Ani,+Ariel,+Sammy,+Rachel

=Lab: Ballistic Pendulum= toc
 * Group Members: Ani Papazian, Ariel Katz, Rachel Caspert, Sammy Wolfin**
 * Date Completed: 4/4/11**
 * Date Due: 4/5/11**

What is the initial velocity of a ballistic pendulum? Is momentum conserved? (Is the total initial momentum equal to the total final momentum?)
 * Problem:**

To find the initial velocity of a ballistic pendulum using the law of conservation of momentum, work-energy, and projectile motion. And, to verify the law of conservation of momentum.
 * Purpose:**

The initial velocity of a ballistic pendulum can be determined using the law of conservation of momentum. Momentum should be conserved, based on the law of conservation of energy. If momentum is conserved, the velocity found using the law of conservation of momentum equation should equal the velocity found using projectile motion. Due to the law of conservation of momentum, the total momentum before the pendulum is swung equals the net momentum after the pendulum is swung.
 * Hypothesis/Rationale:**

SAMMY
 * Materials:**

SAMMY
 * Procedure:**


 * Set up**:








 * Data:**


 * Sample Calculations:**
 * Using momentum conservation:**


 * Using projectile motion:**


 * Discussion Questions:**

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


 * 2. Consider the collision between the ball and pendulum. **
 * ** Is it elastic or inelastic? ** inelastic, KE is not conserved
 * ** Is energy conserved? ** yes, although the kinetic energy isn't conserved into kinetic energy, it is transformed to other types, like GPE (gravitational potential energy)
 * ** Is momentum conserved? ** yes

RACHEL
 * 3. Consider the swing and rise of the pendulum and embedded ball **
 * ** Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? **
 * ** How about momentum? **


 * 4. It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum. Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum.[[image:question_calcs_a_ariel.png]]**

No, it would not be valid to assume that energy was conserved during the collision, as there is a 73% loss in kinetic energy. The values agree with each other. There is a percent difference of about 7% between .73 and .78.
 * ** 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?**
 * ** 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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 * 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.) **

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

We initially hypothesized that we could find the initial velocity of the ball fired into the ballistic pendulum with two methods: projectile motion and conservation of momentum. We hypothesized that if momentum is conserved in this experiment, then the velocities calculated using the two different methods should equal each other. By measuring the height of the pendulum, we were able to calculate the final velocity of the ball, and using projectile motion equations (see sample calculations), we were able to come up with the initial velocity. Afterwards, we wanted to compare these values of initial velocity (found using projectile motion) to the values of initial velocity we found next (using conservation of momentum equations). We then calculated the percent differences (in the excel spreadsheet) which ranged from 2.42%-6.53%, which is negligible. For example, in our first trial using the medium-range speed on the launcher, we calculated an initial velocity of 3.53 m/s with projectile motion and 3.36 m/s with conservation of momentum. These results were very close, suggesting that momentum was conserved in this experiment. All of the percent error values are less than 7%, showing small sources of error in this experiment. However, as always, there is possibility of human error - marking the wrong spot that the ball hit the ground (which we tried to eliminate using carbon paper), rounding our measurements, and measuring the angle on the launcher incorrectly. In addition, it is possible that the launcher did not, in fact, launch the ball at the same initial velocity each time - the launchers are not known for consistency. Using more accurate tools in future experiments would probably result in less error. = = =Lab: 2-D Collisions with Hover Pucks=
 * Conclusion/Error Analysis:**
 * Group Members: Ani Papazian, Ariel Katz, Rachel Caspert, Sammy Wolfin (absent)**
 * Date Completed: 3/30/11**
 * Date Due: 4/1/11**

SAMMY
 * Problem:**

The purpose is to prove that momentum is conserved in this specific glancing collision on a two dimensional level. Momentum must be conserved in both an elastic and inelastic collision.
 * Purpose:**

In a two dimensional glancing collision momentum will be conserved whether it is elastic or inelastic.
 * Hypothesis/Rationale:**

We will be using 2 hover pucks and their launchers, a plumb bob, measuring tape, tape, protractor, sandbangs, and stopwatches. In addition we will be using excel on the computers to do calculations and make graphs.
 * Materials:**


 * Procedure:**
 * 1) Place puck A and puck B on the ground, marking their starting points with tape.
 * 2) Push each puck towards each other, so they collide
 * 3) Using timer, time each puck from push-off to collision, record time
 * 4) Mark the point of their collision, measure with a meter stick each puck's starting distance from the point of collision and record
 * 5) Stop both A and B a little after they collide, marking each's distance from the collision with tape and simultaneously timing them from collision to stop
 * 6) Using a meter stick, measure the distance of both puck's endpoints from the collision site and record
 * 7) Using a protractor, measure the final angles of puck A and puck B based on the tile lines as axes, record
 * 8) Repeat with many trials adjusting initial positions, initial speeds and types of collisions


