Navin,+Jimmy,+Steven

=__The Law of the Conservation of Momentum Lab__=


 * __Problem:__** Is the law of the Conservation of Momentum true, and does the initial momentum remain the same as the final momentum during a collision?


 * __Purpose:__** To find if the Law of the Conservation of Momentum applies to real head on collisions in different situations.


 * __Hypothesis:__** The law of the conservation of momentum will be true in our results because the net momentum (m1v1+m2v2) will equal the momentum after the collision (m1v1f+m2v2f).


 * __Materials:__**
 * Track
 * 2 carts
 * 2 motion sensors
 * laptop (with Datastudio)
 * mass
 * Excel spreadsheet


 * __Procedure:__**
 * 1) Get two sensors at each end of a frictionless track to measure distance over time.
 * 2) Place two carts on the track and in between the sensors
 * 3) Depending on which of the six ways you are planning on crashing the carts, place the carts a certain distance away from each other.
 * 4) With the sensors on recording, have the carts go through each of the collisions and record the data.
 * 5) two cars moving and bounce after colliding.
 * 6) Two cars moving and stick together after colliding.
 * 7) One car moving and bounces into the other during the collision.
 * 8) One car moving and sticks with the other during the collision.
 * 9) The two cars start together and 'explode' apart from one another.
 * 10) With the data recorded, use excel to find the momentum.
 * 11) Repeat steps 1-5 with varying masses on the carts to see how it affects the resulting momentum.


 * __Data:__**


 * Collison Type || Cart #1 Mass (kg) || Cart #2 Mass (kg) || Cart #1 Vi (m/s) || Cart #2 Vi (m/s) || Cart #1 Vf (m/s) || Cart #2 Vf (m/s) || Pi 1(kgm/s) || Pi 2(kgm/s) || Pf 1(kgm/s) || Pf 2(kgm/s) || Pav (kgm/s) || Percent Difference1 || KEi || KEf ||
 * One Bounce || 0.50 || 0.50 || 0.00 || 0.05 || 0.06 || 0.04 || 0.00 || 0.03 || 0.03 || 0.02 || 0.02 || 133.3333333 || 0.00125 || 0.005 ||
 * One Stick || 0.50 || 0.50 || 0.00 || 0.14 || 0.20 || 0.20 || 0.00 || 0.07 || 0.10 || 0.10 || 0.07 || 192.5925926 || 0.0098 || 0.08 ||
 * Two Bounce || 0.50 || 0.50 || -0.42 || 0.56 || 0.40 || -0.18 || -0.21 || 0.28 || 0.20 || -0.09 || 0.05 || 88.88888889 || 0.0098 || 0.0242 ||
 * Two Stick || 0.50 || 0.50 || -0.17 || 0.19 || 0.00 || 0.00 || -0.09 || 0.10 || 0.00 || 0.00 || 0.00 || 400 || 0.0002 || 0 ||
 * Explosion || 0.50 || 0.50 || 0.00 || 0.00 || 0.25 || -0.21 || 0.00 || 0.00 || 0.13 || -0.11 || 0.01 ||  || 0 || 0.0008 ||
 * One Bounce || 0.50 || 1.00 || 0.00 || 0.39 || 0.37 || 0.25 || 0.00 || 0.39 || 0.19 || 0.25 || 0.21 || 21.81818182 || 0.114075 || 0.2883 ||
 * One Stick || 0.50 || 1.00 || 0.00 || 0.32 || 0.26 || 0.26 || 0.00 || 0.32 || 0.13 || 0.26 || 0.18 || 39.43661972 || 0.0768 || 0.2028 ||
 * Two Bounce || 0.50 || 1.00 || -0.28 || 0.18 || 0.21 || -0.07 || -0.14 || 0.18 || 0.11 || -0.07 || 0.02 || 26.66666667 || 0.0075 || 0.0147 ||
 * Two Stick || 0.50 || 1.00 || -0.28 || 0.50 || 0.26 || 0.26 || -0.14 || 0.50 || 0.13 || 0.26 || 0.19 || 16 || 0.0363 || 0.2028 ||
 * Explosion || 0.50 || 1.00 || 0.00 || 0.00 || 0.28 || -0.14 || 0.00 || 0.00 || 0.14 || -0.14 || 0.00 ||  || 0 || 0.0147 ||

1. Is momentum conserved in this experiment? Explain, using actual data from the lab.
 * __Discussion Questions:__**

Because our percent differences were so big it appears as if momentum was not conserved. The first few trials we had an immense amount of error, including 192% for the "One Stick" Collision. Theoretically momentum is conserved, but our data can not support this conclusion.

2. When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is.

The cart with the less mass has a higher velocity. Based on the equation p = mv, if the mass decreases, the velocity increases.

3. When carts of unequal masses push away from each other, which cart has more momentum?

The carts, theoretically, have equal momenta. Initial momentum will equal final momentum, due to the law of conservation of momentum. The initial velocity of both carts is zero, but there masses are different. But the cart that has more mass will move slower than the other, thereby accounting for the difference in velocity, causing the momenta to be equal in the end.

4. Is the momentum dependent on which cart has its plunger cocked? Explain why or why.

The momentum is not dependent on the cart with the plunger because the plunger only increases the contact time of the two carts. This decreases the force between them and momentum is conserved.


 * __Conclusion:__**

We could not prove the legitimacy of the law of conservation of momentum. Our data was skewed by many factors that attributed to the high percent differences. For the explosion we could not calculate percent difference due to the fact that initial momentum was 0, making the percent difference 200% every time.

__ **Crushing Can Lab** __

__**Problem:**__

How much force causes a can to crush a certain distance? How can this experiment be compared to a car crash?

**__Purpose:__**

To find what the total crush energy using damage measurements with an aluminum soda can. Then these findings will be compared to a real car crash.

**__Hypothesis:__**

The crush energy calculated will equal the kinetic energy of the situation

**__Materials:__**


 * Three aluminum cans
 * Ruler
 * Metal ball
 * Note cards
 * Excel spreadsheet

**__Procedure:__**


 * 1) Use the ruler to measure the distance the ball is above the can.
 * 2) Release the ball over the can.
 * 3) Measure the width of the dent.
 * 4) Sculpt the notecard so it fits into the dent.
 * 5) Split up the note card into five equal sections.
 * 6) Find the crush energy for each section.
 * 7) Add up each section's crush energies to get the total crush energy.

**__Data:__**

**__Discussion Questions:__**

**__Conclusion:__**

= **__Hover Puck Lab__** =

__Problem:__ Does the law of the conservation of momentum hold true for two dimensional collisions? Is it true for elastic collisions and/or inelastic collisions?

__Purpose:__ To find if the conservation of momentum is true in two dimensional collisions at an angle in elastic and inelastic collisions.

__Hypothesis:__ The law of the conservation of momentum remains true with all collisions, elastic or inelastic, and regardless of the angles that they hit.

__Materials:__
 * 1) Two awesome hover pucks
 * 2) Measuring tape
 * 3) 1 timer to record how long it takes for the pucks to collide
 * 4) An excel spreadsheet
 * 5) two people to time the hover pucks after colliding and stop the pucks.
 * 6) Charger for the hover pucks
 * 7) Tape to label the initial positions of each hover puck.

__Procedure:__


 * 1) Make sure that both hover pucks are charged and functional.
 * 2) Place the hover pucks a set distance apart from one another, and record the distance.
 * 3) Push the hover pucks so that they collide at an angle. It is important to have someone time how long it takes for the pucks to hit one another, and another person to stop the hover pucks after colliding and time them after the collision.
 * 4) Keep the hover pucks exactly where they are and place tape there to mark where the hover puck stopped. This way, you can remove and turn off the hover pucks.
 * 5) Using the time for the first puck to hit the second, calculate the velocity(s) involved before the collision.
 * 6) Measure the distance that each puck travels away from the point of collision, and use the time recorded to calculate each puck's velocity after the collision.
 * 7) With the point of impact and the point where one of the hover pucks was stopped, create a right triangle where the distance between the point of collision and the end point is the hypotenuse.
 * 8) Measure the other legs of the right triangle, and use trigonometry to find the angle that each puck moved after the collision.
 * 9) Using the angles and velocities recorded, create an equation for the x and y axis momentum so that PiX=PfX and PiY=PfY
 * 10) Solve the equations to find if momentum was conserved.

__Data:__


 * Type of Collision || MA || Vai || Vaf || θA-B4 || θA-After || MB || VBi || VBf || θB-B4 || θB-After || PBefore-X || PAfter-X || PBefore-Y || PAfter-Y || Percent error ||
 * One Hit || 0.3 || 2.36 || 0.49 || 0 || 5.35 || 0.3 || 0 || 1.61 || 0 || 0.45 || 0.71 || 0.53 || 0 || 0.1 || 11.27 ||
 * One Hit || 0.3 || 2.71 || 0.26 || 0 || 0.79 || 0.3 || 0 || 1.58 || 0 || 0.11 || 0.82 || 0.53 || 0 || 0.11 || 21.95 ||
 * One Hit || 0.3 || 1.81 || 0.24 || 0 || 0.98 || 0.3 || 0 || 1.95 || 0 || 6.15 || 0.55 || 0.63 || 0 || -0.02 || 10.91 ||

__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 the most kinetic energy, while inelastic collisions lose kinetic energy. A maximum loss of kinetic energy would come from a collision that is extremely inelastic.

2. Consider the collision between the two hoverpucks. a. Is it elastic or inelastic? b. Is energy conserved? c. Is momentum conserved?
 * A collision between two hover pucks is inelastic, and but some of the energy is conserved. Some energy, however, is lost to friction and human error in recording our data. According to our results, momentum is almost entirely preserved, with some change possibly coming from friction and human error.

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? 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.

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

__Conclusion:__

=__Ballistic Pendulum Lab__=

__Purpose:__ To find the relationship between initial and final momenta of a ball fired into a ballistic pendulum.

__Hypothesis:__ As mass increases so does the initial and final momenta which are equal. This is proven by the law of conservation of momentum and the equation p=mv

__Materials:__
 * Projectile Launcher
 * Steel Ball
 * Pendulum
 * Plunger
 * Meter Stick
 * Carbon Paper
 * Measuring Tape

__Procedure:__ 1. Find the initial velocity of the launcher by using projectile motion 2. Put the ball in the launcher and prepare to shoot 3. Pull the string for the launcher and release the ball, which will move the pendulum 4. Move the angle dial back about a degree or so and repeat step 2 and 3 5. Record the angle 6. Change the mass of the pendulum and repeat steps 2 through 5

__Data:__

__Calculations:__

__Conclusion:__

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