Group3_6_ch6

toc Group 3 Jake Greenstein Remzi Tonuzi Lerna Girgin Brianna Behrens
 * Honors Physics Period 6 **

=The Law of Conservation of Energy= A: Brianna Behrens B: Jake Greenstein C: Lerna Girgin D: Remzi Tonuzi


 * Objective:** Find the relationship between changes in kinetic energy and changes in gravitational potential energy.


 * Hypothesis:** The initial energy of a system should equal the final energy of the system, due to the Law of Conservation of Energy.


 * Methods & Materials:**

** Station 1: ** Set up a ramp on an incline, with a photogate at the end. Drop a cart down a ramp, with a picket-fence attached. Record the time in gate. Measure the change in height, and length of black picket. Weigh the cart & fence.

**Station 2:**

Using a horizontal launcher, launch a ball at short range through a photogate. Measure the diameter of the ball, and record the time in gate. Weigh the mass of the ball. **Station 3:**

Hanging a mass on a string as a pendulum, raise it 20 cm from its start position, and drop it. Measure the time in gate using a photogate, and measure the width of the mass. Weigh the mass. **Station 4:**

Starting on the short end of the ramp, hold a metal ball at its highest point. Record the initial height, drop it, and record the height of its next highest point. Weigh the ball. **Station 5:**

Launch a ball vertically on short range. Record the time in gate, and measure the diameter of the ball. Weight the ball. **Station 6:**

Hold a ball at the top of a roller coaster ramp. Measure the height. Drop the ball, and record the time in gate at the top of the loop. Measure the diameter of the ball, and its height at the top of the loop. Weight the ball.


 * Data Table:**

Station 1; Station 2; Station 3; Station 4; Station 5; Station 6;


 * Sample Calculations/Analysis:**

**Station 1:** **Station 2:**Due to errors while performing this station, the data for this station was taken from period 2.

**Station 3:**

**Station 4:**

**Station 5:**

**Station 6:**



Our hypothesis for these six experiments was that the initial energy of a system should equal the final energy of the system due to the Law of Conservation of Energy. Our hypothesis was true, with the exception of one of the experiments, which had a percent difference of 47.9%. We compared the initial energy to final energy over total energy multiplied by 100 to find our percent difference. This was the third experiment. The other five experiments had percent differences under 14%, which is excellent. This means that our experiments were fairly accurate in that the final energy was pretty close to the initial energy of each experiment. Station one had a low percent difference of 8.38%. The percent difference of station two, the horizontal launch station, was very low, being 2.63%. Our original data for this experiment wasn’t useable because the experiment wasn’t set up correctly. There should have been a photogate in front of the launcher and one on the ground rather than two very close together in front of the launcher. We used period 2’s data instead. Station three is where most of the difference occurred. This experiment involved swinging a pendulum through a photogate. It contained 47.9% difference. The fourth experiment contained a percent difference of 13.53%. This is because the friction force wasn’t accounted for while the ball was rolling up and down the ramp, so the initial and final energies were different. The fifth and sixth stations had very low difference, fifth – 2.22% and the sixth – 1.26%. The experiments that had low percent differences kept the initial and final energies relatively close. The third experiment with the highest percent difference of 47.9% meant that the pendulum swung and lost energy in places we couldn’t justify. Overall, the results are pretty good except for station three of course. This proves that energy is transferred and not created or destroyed because of the low percent differences of our experiments.
 * Conclusion:**

=The Law of Conservation of Energy for Force of Spring= February 7, 2012

Part A-Remzi Part B-Lerna Part C-Jake Pard D-Brianna

-To directly determine the spring constant k of several springs by measuring the elongation of the spring for specific applied forces. -To measure the elastic potential energy of the spring. -To use a graph to find the work done in stretching the spring. -To measure the gravitational potential and kinetic energy at 3 positions during the spring oscillation.
 * __Objectives__: **

**__Hypothesis__:** The least compressed springs with the smallest change in distance will have the smallest k constant and the most compressed will have the greatest k constant and a greater change in distance. If the white spring k constant is 80,000, for example, the red will have a smaller value. The EPE of the red spring will smaller when the spring is compressed and bigger when it is elongated. As there are more masses put on the spring, work will also be increased. The GPE will be greater with the spring is compressed and the kinetic energy will be greater when the spring is elongated. This is all due to the law of conservation of energy and beacaus Kinetic and Gravitational energy are equal changes in them should balance.