 * Data:**



faded = initial position, opaque = final position The line drawn is equal to 1 meter in scale. This diagram shows our first trial.
 * Scale Diagram of Collisions:**




 * Sample Calculations:**

RACHEL **a. Is it elastic or inelastic?** Inelastic, kinetic energy is not conserved.
 * Discussion Questions:**
 * 1. In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy? **
 * 2. Consider the collision between the two hoverpucks. **

Although it should have theoretically been conserved, due to large percent errors we cannot conclude that in our experiment the momentum was actually conserved. This could be due to loss of energy, etc. (which would change the velocities, changing the momentum)
 * b. Is energy conserved? ** No, energy is lost - although hoverpucks are designed to negate effects of friction, friction is still a cause of lost energy. In addition, the actual act of collision between the two pucks resulted in loss of some energy.
 * c. Is momentum conserved? **


 * 3. It would greatly simplify the calculations if kinetic energy were conserved in the collision between two hover pucks. **
 * a. Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision. **
 * b. What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy. **
 * [[image:qb_ke_good_ariel.png]] ﻿ **

According to the calculations, it shows that kinetic energy was actually gained throughout the collision. Since we know that there were many sources of error regarding the velocity calculations, there is no way to assume that energy was conserved in the collision.
 * 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. **

Although this value is positive, and part b is negative, the values are somewhat comparable. There is an 18% percent difference between the two.

SAMMY
 * 4. What assumptions did we make that may affect our results? How would you change this lab to address these issues? **

The Law of Conservation of momentum states that total momentum before and after a collision should equal each other. This law holds true with glancing collisions. Therefore, mv + m2v2 = mvf+m2v2f. Although this law is a proven and scientifically respected law, our results were not completely consistent with it. In our first trial, there was a very high percent difference between the initial momentum and final momentum. On the x-axis, there was a 2250% difference in the momenta at the beginning and end of the collision. On the y-axis, there was a 100% difference. In our second trial, there was a 6% difference on the x axis and a 38% difference on the y-axis. In the ideal world, the experiment would yield a percent difference close to zero, as momentum should be conserved throughout a collision. There are many variables that led to error while collecting our results. The timing could have been more precise. The distances calculated may have been a little bit misleading since the hover pucks continued to move. Since velocity is calculated by dividing distance by time, the velocity may not be accurate. Also, kinetic energy of rotation "takes away" velocity. Additionally, it was difficult to mark exactly where the pucks hit into each other since it varies every time. This could have led to the angle measurements not being perfect despite leaving the x axis the same for all measurements. All of these sources of error will lead to potentially inaccurate results and a high percent error. In order to compensate for these sources of error, the procedure can be modified. It would be ideal to use a photogate to calculate velocity in order to have a more accurate and precise measurement. In the future, filming the collision can work as a useful tool because we will be able to project the collision and use a scale to calculate the measurements more accurately and precisely. It would also be ideal to use a larger group in order to avoid error due to multitasking. = =
 * Conclusion/Error Analysis:**

=Lab: Law of Conservation of Momentum=
 * Group Members: Ani Papazian, Ariel Katz, Rachel Caspert, Sammy Wolfin (absent)**
 * Date Completed: 3/28/11**
 * Date Due: 3/29/11**

Can the law of conservation of momentum be supported in various crash scenarios?
 * Problem:**

To determine if momentum is conserved in various crash scenarios.
 * Purpose:**

The momentum at the beginning of the collision will equal the momentum at the end of the collision in various crash scenarios. This hypothesis can be supported by the fact that: This equation shows the law of conservation of momentum. The total momentum at the beginning equals the total momentum at the end of a collision or explosion.
 * Hypothesis/Rationale:**

Track 2 cars weights of multiple masses computer (data studio) 2 velocity sensors
 * Materials:**

- Set up track with 2 cars on it - Plug the velocity sensors into data studio - Set up multiple crash scenerios (head on, one car at rest, cars moving at different velocities, cars with different masses, etc) - Record data from the graph that forms - Repeat for all crash scenarios - It is impossible to have multiple trials of one crash, so perform multiple crash scenarios and record
 * Procedure:**

media type="file" key="lab videoooo ariel.mov" width="300" height="300"


 * Data:**
 * Head-on Collision**



One At Rest, Moving in the Same Direction

Explosion

One at Rest, then Bounce Apart

Once at Rest, then Stick Together



Catch up


 * Excel:**






 * Calculations:**

1) Is momentum conserved in this experiment? Explain, using actual data from the lab. Based on our actual results from this lab, it is impossible to conclude that momentum is conserved in this experiment. This is because we had a percent difference. Because there was a percent difference, the values we recorded when plugged back into the equation that shows the law of conservation of momentum, both sides of the equation are not equal. Because of these results, although it makes sense for momentum to be conserved, we are not able to conclude that it did. The reason for the percent difference could have been because of the crash scenarios being hard to record accurately and friction.
 * Discussion Questions:**

2) When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is. When carts push away from each other, like in an explosion, the cart with less mass has a higher final velocity. If the two masses were equal, the two carts would have equal final velocities but in separate directions. But, since one cart is heavier, it takes more energy to move it at the same speed, but each cart has equal momentum which results in the heavier cart unable to move as quickly as the lighter one is. Also, in this type of collision, impulse and momentum are conserved. Since impulse=mv and the mass is greater, the velocity is smaller - they have an inverse relationship.

3) When carts of unequal masses push away from each other, which cart has more momentum? The final momentum needs to equal the initial momentum according to the law of conservation of momentum. The masses pushing away from each other can be compared to an explosion. Assuming that they both start at rest, the net initial momentum equals zero since velocity equals zero and initial momentum is calculated by adding together mass 1 x initial velocity and mass 2 x initial velocity 2. Therefore, the net final momentum has to equal zero as well. This means that the momentum of the two masses will need to be equal, but in opposite directions. The heavier mass will have a lower velocity and the lighter mass will have a higher velocity. This way mass 1 x final velocity + mass 2 x final velocity 2 will equal zero. Regardless of the mass the momentum of the carts will be equal to each other since the both mass and velocity change.

4) Is the momentum dependent on which cart has its plunger cocked? Explain why or why not. The momentum is not dependent on which cart has its plunger cocked. This is because energy cannot be created or destroyed. With one plunger cocked, the time of contact may changed, but energy should always be conserved. Although our results don't show a conservation in momentum, it can be assumed that which plunger cocked does not change momentum in the end.

RACHEL - USE SPECIFICS AND EXAMPLES FROM THE DATA DIJFLDKJFLDJFK
 * Conclusion:**

RACHEL
 * Error Analysis:**

=Lab: Crush Zone Energy=
 * Group Members: Ani Papazian, Ariel Katz, Rachel Caspert, Sammy Wolfin**
 * Date Completed: 3/21/11**
 * Date Due: 3/25/11**

What is the crush energy in the damaged zone of an aluminum can?
 * Problem:**

To determine the crush zone energy when a ball is dropped on an aluminum can.
 * Purpose:**

The ball dropped on the can will leave a crush zone and the crush zone energy is related to kinetic energy. This is because GPE at the beginning equals kinetic energy at the end due to the equation: GPE + KE + EPE + work = GPEf + KEf + EPEf.
 * Hypothesis/Rationale:**

Aluminum cans Aluminum balls Meter stick Index card Ruler
 * Materials:**

1. Place can sideways on table with an aluminum ball held a certain distance up. 2. Drop the ball. 3. Cut an index card so it fits as perfectly as it can in the dent the ball left. 4. Cut the newly cut index card into equal sections. 5. Measure the length of each section. 6. Do all the calculations with each measurement to determine the crush zone energy.
 * Procedure:**

media type="file" key="movvveecrush.mov" width="300" height="300"




 * Excel:**




 * Calculations/Percent Error:**

In conclusion, our lab on the Crush energy of the can was for the most part, successful. We figured out before the lab that the GPE or KE (which have the same value in this lab) should equal the Crush Energy of the can. Although we had a percent error, it was rather small, also showing our great success in the lab. There were a few sources of error however. Human error played a huge role in this lab. This is because we had to measure by hand. Because we measured by hand, our measurements of the crush zone, and how high up the ball was before it was dropped could have been slightly off. Cutting the card to fit the crush zone was tedious and difficult, and this could have provided error as well. Also, when we converted from centimeters to inches, we had to round our values. We originally measured all in centimeters, so when we changed to inches some of the values were rounded and altered. This was another source of error in our data. If we were to do this in the future, the method would be altered. The original method is designed for a car, not a soda can. This made it somewhat harder to do on such a small scale, so some things would have to be changed. Using crush energy to solve for velocity is not as accurate as other methods would be. Our group thinks that Kinematics could have helped us more in this particular lab and maybe would have been more accurate. Overall however, our experiment was rather successful and proved our hypothesis to be correct. Although the energy didn't match up exactly when put into the equation given in our hypothesis, the percent error was rather small.
 * Conclusion:**