe is to have more structural support so that less energy will be lost, allowing the coaster to successfully make it around the loop. However, our acceleration at that point was within the limit of 4G's, so in that aspect the coaster is safe. At all other points on the roller coaster, the acceleration does not exceed 4 g's, which is the maximum safe limit that human beings can endure for the duration of a roller coaster ride (the max G's survived was just under 180 G's... by a race car driver who went from 173 km/h to 0 in a distance of 66 cm... incredible).

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 16px; text-decoration: none; vertical-align: baseline;">Errors and Uncertainties: <span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 16px; text-decoration: none; vertical-align: baseline;">There were many sources of errors on our roller coaster. Our total energy does not match our final energy; we lost about 97% of our energy. Two major reasons why this occurred were that friction was working against the metal ball, and that the structures were not entirely stable so the structure absorbed some energy. The latter reason probably had more of an impact on the efficiency of the roller coaster. The points where this was most obvious was in the vertical and horizontal loops; the percent error in KE was nearly 100% at those points. In addition, the photogate timer might not have measured the time it took for the diameter to pass through, but rather a chord of the sphere. That would make the velocity larger than it was supposed to be. We also had trouble because sometimes the roller coaster would shake and the photogate would measure the paper instead of the ball. The best way to make sure we got accurate results would be to construct a much more stable, less flimsy roller coaster.

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 16px; text-decoration: none; vertical-align: baseline;">In general, a real roller coaster would have to be much larger, weigh a lot more, and be a lot more sturdier.

=__LCM Lab__= Part A: Kosuke Seki Part B: Robert Kwark Part C: Max Llewellyn Part D: Noah Pardes

__<span style="font-family: Arial,Helvetica,sans-serif;">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? __

__<span style="font-family: Arial,Helvetica,sans-serif;">Hypothesis: __<span style="font-family: Arial,Helvetica,sans-serif;"> The initial momentum and final momentum of a system should be conserved because of the law of conservation of momentum. The explosion and the both in motion (sticking together) will be the inelastic collisions, while the others will be the elastic collisions.

__<span style="font-family: Arial,Helvetica,sans-serif;">Video of Procedure: __ <span style="font-family: Arial,Helvetica,sans-serif; line-height: 0px; overflow: hidden;">media type="file" key="Movie on 2012-03-08 at 11.40.mov" width="300" height="300"

__Data:__



__Excel Sheet:__

__<span style="font-family: Arial,Helvetica,sans-serif;">Sample Calculations: __

__<span style="font-family: Arial,Helvetica,sans-serif;">Analysis Questions: __ <span style="font-family: 'Times New Roman',Times,serif;">1. Is momentum conserved in this experiment? Explain, using actual data from the lab. <span style="font-family: 'Times New Roman',Times,serif;">-Momentum is conserved in nearly all of our experiments. In most cases, the % difference was very small, under 9%. This small range of difference could be attributed to a number of factors, like friction, some preliminary motion before hand, the cart hitting the sensor, etc. And for most of the types of collisions, only one of the trials had an outlier percent difference value (for example, the Together Fusion collision type with .016%, .95%, and an outlier of 4.59% difference). The only exception is in the explosion, where the the carts started with no momentum or velocity but suddenly sped up, resulting in a 200% difference. Thus, we concluded that in every collision except the explosion, momentum was conserved.

<span style="font-family: 'Times New Roman',Times,serif;">2. When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is. <span style="font-family: 'Times New Roman',Times,serif;">-The lighter cart has a higher velocity. When the cart with the greater mass pushes against the cart with the smaller mass in the collision, the force exerted upon the smaller one is greater then the force exerted on the larger one. Also, momentum is mass times velocity, which means that these two magnitudes must balance each other out (when set equal to each other). As mass decreases, velocity increases, and since the cart has a smaller mass, its velocity must compensate by increasing.

<span style="font-family: 'Times New Roman',Times,serif;">3. When carts of unequal masses push away from each other, which cart has more momentum? <span style="font-family: 'Times New Roman',Times,serif; font-size: 14.4px;">-The cart with the larger mass. Momentum is mass times velocity, and therefore the greater the mass, the greater the momentum.

<span style="font-family: Arial,Helvetica,sans-serif;">4. Is the momentum dependent on which cart has its plunger cocked? Explain why or why. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 14.4px;">-<span style="font-family: 'Times New Roman',Times,serif; font-size: 14.4px;">Momentum is not dependent on which cart has the cocked plunger. The two factors are mass and velocity. The plunger should have an equal affect on the two cars because it has the same force acting upon it, which would make the plunger independent of which cart it is attached to.

__<span style="font-family: Arial,Helvetica,sans-serif;">Conclusion: __ The results obtained from this lab activity support the hypothesis that <span style="font-family: Arial,Helvetica,sans-serif;">initial momentum and final momentum of a system should be conserved because of the law of conservation of momentum. The trials that had large differences between their initial and final momentum's were elastic collisions, meaning that the kinetic energy is conserved. Similarly, for the trials that had minute differences between their beginning and final momentum's were inelastic collisions, where the kinetic energy was ** not ** conserved. The low percent differences suggest that the results were very precise. Nonetheless, there were several areas where errors could have occurred. For example, as masses were added to one of the carts, we didn't remeasure the total mass of the system, so it's possible that although we ** assumed ** that each mass weighed the same as the first one (.497 kg), however we didn't test this to make it certain. Additionally, it's possible that when the carts were given an initial push, it's possible that something (such as a hand) got in the way of the sensor, which would have impacted the results on Data Studio. Finally, at the end of the run, the cart hit the sensor which shifted position a little bit, affecting the data. If this lab were to be done in the future, there are several ways in which the procedure could be improved. One way is by using a cart that has a motor to collide into a regular (non-motor) dynamics cart so that the initial velocity can't be harmed by an outside force. This lab is extremely applicable to everyday life. For example, car accidents, collisions in sports, and other explosion/collision situations can be related to this activity, and the momentums can be determined.

= Ballistic Pendulum Lab: = 3/16/12

Part A: Noah Part B: Rob Part C: Kosuke Part D: Max

__Objective:__ What is the initial speed of a ball fired into a ballistic pendulum?

<span style="font-family: Arial,Helvetica,sans-serif;">__Hypothesis:__ By using three methods, we will be able to determine the initial speed of a ball fired into a ballistic pendulum. The photo-gate will probably produce the most accurate results, and the LCE technique will probably be a little less accurate since there is a little energy lost.

__ Data: __



__**Procedure**__: media type="file" key="Movie on 2012-03-16 at 11.26.mov" width="300" height="300"

__**Sample Calculations:**__ Average of Angle:
 * Note: This will also work for any other average, including average time and average distance. Writing sample calculations for all the other averages is just busywork.

__Photo-gate:__

__Projectile Motion (horizontal launch):__ //Y-axis://

//X-axis://

__Ballistic Pendulum:__

__Percent Difference (Projectile Motion):__


 * Percent Difference of Photo-gate: || 0.147 ||
 * Percent Difference of Ballistic Pendulum: || 2.933 ||

1. In general, what kind of collision conserves kinetic energy?What kind doesn’t? What kind results in maximum loss of kinetic energy?
 * Generally, elastic collisions conserve kinetic energy, while inelastic ones don't. A maximum loss of kinetic energy would be an inelastic one when there is a complete loss of motion, such as when a car hits the center barrier.

2. Consider the collision between the ball and pendulum. a.Is it elastic or inelastic? b.Is energy conserved? c.Is momentum conserved?
 * Inelastic
 * Not perfectly conserved.
 * Momentum is conserved because of 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? b.How about momentum?
 * Not perfectly, but energy is conserved, because even though there is a loss of kinetic energy, there is a gain in gravitational potential energy.
 * Momentum is conserved because of the law of conservation of momentum.

4. It would greatly simplify the calculations if kinetic energy were conserved in the collision between 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? 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.
 * yes
 * (ab both here)
 * [[image:Screen_shot_2012-03-18_at_8.26.38_PM.png]]
 * NO
 * [[image:Screen_shot_2012-03-18_at_8.07.59_PM.png]]
 * It is basically the exact same thing.

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.) 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? 7.
 * Increasing the mass seems to increase the height of the pendulum, as well as theta (obviously). Increasing the pendulum mass, however, does the converse and lowers the height and theta.
 * This is because of the Law of conservation of momentum.
 * There is not a significant difference between the three values of velocity that we measured. Things that would increase the difference in speeds are: not getting the diameter of the ball to pass through the photo-gate, the inconsistencies in the launchers, and possibly poor measurements.
 * To make a ballistic pendulum that was more accurate, I would try to make it as idiot-proof as possible by making everything digital. Also, making the collision between the pendulum and ball more elastic would make for better results, as there would be less energy lost.

__Conclusion:__ Our hypothesis was partially accurate. The three different techniques we used yielded similar results. When we used kinematics, we simply launched the ball with the launcher and treated the situation like a projectile. We measured the height of the table and launcher, and the distance the ball traveled. Using this information, we found the time the ball was in the air, and from this, the initial velocity. The average initial velocity for the ball using kinematics was 5.630 m/s. We also used a photo-gate to determine the initial velocity. We set the photo-gate to "time in gate" and put it in front of the launcher. We found the diameter of the ball and used the equation v=d/t to find the initial velocity. The average initial velocity using the photo gate technique is 5.676 m/s. The third technique we used was using the Laws of Conservation of Matter. We used the ballistic pendulum model and got an average initial velocity of 5.697 m/s. We hypothesized that the photo gate would have the most accurate results and the LCE technique would yield the least accurate results. During our lab however, we found that the highest percent different, 2.933%, comes from the ballistic pendulum and the lowest percent difference, 0.147%, comes from using the photo-gate. However, since our highest percent difference is only 2.933%, we still got excellent results. Obviously, since the percent error is not 0% for all the trials, there were a few experimental errors. First off, the launchers were not consistent. Even though we set them at the exact same setting each time, they launched the balls at different distances. To fix this, we could put in new springs in the launchers and warm them up before using them. Another error is that could have occurred is that the photo gate could have been set on an angle, capturing the ball for more or less of the time it was actually supposed to. To fix this, we should make the sure photo gate is completely straight by using a level. We also could have measured poorly for the kinematics portion of the lab. To fix this, each group member should have made measurements, and we should have taken the average. Another way to get more accurate results is to perform more trials for each technique. This lab was an example of an inelastic collision. These are pretty common in real life, and examples include glancing car crashes. Projectiles are also pretty common, and examples include cannons and throwing a ball. The experiment we conducted is comparable to a person throwing a ball off a cliff or building. It is important to study inelastic collisions like ballistic pendulums because they help us design better cars and vehicles. Projectiles are also important as most sports involve some form of a projectile.