 * __Methods and Procedure: __** Obtain all necessary materials. Take the springs and hook them up to the clamps on the ring stand. Next, use a meter stick to measure the distance from the table to each of the springs. Then, begin the five trials for each of the springs by placing different masses on each spring. Start off with just the 200g mass and work up to 400g and make sure to measure the distance from the table to the spring after putting on each mass. For part 2 of the lab, take a piece of cardboard and tape it to a 500g mass. Hook the mass on the red spring. Take a motion sensor and place it at the bottom of the spring to observe the graph for the three different positions of the spring when someone pulls it down. These are positions A, when the spring is elongated, B, when the spring is half way, and C when the spring is fully compressed.

__**Pictures: **__

Part I Part II A = Maximum, B = Equilibrium, and C = minimum
 * <span style="font-family: 'Times New Roman',Times,serif;">__Data__: **

f

<span style="font-family: 'Times New Roman',Times,serif; font-size: 160%;">**__Analysis:__**
 * __<span style="font-family: 'Times New Roman',Times,serif;">Graph: __**


 * __<span style="font-family: 'Times New Roman',Times,serif;">Sample Calculation - __**

__**Percent Error -**__

__**Percent Difference -**__

Initial and Total energy on Part II chart*

<span style="font-family: 'Times New Roman',Times,serif;">__**Discussion Questions**__ -
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">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) <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">Yes because the displacement doesn’t affect the spring constant. We can tell because the displacement of the spring versus the applied force is the same for other forces and the lines of best fit are directly proportional for each force.
 * 3) <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">How can you tell which spring is softer by merely looking at the graph?
 * 4) The line with a smaller constant will have a smaller slope because the line of best fit represents the spring constant.
 * 5) <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">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) <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">GPE is active when the hanging mass is at rest. When the spring is stretched, there is only EPE. KE and EPE are active when the spring is stretched and then released causing movement of the spring.

<span style="font-family: 'Times New Roman',Times,serif;">After completing this lab, our original hypothesis proved to be correct; the red spring did have the smallest constant k. As seen in the graph of the data above, the line with the smallest slope, evidently depicting the data of the red spring, has the smallest k value. The spring with the most ability to stretch would have a smaller k. All of the percent errors for the data were relatively close in range, from 0.253% of blue to 2.29% of white. The red spring had a percent error of 1.17% and the yellow had a percentage of 1.534%. Additionally, the percent differences pertaining to the results of other groups ranged from blue with a percentage of 2.57% and yellow with a value of 5.91%. White had a value of 4.28% and red had a percentage of 4.82%. Many aspects of the procedure can be attributed to the errors in the results. For example, the measurement of the change in distances may not have been entirely accurate due to placement of the meter stick and the precision of the decimal places. Also, because the springs were continuously oscillating due to surrounding factors such as the fan and ventilator, it was difficult to attain an accurate reading. Another contributing factor of error was reading the graph for the second part of the lab, which required multiple readings to gather the correct position of the point. To address these errors and improve the lab procedure, the experiment could be completed in a room without a vent, thus reducing the error in measuring the change in distances. Without a fan to continue the oscillation of the springs, reading the meter stick would be significantly easier. Also, multiple group members could have read the graph of the second part in order to give additional views of the position of each point. A real life application of this lab would be the use of bungee cords and determining the k value of the cord. This is important because by knowing the k constant of the cord, the maximum mass of the bungee jumper could be determined as well. Knowing the k value would make the use of bungee cords much safer for the jumpers.
 * __<span style="font-family: 'Times New Roman',Times,serif;">Conclusion: __**

=<span style="font-family: 'Times New Roman',Times,serif;">Roller Coaster Physics =

<span style="font-family: Arial,Helvetica,sans-serif;">Design & Construction- All <span style="font-family: Arial,Helvetica,sans-serif;">Experimental Calculations- Lerna, Remzi, Brianna <span style="font-family: Arial,Helvetica,sans-serif;">Theoretical Calculations- Jake <span style="font-family: Arial,Helvetica,sans-serif;">Written Analysis- All <span style="font-family: Arial,Helvetica,sans-serif;">Sample Calculations- Lerna, Jake

