Spencer,+Nicole,+Jillian,+and+Dylan

= = Lab: Reaction Time
 * Lab Group:** Spencer, Dylan, Jillian, Nicole
 * Date:** 3/18/11


 * Data:**


 * Sample Calculation:**

=Lab: Measuring Crush Energy=
 * Lab Group:** Spencer, Dylan, Jillian, Nicole
 * Date:** 3/22/11


 * Objective:** Estimate the Crush Energy from Damage Measurements on an aluminum soda can. The can will serve as an approximate model of an automobile.


 * Hypothesis:** The crush energy is the same (will be equal to) the initial kinetic energy and the initial potential energy of the ball.

- Soda cans - Metal ball bearing - Balance - Meter stick - Small ruler - Counter gauge
 * Materials:**


 * Procedure:**
 * 1) Find the mass and height of the can.
 * 2) Drop the ball onto the can from .5m high.
 * 3) Take a can that has not been used and trace it onto a piece of paper. Then take the crushed can and trace that on the same paper.
 * 4) Divide the crush into different zones.
 * 5) Determine the width and depth of each zone. Find the crush energies of each.
 * 6) Add the energies together to get the total crush energy. Set total crush energy equal to the car’s initial kinetic energy and find initial velocity.

Crush Energy: Velocity:
 * Data:**

Sample Calculation:

Our data doesn't allow me to conclude that the crush energy will equal to the initial potential energy and the initial potential energy, though we know that this is true. Our biggest source of error probably stems from the way we cut the paper. After dropping the ball on the can, we had to cut a piece of paper in the shape of the indent. This could very easily have been off, thus throwing off the rest of our calculations.
 * Conclusion:**

=Lab: Law of Conservation of Momentum=
 * Lab Group:** Spencer, Dylan, Jiliian, Nicole
 * Date:** 3/25/11


 * Objective:** To prove the Law of Conservation of Momentum is true.

(Rationale: The Law of Conservation of Momentum states that all the momentum in the beginning must equal the momentum in the end as long as it is in an isolated system.)
 * Hypothesis:** The initial momentum of the carts will equal the final momentum of the carts.

- 2 motion detectors - 2 500g carts - Multiple masses
 * Materials:**

1. Set up cars according to each trial 2. Push together car(s) 3. Use data studio to record velocity initial and final of each car for the same times 4. Repeat adding additional masses 5. Do this for trials 1-10 6. Use excel to calculate the percent differences
 * Procedure:**
 * TRIALS For excel worksheet**:
 * 1) Start at opposite sides move together
 * 2) Start at opposite sides move together one has a larger mass
 * 3) One’s at rest and they end together
 * 4) One’s at rest and they end together one has larger mass
 * 5) Explosion
 * 6) Explosion one has larger mass
 * 7) Moving in same direction and end together (both moving initially)
 * 8) Moving in same direction and end together (one has larger mass)
 * 9) Moving in same direction and bounce apart (both moving initially)
 * 10) Moving in same direction and bounce apart (one has larger mass)


 * Data**

.5 kg cart .49 kg cart


 * Discussion Questions:**
 * 1) Is momentum conserved in this experiment? Explain, using actual data from the lab. - Yes, momentum was conserved in this experiment. According to the equation m1vi1+m2vi2=m1vf1+m2vf2, momentum should be conserved. In this experiment, we calculated the momentum before and after each crash using the velocities found on data studio and the mass. If you look at our second trial, the momentum initially was -0.0221 and the momentum final was -0.0213, giving us a percent difference of only 3.69%. This is a good percent difference and shows how the momentum was conserved.
 * 2) When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is. - Because momentum equals mass times velocity, and the law of conservation says the momentum in the beginning must equal the momentum at the end, as mass decreases the velocity increases. Therefore the cart with the lighter mass will have a larger velocity.
 * 3) When carts of unequal masses push away from each other, which cart has more momentum? **-** The two carts should have equal momentums. Because of the law of conservation of momentum, the initial momentum will equal the final momentum. Because initial is zero, the momentums of the two carts should equal each other. Since they have equal momentums though, the heavier cart has will move slower than the one with a smaller mass, so the difference in the masses becomes balanced.
 * 4) Is the momentum dependent on which cart has its plunger cocked? Explain why or why. -No, it does not matter which cart has its plunger cocked. When the explosion happens, the momentum of the carts will change due to the plunger moving at a different velocity then both of the carts. Since the plunger will eventually be moving at the same speed as the cart, it makes no difference to the momentum.


