Group1_6_ch6

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Lab: The Law of Conservation of Energy 1/31/1
Task A: MaddiTask B: BenTask C: JoeTask D: Magna __// Objectives: //__ What is the relationship between changes in kinetic energy and changes in gravitational potential energy?

__ //Hypothesis:// __ The Law of Conservation Of Energy states that energy can't be created or destroyed, so hypothesize that the relationship between kinetic energy and gravitational potential energy is that they are included in initial and final energies, which are equal. __//Procedure and Setup Pictures://__
 * Station One - At station one, we measured the end of the cart when it was at the top of the ramp, and then the back again at the bottom for initial and final heights. To conduct the experiment, we would place the vehicle at the top of the cart, with the plastic piece mounted on top of the cart, and then let it roll down so that the top row of tape on the plastic would pass through the photogates.
 * Station Two - At station two, we measured from the ground to the counter top with the meter stick, then used a smaller ruler to measure from the counter top to the center of the hole where the ball leaves the launcher for our initial height, and then we used this same value for final height, because we hadn't seen the ball drop any noticeable value after having passed through the two photogates. When launched, the ball passed through the two sensors, so we were able to use the time between them, as well as the measurement between of distance between the the seams of each photogate for values to find velocity. We also needed to measure the mass of the ball to solve for energy later.
 * *However, this was not correct. Results would be more sensible if we placed the photogate on the ground.
 * Station Three - At station three, we measured the initial height of 20cm from the final height, which was the wooden piece at rest in the photo gate. Then, we measured from the counter top to the photo gate for the final height, and also added it to the initial 20cm to find the correct initial height. We then found the mass of the wooden dowel and it's diameter, then let it go from 20cm so that it passed through the sensor. We used the time through the sensor to find the velocities.
 * Station Four - At station four, we measured from the counter top to the bottom of the ball, when it was placed on the shorter side for our initial height value. Then, we would let go of the ball and find where, on average, it would stop moving on the other side. We recorded this position from the counter top, and used it for our final height, and our final and initial velocities were both zero. We also needed to weigh the ball, as it was necessary to find energy for it.


 * Station Five - At this station, we measured initial height from the the center of the ball inside the launcher. Then, we launched the ball, and recorded it's max height with a meter stick. For this lab, we had to take the weight of the ball as well as find the diameter. The diameter was necessary as it was the distance, because the sensor recorded the amount of time that the ball went passed through it
 * Station Six - At station six, we measured initial height at the top of the "coaster," and measured final height at the top of the loop, where the photogate was located. We then let the ball roll down the ramp, so that it rolled around and through the sensor. We used the amount of time the ball was in the gate, the ball's diameter, as well as it's mass to solve for energy.

__//Data://__
 * Period 2 Data:**





In the station below we had to use some data from period two. We did this part of the experiment wrong so we supplemented the data we collected with the average final velocity from period 2 (what we did wrong). 









__//Conclusions://__ The hypothesis states that due to the Law of Conservation of Energy, that no energy will be created or destroyed in the experiments, therefore the relationship between the initial energy and the final energy is that they are equal. The data collected shows that this is true, expect for the second and third station, which both yielded a percent difference over 50%. Stations one, four, and five have less then 10% differences which means that the experiment was very good at keeping all of the energy that was used in the initial part of the experiment to the end of the experiment, while some of the others were not. Station six had a 21.3% difference which is easily explained by the fact that it was a longer distance and that it had more time to lose it's energy. In experiment two which had the highest percent difference, the photo gates used to take the time of the ball should have been placed on the floor. The data that was collected would have been more relevant to the experiment that way. Experiment three, with the wooden pendulum was the second highest percent difference. The reason that this is could be due to the fact that as the pendulum swung it lost energy other places that weren't accounted for. The data was very strong and overall had low percent differences between the initial and final energies, which proves the hypothesis of energy not being created or destroyed.

Lab: The Law of Conservation of Energy for a Mass on the Spring
Task A: MagnaTask B: MaddiTask C: BenTask D: Joey Objectives and Hypotheses:
 * To directly determine the spring constant k of several springs by measuring the elongation of the spring for specific applied forces.
 * When forces are applied, soft springs will elongate more than hard springs. Therefore soft springs will have a smaller constant k than hard springs.
 * To measure the elastic potential energy of the spring.
 * The elastic potential energy of a soft spring will be greater than that of a hard spring. This is because the equation for elastic potential energy is EPE = ½ * k * x^2. Because soft springs have a low k constant and less elongation (x in the equation), EPE will be small. Because hard springs have a high constant k and more elongation, EPE will be large.
 * To use a graph to find the work done in stretching the spring.
 * In the equation of the line on the distance vs. applied force graph, the slope is the constant k of the spring. The slope (k) of the hard spring will be steeper than the slope (k) soft spring. Because work = area under the graph, the area under the hard spring graph will be greater than the area under the soft spring graph.
 * To measure the gravitational potential and kinetic energy at 3 positions during the spring oscillation.
 * Max height
 * GPE will be greatest because the vertical height is greatest
 * Kinetic energy will be smallest because it is slowing down
 * Middle
 * GPE will be medium because the vertical height is in the middle
 * Kinetic energy will be greatest because it has not yet started slowing down
 * Bottom
 * GPE will be lowest because the vertical height is lowest
 * Kinetic energy will be smallest because it is slowing down

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Materials and Methods: First, we attached four springs of equal length to a clamp on a ring stand. Next, we added increments of weight to the end of the springs and measured the elongation of each spring with a meter stick. We repeated this process a total of five times. We used this information to calculate the constant k of each spring. We next measured the speed and position of the spring using a motion detector and data studio. We released the spring and collected this data during the spring oscillation.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**Pictures of Setups**:

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Data: <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**Graphs**:
 * Sample Calculations:**



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Analysis: <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">

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?
 * 2) Yes, the data for displacement of the spring versus forces shows that the spring constant is constant for different forces. Since the lines of best fit are directly proportional, as well as have a high regression value, then we can see that the data that we found is very similar. The combination of consistent data, as well as a directly proportional line of best fit, shows that the "k" value is constant.
 * 3) How can you tell which spring is softer by merely looking at the graph?
 * 4) Since the slope of the lines of best fit is the spring constant, a line with a smaller slope will have a smaller constant than a line with the larger slope.
 * 5) 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.
 * 6) In part 2 of the lab, we measured the energy and velocity of the red spring in several locations, these locations being equilibrium, max height, and min height. As the mass recoils past equilibrium, it has gravitational potential energy, elastic potential energy, and kinetic energy. At the minimum displacement, the mass has gravitational potential energy, as well as kinetic energy. Finally, at the maximum displacement, the mass only has elastic potential energy. At all points in this experiment, there should be the same amount of total energy for each position.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Conclusion: Our first hypothesis was found to be correct because the softer the spring was the smaller its spring constant was, this was proven when the red, the softest spring had the smallest spring constant. Our second hypothesis was also true because the EPE value of a soft spring was larger than the EPE of a harder spring. Our third hypothesis was proved correct by our graph. The slope of the line was largest in hard springs, the area under a hard spring was larger than that of a soft spring, and the graph did tell us the experimental spring force constants. Our final hypothesis was also correct. The three parts of the hypothesis are proven by the excel charts above. The fact that we were able to create 4 hypothesis that were correct is pretty good!

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">During this experiment we were tasked with finding the spring constant for multiple spring and then comparing it to a theoretical value. We compared the experimental value for each of the springs to the theoretical and determined the percent error and percent difference. The theoretical value that we got for the red spring was 26.653, the actual was 25. The percent error was 6.612% and the percent difference when comparing to class data (26.653 to class average of 25.874) was only 3.011% both of which are decent values. We found the white springs experimental to be 37.579 and the theoretical to be 40. The percent error was again low at 6.053% and the percent difference when comparing to the class data (37.579 to class average of 40.519) was 7.256%. The blue spring was found to have a spring constant of 30.837 with the actual being 30. The percent error was a low 2.79% and the percent difference (30.837 to class average of 30.569) was only 0.877%. The final spring we tested was the green spring, we found it to have a spring constant of 51.668 with the actual being 50. The percent error was 3.336% and the percent difference (51.668 to class average of 50.558) was 2.196%. This portion of the experiment was conducted well because all of our percent errors and percent differences were below 10% which means our results were good. For the second part of the lab we used the motion detector and a data-studio graph. When calculating the percent difference we found that most of ours results when compared to the averages were between 1.280-6.633% which is reasonable. For each of the three points minimum height, equilibrium, and maximum height we took three points of data. We averaged them and than found the percent difference when comparing to each entry.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">The experiment that we conducted was fairly accurate. There are a few sources of error that should be discussed. One possible source of error occurs when the person is measuring the spring after adding more masses. By mis-measuring the distance, all of the values for that specific spring would become slightly off. Another source of error could occur if a person attempted to measure the spring while it was still slightly moving. The way that we could fix this is by measuring with a more precise device or potentially having multiple people measure and than take the average. It would also improve the results if each group member allowed the spring sufficient time to stop moving before taking their measurement. The second part of the experiment was rather accurate. We used the motion detector locked onto a piece of cardboard attached to the spring. The only potential source of error that I could see is if the motion detector is not positioned correctly the results could be slightly off. It is also important to make sure the spring is moving above the lens of the detector. Its simple, make sure the detector is directly under the cardboard for the best results.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">A real life example would have to do with bungee jumping. When a person goes and bungee jumps into a gorge or river they trust that the spring/bungee will hold their weight. The owner of the bungee jumping place needs to make sure that the spring is capable of holding that amount of weight. He will determine the maximum weight a person can be and safely jump. Another example that we wouldn't really think of is a pen. The pen normally has one or two springs inside of it that move the mechanism up and down allowing the pen to extend and retract the tip. Springs are all around us, effecting many of the things we do in everyday life.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Roller coaster project: The Leap of Faith A new roller coaster brought to you by period 6 honors physics:




 * Sample Calculations:**

__Acceleration and g's calculation__ Theoretical Velocity % error

**//Part 3://**

The law of conservation of energy says that energy can not be created nor destroyed. Our roller coaster however experiences a work force out: friction. This caused the total energy to get smaller and smaller as the metal ball moves further down the roller coaster. Which means some of the energy was dissipated during the ride.
 * Energy Conservation:**

Power is the rate at which some work is done. In order for our ball to reach the starting point, the top of the coaster we needed to do work. At the top of the hill we have GPE. When we calculated it we came up with the value 0.243 J. We then inserted this into the power equation (P=w/t). We decided that a time of 2 seconds was reasonable. We wanted our guests to get right to the ride to maximize the number of rides we could give per day. We found we would need 0.123 watts of power.
 * Power:**

The metal ball used for testing the roller coaster spends the majority of its “ride” going down various slopes. This tells us that there is definitely acceleration. When the ball is released at the top point it accelerates down the incline picking up speed, thus gaining the speed needed to complete the ride in its entirety. As the slope of the incline changes the acceleration would also change, thus resulting in different accelerations throughout the duration of the ride. It is also important to understand that despite the various accelerations that occur the total energy remains the same, however some of it dissipates as the ride progresses.
 * Acceleration:**

Newtons three laws of motion affect almost every aspects of our lives. Our roller coaster exhibits all three of newtons laws. Newtons first law of motions states that an object in motion will stay in motion or that an object at rest will stay at rest unless acted upon by an unbalanced force. Our roller coaster demonstrates this law at the start of the ride. Initially the ball is at rest at the top of the coaster, the force of gravity pulls on the ball which sends it rolling down the track. Newtons second law of motion states that acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). Our roller coaster shows this because when the ball goes down a steep hill gravity causes the ball to speed up and when it goes up a hill the ball slows down. Newtons third law of motion states every action has an equal and opposite reaction. Our coaster demonstrates this at the end. When the ball nears the end of the tracks it hits into the wall of the horizontal loop which absorbs a large amount of the energy the ball had causing the ball to come to a complete stop thus ending the ride.
 * Newton’s Laws:**

The force placed on an object by gravity is equal to -9.8 m/s2. Gravity is the force that pulls everything down towards the surface of the earth (ground). Gravity acts on all object on earth. In our coaster gravity is pulling the ball down sending it rolling, the normal force of the track keeps the ball from touching the ground as it makes its way to the bottom. Apparent weight can be described as a change in the direction of weight. An example that occurs on our roller coaster would be at the vertical loop. At the top of the loop a person experiences a feeling of weightlessness. This occurs because there is no force supporting your body (essentially free fall like feeling) meaning that if you were not strapped into the cart you would be in free fall and probably hurt yourself badly.
 * Gravitation and Apparent Weight:**

Our roller coaster has a theoretical spring system in place to stop the cart in the event of the “brakes” failing. We can use Hooke’s Law to determine both the spring constant and the distance that the spring would compress when hit by the cart. Hooke’s Law says the strain is directly proportion to stress. Hooke’s Law is represented using the equation F=-kx, where k is the constant and x is compression/displacement. In our theoretical spring system the equation we used to determine the spring constant was GPE + KE = EPE. We settled on a compression (x) of .08m. We solved and determined that our spring would need a constant of 8 n/m in order to stop the ball.
 * Hooke's Law**

Circular motion is one of the many concepts applied on our roller coaster. We can describe circular motion as moving an object along the circumference of a circle. Our roller coaster has two circles, the horizontal loop and the vertical loop. Both are placed strategically. The two loops require a huge amount of energy for the cart to move around them. Thus we placed the circular loops right after hills in order for the ball to have the velocity required to move around it. It was also important for the hill not to be too long or at too sharp of an angle because that would cause the cart to hop the wall of the loop killing the passengers. (which is not good)
 * Circular Motion:**

**//Part 4://** Our percent error is quite high for some parts. This is mainly due to the fact that we lost a lot of stability in our roller coaster as we cut it apart to take the velocities. On some of the spot the ball would jump because the track lost it's tension and ability to keep the ball rolling. Also because the roller coaster is made out of paper, a large amount of energy was lost throughout the runs.


 * //Part 5://**

As the owners of the park we considered a couple options when buying the motor to bring the carts to the top of the hill. We went through several options and finally selected the caterpillar 500 watt diesel power supply. We decided that it would be smart to go with a good name company that provides durable products. Also by going with a slightly large unit we can ensure that the cart will have no problem reaching the top of the roller coaster for many year to come.



In this small scale experiment, we based our spring constant off the want to have the ball stop in .08 m. With this distance as a base, we found that we would need a spring constant of 8 N/m. Using this information, we found that the acceleration on the ball (the person/coaster) when stopping was 8.284m/s^2. Given that the average human can safely be accelerated at 4g's (39.2 m/s^2), our coaster is well within the safety constraints.
 * //5F - Stopping Spring System//**
 * Safety of the Spring Stopping System** -


 * //5E - Stopping The Ball//**

After creating and testing our roller coaster, we have found that it is not safe for public use. In order to for the roller coaster to be safe, the acceleration must not exceed 4g’s, or be under one. The first hill, which is where it starts, is a hard drop that leads into the horizontal loop. The acceleration at the top and bottom are both higher than 4g’s. The beginning is about 4.5g’s and at the of the hill right before the horizontal loop is 75.87g’s which would be physically impossible for any human to endure. The bottom of this incline is really the most strenuous part of our roller coaster, it has the highest value for g’s. As the ball turns around the horizontal loop, it slows down considerably and is 1.25g’s which is a good value for this area, we had to add covers onto this part to keep the track from buckling. As soon as the ball is outside of the first loop, it goes up a hill, and then shoots down into a vertical loop. This is a tricky and difficult place to be sure that it is safe, our average g amount for the top of the hump is 0.917g’s, which is very close to 1g, so as the ball passes this place it tends to feel a ‘jump’ because the lack of the .09g’s. As the ball goes from the top of the hill and accelerates to the bottom, the g’s change from about 1g to 4.5g’s for just a slight second before whizzing around the vertical loop. This amount of g’s is okay in this spot because it is just for a very slight second and then decreases. The person on the ride wouldn’t register the feeling before it was even gone. The scariest part of our roller coaster is the vertical loop, we know that the amount of g’s that is necessary to pass the top of the vertical loop is a minimum of 1g, but we have calculated that there was only 0.202 g’s when the ball was passing the top. This is most likely caused by the fact that when we recorded all of the time for specific location as well as the velocity, we had already started to cut the roller coaster apart. This is a problem because out coaster lost a lot of it’s stability and ability to work. The real amount of g’s at this spot was more, because in our three test runs that we submitted the ball easily went through the loop and continued down the roller coaster. After the top of the loop the rest of the roller coaster is very safe, after ball passes the top of the loop, it goes to the bottom of the loop and picks up enough speed that the g’s come to equal 3.677g’s. This is a great value for here, it easily fits in the guidelines for accepted g’s on a rollercoaster. At the top of the last hill the g’s are 0.732g’s which could be a little difficult for the rider to handle, but is safe with the right bars installed to keep people in their seats. The last hill ends with a low amount of g’s just 1.436g’s and then it finishes at 3.27g’s right before the circle that ends the roller coaster. The largest safety problem with our roller coaster is the huge acceleration on the first hill that most people wouldn’t survive. In order to make the other parts safe for riders there would need to have bars installed on all the seat so that people wouldn’t go flying out of the seats at the tops of the hills and the top of the vertical loop.
 * //Part 6://**

**//Part 7://**

__**Our roller coaster side view:**__ Picture:

Sketch:

__**Our roller coaster top view:**__ Picture:

Sketch:

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**__Our Roller coaster video:__** <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">media type="file" key="Magna Leffler, Joey Miller, Ben Sherman, Maddi Steele .mov" width="300" height="300"

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Elastic and inelastic collisions lab <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task A: Joey <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task B: Magna <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task C: Maddi <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task D: Ben

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Objective:
 * 1) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">** What is the relationship between the initial momentum and final momentum of a system **
 * 2) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">** Which collisions are elastic collisions and which ones are inelastic collisions? **

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Hypothesis:
 * 1) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Based on the law of conservation of momentum, the initial and the final momentum should be equal
 * 2) We believe that crashes 1, 2, 3, and 5 are all elastic crashes. This is based on the fact that either car A or B (or even both) start with a velocity not equaling zero and then either car or both end with a velocity not equaling zero. For crashes 4 and 6, we believe that they are inelastic because they either start with a velocity of zero, or end with a velocity of zero, so the initial KE wouldn't equal the Final KE. The deciding factor of this is the velocity because mass stays the same. If the velocity for the entire system changes drastically in a crash, the energy will not be conserved.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Methods and Materials: First we weighed and recorded each of our cars and weights. Then we attached a motion sensor to each side of the track. For each of the six different crashes we recorded the velocities in data studio, then put them into an excel sheet for calculations. We used two people to control the cars, and based on which lab we were working on had the cars crash head on, have a fender bender, or even explode away from each other.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Pictures: <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Analysis:

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Theoretical Problem for Analysis Question 3: <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden; text-align: left;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden; text-align: left;">
 * 1) Is momentum conserved in this experiment? Explain, using actual data from the lab.
 * 2) Yes momentum is conserved in all of the experiments but one. We know that it’s conserved based on the percent differences which all average out to under 20%. This shows that momentum is conserved because the initial and the final are very close and only have small changes to them. The only experiment that did not conserve momentum was the explosion. This doesn’t conserve momentum because it has a 200% difference.
 * 3) When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is.
 * 4) The Momentum equation is linear, so as one variable increases the other decreases. This is used to determine which car, the one with more mass or the one with less mass, has the greater velocity. The lighter car will have the greater velocity, because as the mass decreases the velocity will increase.
 * 5) When carts of unequal masses push away from each other, which cart has more momentum?
 * 6) Momentum =Mass X velocity, if the mass is large, the momentum will be as well. (See theoretical problems)
 * 7) Is the momentum dependent on which cart has its plunger cocked? Explain why or why.
 * 8) No, the momentum is not dependent on which cart has the plunger because they both have the same force acting on it, one is just a force going in the negative direction.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Conclusion:After completing this lab, I have found our hypothesis to be partly correct. For the first part of the hypothesis, that the initial and final momentum should be equal, is correct for elastic collisions, but not inelastic collisions. This was seen in the data; for an elastic collision, initial and final momentum should be equal (or close to it, given that this data is actual instead of theoretical), and it is for most of the trials. On the other hand, in an inelastic collision, kinetic energy is converted into another form of energy or heat, meaning that they should NOT be the same on both the initial and final momentum of the trial. This too was found to be true, but this is where the second part our hypothesis is found to be incorrect. We hypothesized that experiments four and six are inelastic because we assumed that in experiment four, the carts would stop when colliding and sticking, which they didn't, and little energy was lost, so it was found to be elastic. For experiment six, significant amounts of energy were lost, this being because the collision was inelastic. Also hypothesized was that experiments one, three, five, and two were elastic. After running the experiments, we found that this was true, because the percent difference for kinetic energy was relatively low for all of these experiments (as well as four). <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">To continue with the correctness of our hypothesis, for all of the experiments except the explosion, the kinetic energy percent difference ranged from 3% to 33%, which is an acceptable range. With these values, it shows that the experiments with the exception of the explosion were elastic, because energy was being relatively conserved. On the other hand, the explosions had percent difference values of 200%, which, although extremely high, is also sensible. Since the experiments with high percent errors were inelastic, this fits with the profile. The percent difference comparing the initial and final velocities was so high for the explosion because the carts were starting out with a velocity of zero, then rapidly increasing to a much higher velocity. When the percent difference was found for something like this, it was bound to be very high. The reason we compared percent difference of velocity between the initial and final velocities of the carts is because in an elastic collision, velocity remains constant throughout the experiment because the energy is conserved. In an inelastic collision, the initial energy is not conserved or is changed. So, a high percent error (like 200%), shows that the initial energy was far different than that of the final energy. In this experiment, especially during data collection, there were many points where the sensor readings would spike up, which may have been a potential source of error. When we analyzed the graph to find the data we needed, we may have selected the incorrect point on the graph, or not selected two points that were consistent with both sensor readouts. These spikes could have been caused by something getting in the way of the sensor; either the connection cable, a hand, or another object that could have found its way in front of the sensor. To correct such an issue, the test should be redone in a housing, in which the sensors, carts, and track are enclosed in something as to prevent any objects from interfering with the sensors. In this box, the carts would need to be motorized, with some form of variable speed control so that the scenarios could be accurately reenacted. In everyday life, we see examples of inelastic and elastic collisions all the time. First off, one example of an elastic collision is when you play pool. When a moving ball hits another, the other ball starts to move when hit, and kinetic energy is conserved. Although sound is heard (energy being converted), it is too miniscule to consider the collision inelastic. An example of an inelastic collision is a high speed car crash. At a high speed, if one car hits the others bumper, the bumper will crumble, and the behind car will not bounce back. At a lower speed, the bumper would keep its structural integrity and the behind car would merely bounce back after hitting the bumper, and the bumper would not crumble.

LAB: Ballistic Pendulum
<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task A: Ben <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task B: Maddi <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task C: Magna <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Task D: Joey

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">**Objective**: What is the initial speed of a ball fired into a ballistic pendulum?
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">The initial speed of a ball fired into the ballistic pendulum appears to be around 6 m/s. This hypothesis is based off of the ball-in-cup experiment.

First, we found the initial velocity of a metal ball using kinematics. To do so, we launched the ball at medium speed from a launcher onto carbon paper on the ground. We used a clamp to keep the launcher stable on the table. We then used a meter stick to measure the distance traveled by the ball. Next, we verified the initial velocity of a metal ball using a photogate and Data Studio. Using the same launcher setup, we launched the ball at medium speed through the photogate and Data Studio recorded its velocity. Last, we did our experiment to find the initial velocity of a metal ball fired into a ballistic pendulum. We first attached a ballistic pendulum to our previous launcher setup. We next launched the ball at medium speed into the ballistic pendulum, and recorded the maximum angle reached by the pendulum. Then, we set the angle indicator to an angle 1-2 degrees less than that reached in the previous step. We repeated this procedure multiple times, and recorded the maximum angle reached by the ballistic pendulum each time.
 * Methods and Materials:**

Picture:

Video: media type="file" key="IMG_0899.MOV" width="300" height="300" media type="file" key="IMG_0900.MOV" width="300" height="300"

Data Chart:

Sample Calcs:

Analysis

In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy? a.Elastic collisions conserve kinetic energy while Inelastic collisions do not. We found from the last lab that we did that the explosion had the highest loss of kinetic energy.
 * Consider the collision between the ball and pendulum. Is it elastic or inelastic?
 * We believe that the collision between the ball and pendulum was inelastic.
 * Is energy conserved?
 * No energy is not conserved when the ball and pendulum collide.
 * Is momentum conserved?
 * Yes momentum is conserved, this is because the law of conservation of momentum which all collisions abide to.

Consider the swing and rise of the pendulum and embedded ball. It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum.
 * Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height?
 * No energy is not conserved. This is because as the ball enters the pendulum it hits the clamp which makes it lose energy. Also it hits the back of the pendulum and is kept in the pendulum. Making the ball lose all of it’s initial energy.
 * How about momentum?
 * Yes this is based on the law of Conservation of Momentum which states that the total initial energy must equal the total final energy.
 * Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum.
 * [[image:Screen_shot_2012-03-20_at_12.12.25_PM.png]]
 * What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.
 * [[image:Screen_shot_2012-03-20_at_12.12.35_PM.png]]
 * According to your calculations, would it be valid to assume that energy was conserved in that collision?
 * Based on our calculations energy was not conserved in this collisoon, a total of 78.88% of the energy was lost when the ball hit the pendulum.
 * Calculate the ratio M/(m+M). Compare this ratio with the ratio calculated in part (b). Theoretically, there two ratios should be the same. State the level of agreement for these two quantities for your data.
 * [[image:Screen_shot_2012-03-20_at_12.15.48_PM.png]]
 * Our ratios are extremely similar, there was only a slight difference. This is good because it shows that our lab went extremely well, and that our data was congruent.

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.)
 * If the mass of the ball increases, the pendulum will swing higher upon impact. If the pendulum’s mass is increased, then the ball won’t have as much of an impact and it will not swing very high.

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 three calculated velocities were very close, which is very good because it means that our overall results were very congruent. Factors that could change this is when calculating the velocity using kinematics you are dealing with the x axis as well so the ball may go a certain distance but left or right skewing the results. The calculated velocity from the pendulum may be off because the angle may not have been perfect due to friction which may have slowed down the pendulum. The best way would be to use the photogate’s velocity which measured it right at the beginning with no friction or anything else to change it’s path. I would change it so that it ran on a path so that there would be no left and right movement. This would get rid of the uncertainty in the x axis which would help the results be more perfect.

Conclusion: The objective of the lab was to find the velocity of a ball. We used a few different methods. First we tested using a ballistic pendulum, then kinematics, and finally using a photogate sensor. We predicted that based on a pervious lab report (the ball in cup) that the velocity would be around 6m/s. The data that we got during the experiment fits our prediction pretty well. The pendulum supplied us with an average velocity of 5.74m/s. The kinematics and photogate methods produced average velocities of 5.55m/s and 5.31m/s respectively. These results are all close to each other which is good. They also are very close to the 6m/s that we predicated so we can say that our prediction was semi-correct!

All three of our calculated velocities were very close to each other. This means that our tests were successful and that there is not much error. If we examine the lab closely we noted that: The calculated velocity from the pendulum may be off because the angle may not have been perfect due to friction which may have slowed down the pendulum. The best way would be to use the photogate’s velocity which measured it right at the beginning with no friction to change it’s path. Small changes would minimize our error even more providing us with nearly perfect results.

We could have improved our results by doing a couple of things differently. First when determining the velocities at different points we should have run more trials. We ran between 5-10 trials for each but if we had increased the number of trials our results would have been even more accurate. Another potential source of error that could have effected the results relates to the launcher. The launcher is used often and the spring wears slightly creating slightly different velocities. It is also possible that the launcher could have shifted when we loaded the ball changing the position(kinematics). We used a clamp to hold the launcher steady but we could also have applied adhesive tape to secure it to the lab bench. A final source of error would be in the reading of the angle. When the ball fired into the pendulum it pushed the pendulum outward causing a metal rod to push an angle measurer. When we read the angle it is hard to determine an exact measurement. This would have thrown our results off slightly. We could have tried to minimize this by having multiple group members look at the slide and than averaging those values.

Some real life examples of things that move in a pendulum like state would be a grandfather clock. Also something like a metronome would follow the same pattern as the experiment we ran. For the kinematics and photogate trials we can use the examples of a gun being fired or even a rocket launcher launching a grenade. Many of the things we do in physics relate to real life problems and scenarios.