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//**<span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 200%;">T <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 200%;">h <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 200%;">e <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 200%;">R <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 200%;">a <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 200%;">g <span style="color: #ff00ff; font-family: 'Comic Sans MS',cursive; font-size: 200%;">e <span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 200%;">r **// <span style="font-family: 'Courier New',Courier,monospace; font-size: 140%;">__The Craziest & Most Exciting Roller Coaster of 2012!__

The physics team at Group 3 would like to present an excellent plan for a roller coaster, that should be built at all amusement parks immediately. We've dubbed it "The Rager", due to its intense level of loops, drops and hills. We realize, however, that you cannot build a roller coaster solely on its "awesomeness" factor, so we've taken the initiative to build and test a working model. We have concluded that not only is our design fun and exhilarating, not only are the colors eye catching, but from a practical perspective, the coaster is safe, and we've done the physics to prove it!
 * Sales Pitch**

"The Rager" begins with an initial drop down entering the vertical loop, where it then proceeds to approach the first hill. After passing the first hill, the ball passes through the double horizontal loop. Once reaching the bottom, it rises up the last hill and fall off the small drop and is stopped by our "spring system". Our support beams are cylinders. This is so because using cylinders for support keeps the roller coaster more stable and is much stronger than a rectangular support beam.
 * Written Description**


 * Diagram & Photos**






 * Vertical Loop & Free Body Diagram**

media type="file" key="Remzi, Jake, Lerna, Brianna.mov" width="300" height="300" media type="file" key="Group 3 photogate.mov" width="300" height="300"
 * Testing the roller coaster**
 * Photogate trial**


 * Theoretical Data**




 * Experimental Data**


 * % Error**


 * Sample Calculations**

GPE Theoretical Velocity

Experimental Velocity KE Theoretical Acceleration

Total Energy (down first hill)

Power Minimum Velocity at Top of Vertical Loop

Minimum Height at First Hill Energy Dissipated Percent Error: Down First Hill Actual Acceleration: Down First Hill

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">**Physics Concepts** <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">This roller coaster project encompasses numerous concepts from physics. A large portion of this laboratory assignment is centered around the Law of Conservation of Energy. Essentially, it states that the initial energy must equal the final energy, since energy is transferred and not destroyed. Therefore, in theory, if we can calculate the energy of the ball at the top of the roller coaster, it should equal the energy of the ball at the bottom. However, this is only theoretical, and will not accurately reflect our actual results, which is clear in our percent error table, with values ranging from 27% to 94% error. This is because the ball encounters air resistance and friction on the track, but mostly due to the the absorption of force from the flexibility of the roller coaster itself. Rather than the energy staying in the ball, the roller coaster absorbs a significant portion of the energy, which can be seen in the roller coaster bending and swaying. All of these factors act negatively on the ball, resulting in the appearance of a loss of energy at the end. However, we can solve for the other “missing” energy by comparing the error in our theoretical and experimental results. For example, the work, Force • Displacement, due to friction is negative because all along the track the friction force is opposing the movement of the ball. Although this value may not be big, throughout the coaster this force will oppose motion. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> **Power** <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> Power is defined as the rate at which work is done. It is calculated as work over time. We can calculate the power of the ball at any given point in the coaster. For example, when the ball goes down the first hill or the initial drop, power would be calculated by putting mgh over the experimental data from the photogate (the time). In this case, power would equal (.005)(9.8)(.86)/(.00582) which would be reduced to 7.24 J. Also, we can use this formula for power to calculate the power required to get the ball up to the top of the initial drop. We know the height, allowing us to solve for GPE, and we want the ball to reach the top in 5 seconds. By setting up Power = GPE/t, we get .00843. This means we need a motor that is capable of outputting .00843 Watts, in order to get the ball up a hill to the drop. Any of the small motors available at http://www.surplussales.com/motors/motors-3.html will be sufficient. The park owner need only to choose one of the small motors they have available. The motor will turn a spindle, in turn rotating a rubber track, which has flaps to cradle the ball as it ascends up the incline. At the top of the incline, the ball will then fall down the initial drop, and start the roller coaster. A diagram can be seen below: <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> The law of conservation of energy is a law that states that energy is only transferred, therefore the energy of a system should remain constant. This remained true in our roller coaster, however energy was transferred out of the system. In this roller coaster, the initial energy was greater than the final energy, which means that we have energy that is "missing". The law of conservation of energy tells us that this energy must have gone somewhere outside the system, which it did, since a large amount of energy was absorbed by the roller coaster itself. The paper tracks and paper supports are very flexible, and would bend and absorb energy throughout the ride. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> **Apparent Weight** <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> The apparent weight of ball on the roller coaster is different at each position. Gravity and normal force are the only two forces that affect the apparent weight, which can be described as a change in weight at different positions, such as weightlessness when falling. Weightlessness occurs when the normal force is zero, because there isn’t anything pushing up on the person. For example, at the top of a hill, there wouldn’t be any apparent weight because the normal force equals zero. At the bottom of a hill, the normal force is greater than weight. If we were to draw a free body diagram, the normal force would go towards the center of the circle and the weight down. People would therefore feel heavier at the bottom of a hill because the gravitational force is less than the apparent weight. By manipulating apparent weight in a roller coaster, you can increase the fun factor, giving the rider a rush as they feel themselves become weightless, only to have acceleration then push them back down into their seats. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> **Hooke’s Law** <span style="background-color: #ffffff; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">This roller coaster, like any roller coaster, depends on a spring to stop the car before it crashes at the end. In order to calculate what type of spring to use, we would use Hooke's law. The equation for Hooke's Law is force=-k*x, which means that the greater the force exerted on the spring, the greater the spring will have to compress if k remains constant. Therefore, since we don't want our spring to over-compress, or have to use too long of a spring, we can use a stronger spring. By solving for a k value, we can then compare springs based on their k values, and find a safe and reliable material to use as a spring. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">**Circular Motion** <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">In addition to these physics concepts, circular motion was included in our roller coaster. Circular motion occurs when an object is being accelerated by a centripetal force. This centripetal force, found in horizontal loops and vertical loops, points towards the positive center. On the vertical loop, circular motion is used to calculate the minimum velocity required at the top of the loop. Since gravity is the centripetal force, we calculated that our ball will successfully make it around the loop, without falling out. The theoretical acceleration for the horizontal loop was 1.3 m/s/s, and it ultimately made a safe loop. However, the ball did tend to move along the outside of the track, so as an extra precaution, this roller coaster used side rails to prevent the ball from accidentally falling off the track. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;">**Safety** As proven by hours of construction and multiple trials, the ball can safely drop down our roller coaster model. Constructionally, the use of cylinders as support for the base of the roller coaster kept it sturdy throughout the ball's drop, and rectangular beams supported the side of the tracks. Meanwhile, the speed and acceleration of the ball never reach a point of extremity that would cause it to continuously fly off of the track. The maximum value of acceleration equals 1g, or 9.8 m/s/s, and the minimum value is 1.3 m/s/s. In addition, the maximum velocity reaches 4.11 m/s and decreases to a minimum of 2.78 m/s. Our ball also never had an acceleration greater than 4g's on it, which means that, from an acceleration perspective, it is safe. Also, the ball exceeded the minimum velocity required to make it through the vertical loop, also making it safe for use. The only possible safety concern is the horizontal loop, since the ball tends to ride along the outside of the track. However, this is easily fixed with a guard rail along the side, ensuring that it is impossible to fly off. Throughout our test trials, we observed many things. First, we observed that our roller coaster is safe. Through the applications of physics concepts, we calculated that the acceleration stays within safe limits, the ball successfully makes it through all loops, and the ball never flies off the track. However, we also observed a large percent error in theoretical and experimental results. Because the Law of Conservation of Energy states that energy is transferred, we know that the majority of our error is due to the absorption of energy into the roller coaster. To build this roller coaster again, there are things we would change and things we would keep. For example, we found that our cylindrical supports were very effective in supporting weight. However, in order to make the structure more rigid, we would use more vertical supports, and connect them with horizontal trusses. In addition, we found that the roller coaster was far too flexible, especially in the loops. This is easily fixed by using stronger building materials. Paper is flimsy and delicate, and therefore bends easily. This bending allows the ball to transfer energy into the track and coaster itself, making it bend and sway. If we had used a stronger building material, this would have not been a problem. Real roller coasters use steel. Steel is far less flexible that paper, and therefore, had we done experimental results on a steel coaster, our percent error would have been far smaller. If we wanted to reduce the percent error even further, we need only to use a material less flexible than steel. Carbon fiber would be the ideal material. On bicycles, for example, carbon fiber racing bikes are superior to those made of steel. This is because when the rider pushes the pedals to exert energy, the high rigidity of carbon fiber allows for a better transfer of energy from the rider to the pavement, and lower percent error. Steel, while rigid compared to steel, is not as rigid as carbon fiber. Therefore, in the ideal coaster, we would use all carbon fiber parts to build it, allowing for an extremely low percent error and a faster, safer roller coaster. In the event of an emergency where the brakes fail to stop the coaster, an emergency spring system is a precaution that can prevent a serious accident from occurring. A spring can be used to absorb the remaining energy of the ball, stopping it, and preventing if from going flying off the track. Using the Law of Conservation of Energy, we can use the formula KE = EPE to understand how to transfer the remaining kinetic energy into elastic potential energy. Since the end of the roller coaster is on ground level, the Total Energy (TE) is equal to the Kinetic Energy (KE). Through our experiments we have found that the ball will have .005 joules of KE at the end of the coaster. Therefore, our spring needs to be able to absorb .005 joules. However, there is another problem; since we have other coasters nearby, we don't have much distance to extend the coaster. An extended track is necessary to put the spring on, so the ball can decelerate. Since we are limited to .1 m of space, our x value (distance of compression) is .1. Therefore, by solving for k, the spring constant, we can figure out what type of spring to use, to stop the ball in .1 meters.
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 13px; text-decoration: none; vertical-align: baseline;"> Conservation of Energy **
 * Error & Uncertainty**
 * Emergency Spring System**

Therefore, we can increase the safety of our roller coaster by having an emergency spring system. By laying the spring horizontally on the track, the ball could compress the spring .1 meters and come to a full stop, given that the spring has a k constant of .05. In addition, we need to be sure the spring doesn't stop the ball too fast. If the acceleration exceeds 4g's (39.2 m/s/s) then the emergency spring is unsafe. To calculate the acceleration, we first calculate the time that the ball will take to stop. Then, we can calculate the acceleration.

Finally, the results show that our spring system is safe, with an acceleration under 4 g's. A diagram of the spring system is below.

=Elastic and Inelastic Collisions Lab= March 6, 2012

A: Jake B: Remzi C: Brianna D: Lerna

Determine the relationship between initial momentum and final momentum of a system Determine which of the collisions are elastic and which are inelastic
 * Objective:**


 * Hypothesis:**

According to the law of conservation of momentum, the initial momentum should be equal to the final momentum. Also, inelastic collisions won't conserve Kinetic Energy, but elastic collisions will.


 * Methods & Materials:**

First, we set up the track and leveled it so that gravity didn't influence movement in one direction. We then set up the motion detectors and attached them to each end of the track to detect the initial velocities and collisions of the carts. We plugged the motion detectors into the computers with the USB links and used Data Studio. We put two carts on the track and used them to experiment with various types of collisions.


 * Data:**


 * Cart B Graphs:**










 * Cart A graph:**




 * Pictures:**

media type="file" key="Movie on 2012-03-08 at 13.04.mov" width="300" height="300"
 * Video:**


 * Analysis/Sample Calcualtions:**

Momentum is not conserved in this experiment because in each trial for the varying collisions, the initial kinetic energy is not equal to the final kinetic energy. For example, in the "both in motion (sticking)" collision, the initial kinetic energy ranged from 0.02 to 0.1 and resulted in 0.0 final kinetic energy.
 * 1. Is momentum conserved in this experiment? Explain, using actual data from the lab. **

According to the data table above, the cart with less mass, as in the explosion collision, has a higher velocity. This is because the force of the explosion pushes the cart with less mass at a higher speed.
 * 2. When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is. **

When carts of unequal masses push away from each other, their momentum is equal because the mass • ∆velocity for each results in an equal value, as seen in the explosion collision.
 * 3. When carts of unequal masses push away from each other, which cart has more momentum? **

No it is not, because though the lighter cart has a higher velocity, the heavier cart has a greater mass; therefore, when multiplied together, each cart has equal momentum. The plunger has no effect.
 * 4. Is the momentum dependent on which cart has its plunger cocked? Explain why or why not. **

Explosion Trial 1 Sample Calculations:

The hypotheses made at the beginning of this lab proved to be fairly true according to the data obtained. The initial momentum was either close or exactly the same as the final momentum for each of the trials performed. The initial momentum obtained for explosion trial 2 was 0 and the final was -.001 which equaled to a percent difference of -200%. The initial momentum achieved for trial one when cart A was in motion and B at rest (sticking) was .251 and the final momentum, was .257 and had a percent difference of 2.19% which is very good. However, kinetic energy was not well conserved during some of the elastic and inelastic collisions such as when A was in motion and B was at rest (bouncing) because their percent differences were high. For example, in trial 1 the initial kinetic energy was equal to .06 and the final was 0.05 with a percent difference of 26.34%. This data shows that when the carts bounced off of each other, kinetic energy was conserved and almost equal to what it was when it started. Some of the errors that came across in this experiment were big percent differences. This was the case for when cart A and B were both in motion (bouncing). The initial kinetic energy was .16 and the final was .09 and a percent difference of 53.58% which is fairly high. This error could have been due to the problem of making the track for the carts balanced. Many times during the lab, the carts would roll down one side of the track and it was difficult to make it perfectly balanced. This could have thrown off some of the results like the ones that were obtained for both in motion (bouncing). Another source of error could have been from misreading the graphs that were produced from the trials on datastudio. Several times, the wrong point on the graph was taking instead of the right one, which affected the percent differences. In order to make this lab more accurate, several things would have to be changed. First, to make sure the track was perfectly balanced a balancing tool could have been used. This would have made the carts perfectly at rest and would have provided better results. In addition, when collecting the data points from the graphs, two people could have read the same point to get the exact point. A real life situation of this experiment could be seen in car crashes when the bumper is damaged or has fallen off. By using LCM, one could figure out the magnitude of the momentum that was placed on the car's bumper.
 * Conclusion:**

=Ballistic Pendulum Lab= March 13, 2012

A: Lerna B: Brianna C: Remzi D: Jake


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


 * Hypothesis:** Our group hypothesizes that the ball's initial speed will be 4 m/s. We make this hypothesis based on the knowledge acquired from previous labs, such as the Shoot Your Grade lab. While we used a medium range previously, we will use a smaller range for this lab, along with a heavier ball. This results in a lesser initial velocity, thus justifying our hypothesis of 4 m/s.


 * Methods and Materials:** Before beginning, we acquired all of the necessary and available materials for this lab. For the LCE method, we set the projectile launcher and clamped it to the table. Then we attached the ballistic pendulum to the top of the launcher. The metal ball was set at short range and launched into the pendulum for multiple trials. For the kinematics method, we removed the ballistic pendulum and launched the ball to gage a reasonable landing distance, in order to tape down the black carbon paper. We launched the ball for multiple trials. Then for the photogate method, we positioned a photogate at the opening of the launcher and attached the USB link to the laptop. We recorded multiple trials for this method.

Method 1: LCE media type="file" key="Movie on 2012-03-13 at 12.50.mov" width="300" height="300" Method 2: Kinematics media type="file" key="Movie on 2012-03-13 at 12.53.mov" width="300" height="300" Method 3: Photogate media type="file" key="Movie on 2012-03-13 at 13.06.mov" width="300" height="300"
 * Video:**

Photogate timer
 * Picture:**
 * Data:**


 * Analysis / Sample Calculation**



Percent Error:

Discussion Questions: Discussion Questions:

In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?


 * //** Collisions that conserve kinetic energy are elastic collisions. Inelastic collisions are collisions that don't conserve kinetic energy. This occurred when two objects with the same momentum are moving in opposite directions, crash, and stop completely. This yielded the greatest loss in kinetic energy. **//

Consider the collision between the ball and pendulum. //** It is inelastic. **//
 * 1) Is it elastic or inelastic?

//** No, because KE is not conserved. Some KE is lost due to the inelastic nature of the collision. **//
 * 1) Is energy conserved?

c. Is momentum conserved? //** Yes, the momentum is conserved in all collisions, which we know due to the Law of Conservation of Momentum. **//

Consider the swing and rise of the pendulum and embedded ball.

//** No, because in an inelastic collision, Kinetic energy cannot be conserved, therefore proving that there is no conserved energy. Upon using our Law of Conservation of Energy equations, it is clear that the energy of the system changes. **//
 * 1) 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? //** Yes, momentum is conserved for all collisions. Upon colliding with the ballistic pendulum, the momentum of the ball is transferred to the ballistic pendulum, yielding a new momentum, due to the combination of masses. **//

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.

According to your calculations, would it be valid to assume that energy was conserved in that collision?

//** No, it was not conserved, because there was a difference in the Kinetic Energies. **//

// **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.** **?????**//

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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.)


 * // When the mass of the ball is increased, the height increases, but if the mass of the pendulum increases, it has the opposite effect. The height of the pendulum decreases when it’s mass is increased. //**

Is there a significant difference between the three calculated values of velocity? What factors would increase the difference between these results? How would you build a ballistic pendulum so that momentum method gave better results?

//There wasn't a significant difference for LCE and LCM compared to the Photogate data. There was only a percent error of 3.05% and the difference between the velocities was only .11. As for the Kinematics method compared to the Photogate data, there was a percent error of 13.10%. Although this ins not that high, it was above 10% and indicates that something caused the percent error to be above 10% and had to do with a factor pertaining to the Kinematics method. The difference in velocity was .43, and a factor that caused it could have been the measurements of the distances from the launcher to the carbon paper placed on the ground were off. Also, another factor could have been that the spring, from being used multiple times, became "soft" and decreased the initial velocity by a little bit. Also, a sphere isn't very aerodynamic and so the air resistance in caused part of the difference in the Kinematics method. This is not the best way to measure the initial velocity of the ball. If I were to build a pendulum so that it would give me better results, I would use something, such as a dart, with the same mass as the ball. I would make sure that it could pierce through the pendulum so that it minimizes resistance that the pendulum provides when the ball is entering. I would also lubricate the hinge that the pendulum pivots on so that it minimizes the resistance on that as well. This could give me better results and help reduce the percent error.//


 * Conclusion:**

After obtaining all date for this experiment, the hypothesis was fairly correct. The velocity that was hypothesized was 4 m/s because of previous labs that were done with launchers. However, it wasn't exactly correct as the true velocity when using photogate was 3. 71 m/s. In addition, through analyzing percent error, we decided that kinematics was not the best method in figuring out the velocity. In measuring the initial velocity of the ball, we utilized numerous physics concepts. By solving the problem with 3 different methods, we collected a data set that allows us to compare the accuracy of the results of different methods. We knew from the beginning that the photogate trial would yield the most accurate representation of our velocity. By comparison, the next most accurate method of measuring velocity was the LCE/LCM method. While the ball is first shot, we can calculate the velocity when it hits the ballistic pendulum by using the Law of Conservation of Momentum. Since momentum is never lost and is only transferred to the new system, this yielded accurate mathematical results in comparison to the photogate trials. Then, once the ball is in the catcher, it accelerates and speeds up, which can be represented by the Law of Conservation of Energy. By setting up our equation as KE = GPE, we can solve for the final velocity. With that, we can go back to our LCM equation, plug in Vf, and solve for Vi. Since this method is based on fundamental rules of physics, our results had little percent error. The velocity that was measured using the LCM method was 3.59 m/s for the first trial and when compared to the velocity from the photogate method which was 3.71 m/s the percent error was only 5.04%. The small percent error shows that the LCM method was in fact better. Finally, the Kinematics method was the least accurate. The procedure itself left much room for human error, in making accurate measurements of the distances traveled. Since the ball is being shot the farthest distance in this experiment, it experiences the most air resistance, throwing off our results. This method would be a poor way of trying to calculate initial velocity. For example, in the first trial using the Kinematics method, the velocity obtained was 3.26 m/s and compared to the velocity from the photogate, 3. 71 m/s the percent error was up to 15.67%. Because this is a larger percent error, the LCM method was proven to be better. The large percent errors that came from using the kinematics method could be due to several things. First, the distances could have been measured wrong which could throw off the results. In addition, another source of error could have come from the spring being outstretch after every launch which could have made the velocity smaller each time. In order to fix this, the group could have use a tape measure so that the reading of the measurements could be exact and the group could also have compared the five results of the outstretched spring to a cold spring from an unused launcher. In retrospect, the best way to calculate initial velocity would have been with a motion sensor set up directly across from the launcher. The laser would have directly measured the velocity as the ball accelerated in the launcher, and given the most accurate reading once the ball was launched. This type of experiment applies to real life. In a car accident, detectives need to use evidence and clues to identify who is at fault and how the collision occurred. Since the officers could not have had photogates and motion sensors at the time of the collision, they use clues such as skid marks to calculate the distances the cars traveled. With information such as the mass of the car, the coefficient of friction between the rubber and the street, and the distance skidded, a detective would use the same methods we used to decipher how the collision occurred, how fast the cars were moving, and who was at fault.