 * Conclusion:**

We found momentum to be equal before and after the crash, proving our hypothesis to be true. Because we knew the masses and found the initial and final velocities, we were able to use the equation m1vi1+m2vi2=m1vf1+m2vf2. There were some fluctuating errors in our experiment, the highest being 200% to 3.69% error. These could have been human errors like not pushing the carts at the same time. Also we assumed the track to be level and frictionless, which it possibly was not. In the future, we would use motorized carts so they would go the same time and we would use a frictionless level surface. Even with all of the errors, we found that the momentums were very similar, proving Law of Conservation of Momentum to be correct.

=Lab:Hover Pucks 2D=
 * Group:** Spencer, Dylan, Jillian, Nicole
 * Date:** 3/30/11

Objective: **To show that the momentum is conserved in two dimmensions for elastic and inelastic collsions.**

Rationale: The law of conservation of momentum states all the momentum in te beginning must equal the momentum in the end, As long as it is in an isolated system and friction can be ignored. These hovercrafts have limited friction so we can ignore it and use the LCM to back up our hypothesis.
 * Hypothesis:** Momentum is conserved before and after a collision.

- Ruler - Tape - 2 hovercrafts - Stopwatches
 * Materials:**


 * Procedure:**
 * 1) Find the mass of the two hovercrafts.
 * 2) Tape the initial position of both hovercrafts.
 * 3) Turn them on and tape the position where they crash. Have someone else turn the stopwatch on until they crash.
 * 4) Have someone else start another stopwatch until their ending positions. Follow each hovercraft for a little and then tape where they end.
 * 5) Find the distance from the initial positions to the collision and the distance between the collision and the final position.
 * 6) Record data into excel and record results.

Sample Calculations:
 * Data:**



**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? Elastic collisions conserve kinetic energy and inelastic do not. The collision that result in maximum loss of kinetic energy is a perfectly inelastic collision.

2. Consider the collision between the two hoverpucks. a. Is it elastic or inelastic? -Inelastic b. Is energy conserved? -No, kinetic energy is not conserved in an inelastic collsion. c. Is momentum conserved? -Yes, momentum is always conserved due to the law of conservation of momentum.

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.

c. According to your calculations, would it be valid to assume that energy was conserved in that collision? Our calculations show that the kinetic energy was gained during the collision. We can not assume energy was conserved because there were many errors in this lab.

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. There is a 7% difference between the two.

4. What assumptions did we make that may affect our results? How would you change this lab to address these issues? -We assumed that the ground was frictionless but it might not have been. By not accounting for friction, it could have contributed to our error. Next time, we would calculate the coefficient of friction between the hover puck and the floor.

The Law of Conservation of momentum says the total momentum before a collision is equal to the total momentum after a collision. This law is true with the glancing collisions. Therefore, m1v1 + m2v2 = m1v1f+m2v2f. Though this is proven to be true, our results do not reflect this entirely accurately. In our second trial, there was a very high percent difference between the initial momentum and final momentum. On the y-axis, there was a 287% difference in the momentum at the beginning of the collision and at the end. On the x-axis, all of our % differences are high- around 200%. For our first trial and our third trial though, our percent differences on the y axis are pretty low which is good because this indicates that momentum almost fully conserved in the collision. The reason for this error could have been the timing and the distances. The person timing the first part could have started late and/or ended early. The same goes for the person timing the second part. The people stopping the pucks after the collision could have moved them slightly as well. This would effect all of our measurements and calculations. If we used a photo gate timer in this experiment, our results would probably have been much more accurate.
 * Conclusion:**

pictures:





=Lab: Ballistic Pendulum=
 * Lab Group:** Spencer, Dylan, Jillian, Nicole
 * Date:** 4/4/11


 * Objective**: Comparing the initial velocity of the ball found with the launcher and found with the pendulum.


 * Hypothesis**: By using the law of conservation of momentum we can find the initial velocity.


 * Rationale:** The law of conservation of momentum states the momentum initially (when the pendulum is at rest) should equal the momentum in the end (after the pendulum has been swung). If momentum is equal in the beginning and the end then the velocity found using m1vi +m2vf =m1vf +m2vf should be the same velocity as the velocity found by using projectile equations.

**Materials**:

- Projectile Launcher - Steel ball - Ruler - Carbon paper

**Procedure 1:**
 * Procedure**:
 * 1) Find the mass of the pendulum, stell ball and masses on the pendulum.
 * 2) Tape the carbon paper to the floor, with the projectile launcher on the desk.
 * 3) Put the steel ball in the projectile launcher and launch.
 * 4) Record the distance from the desk to the dot on the carbon paper. Do 9 trials.

**Procedure 2:**
 * 1) Use the projectile launcher and attach the pendulum and set the angle measurement to 0 °
 * 2) Launch steel ball on short range and read the angle measurement. Push the black arrow a few degrees back and launch steel ball again. Do this until you have 3 trials.
 * 3) Repeat steps 1 and 2 for medium range and long range. Record data.


 * Data**:

Sample Calculation



1. In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy? -Elastic collisions conserve kinetic energy and inelastic doesn't. A perfectly inelastic collision will produce maximum loss of kinetic energy.
 * Discussion Questions**:

2. Consider the collision between the ball and pendulum. a. Is it elastic or inelastic? -It is inelastic because kinetic energy was not conserved b. Is energy conserved? -Yes. Kinetic energy is not conserved, however the energy was converted into other forms such as GPE and therefore conserved. c. Is momentum conserved?

=
-Yes. According to the law of conservation of momentum, momentum is always conserved regardless of what kind of collision it is. =====

=
a. 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; the collision is inelastic so kinetic energy is not conserved.

b. How about momentum?
Yes momentum is conserved because of the law of conservation of momentum.

4. It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum. a. Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum. - KEi=(1/2)(m1)(v1-squared) + (1/2)(m2)(v2-squared) KEi=(1/2)(.066)(5.39-squared) + (1/2)(.994)(0-squared) KEi=.959 J KEf=(1/2)(m1f)(v1f-squared) + (1/2)(m2f)(v2f-squared) KEf=(1/2)(.066)((.334-squared) + (1/2)(.994)(.334-squared) KEf=.0037 + .0554  KEf= .0591 J  b. What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.  - (KEloss/KEi) = (.8999/.959)= .9384 - 93.84%  c. According to your calculations, would it be valid to assume that energy was conserved in that collision?  - No we cannot assume that energy was conserved after looking at our calculations because there was a 93.84 % loss of our in our lab.  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.  - .994/(.066+.994) = .9377 This percentage is comparable to the percent loss that I calculated in part b. There is only a percent difference of about .0746%

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.) - LINK DOESN'T WORK

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?

In this experiment, we were seeing if the velocity of the launcher found by a pendulum is the same as found using projectiles. For the short range launch, we got percent differences of 1.4%, 1.37%, and 5.78%. These are really good percent differences in this lab. For the medium range launch, we got percent differences of 18.76%, 18.17%, and 17.38%. For long range launch, we got 18.2%, 17.2%, and 17.45% differences. Some source of error we could have had in this lab was that when the ball launched into the pendulum and raised the angle measurement, a lot of energy was lost. We compensated for this by putting the angle measurement a few degrees lower than the angle we found and repeating the trial, therefore lessening the energy lost by the pendulum moving the angle up. However, there was still some energy loss. Overall, our hypothesis was shown to be correct. Our percent differences were low enough that without human error we can assume the velocities would have been the same.
 * Conclusion**: