Lab: Ballistic Pendulum

Date: April 4th, 2011
Members: Roshni, Allison, Emily
Honors Physics, Period 2

PROBLEM
What is the relationship between initial and final momenta of a ball fired into a ballistic pendulum?

OBJECTIVE
To find the relationship between the initial and final momenta of a ball fired into a ballistic pendulum

HYPOTHESIS
Since the law of conservation of momentum always holds true, and we know that the masses will never change, the initial velocity of the ballistic pendulum can be found because it will equal the final velocity. The initial and final energies will only be different because the collision of the ball and the pendulum will be inelastic.

MATERIALS
Projectile Launcher
Steel ball
Plumb bob
Meterstick
Photogate timers (2) + bracket
Smart timer
C-clamp
Mass balance
String
Ruler

PROCEDURE
  1. Mass the pendulum, steel ball, and the masses on the pendulum.
  2. Set up the carbon paper slightly in front of the projectile launcher and tape to ground.
  3. Load steel ball into the projectile launcher without the pendulum. Experiment with a trial to make sure the ball hits the carbon paper.
  4. Release ball and record length from launcher.
  5. Repeat steps 3-4 three times.
  6. Attach pendulum to the projectile launcher and set angle measure to 0 degrees.
  7. Launch steel ball. Read the angle measure and push the black angle measurer back about 1-2 degrees.
  8. Re-launch steel ball. Read and record angle. Repeat 5 times.
  9. Unscrew the bottom of the pendulum where the masses are and remove one mass.
  10. Repeat steps 7-8.
  11. Again, unscrew the bottom of the pendulum and remove another mass. Repeat steps 7-8 again.


DATA
EB2P3_pendulum_data.png

CALCULATIONS
EBP3_pc1.png
EB2P3_pc2.png
EB2P3_pc3.png
EB2P3_pendata3.png
EB2P3_pendata4.png
EB2P3_pendata5.png

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. In elastic collisions do not.
    • Any collision that causes energy to be lost as heat or any other forms will result in the maximum loss of kinetic energy. These collisions usually involve other forces within the system (e. friction of a bumpy road).
  2. Consider the collision between the ball and the pendulum.
    • Is it elastic or inelastic?
      • It is inelastic.
    • Is energy conserved?
      • Yes. It is converted to other forms so it is not Kinetic Energy anymore, but it is still energy.
    • Is momentum conserved?
      • Yes, because momentum is always conserved.
  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?
      • No (the collision is inelastic, and the metal balls stick together).
    • How about momentum?
      • Yes. Momentum is always conserved (LCM).
  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.
    calcsssssss_ballistic_pendulum.png
    • What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.
    percent_lostttttttttttttt.png
    • According to your calculations, would it be valid to assume that energy was conserved in that collision?
      • No, because we have a 73% loss of kinetic energy.
    • Calculate the ratio M/(m+M). Compare this ratio with the ration calculated in part B. Theoretically, these two ratios should be the same. State the level of agreement for these two quantities for your data.
      • The values match up well.
    mmmmmmmmmm.png
  5. Go to http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/ . 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 DOES NOT 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?
    • LINK DOES NOT WORK


CONCLUSION
After doing this Ballistic Pendulum lab, we found the relationship between the initial and final momenta of a ball fired into a ballistic pendulum. During this lab we found the collision to be inelastic with energy and momentum conserved. Our hypothesis was proven correct because with the masses staying the same and momentum being conserved, the initial velocity will always equal the final velocity. The inelastic collision between the ball and the ballistic pendulum only changes the amount of energy. Although our calculated velocity does not exactly match up with our data, we aren't far off at all. The human error that was apart of this lab is the main reason why our calculations and data aren't the same. While receiving the angle measure of how high the pendulum went, we sometimes moved the angle measurer. This would give us inaccurate readings on what the angle actually was, causing our velocity to be higher or lower. Also, our launcher didn't seem to have the same initial velocity every time which also threw off our data. In conclusion, we found the relationship between the ball and the pendulum and our hypothesis of what the relationship was going to be was correct.

Activity: Hover Puck Collisions

Date: March 30th, 2011
Members: Roshni, Allison, Emily
Honors Physics, Period 2

PROBLEM
What are the final speeds and final angles of the two colliding Hover Pucks?

OBJECTIVE
To use our knowledge of momentum to determine what speed and angle each Hover Puck will be after colliding. By doing this, we will be proving that momentum is conserved on both x and y axes during a collision.

MATERIALS
Stopwatches (4)
Hover Pucks (2)
Masking Tape
Meterstick
Protactor

HYPOTHESIS
If the law of conservation of momentum holds true, momentum and energy will both be conserved in 2 dimensions for both inelastic as well as elastic collisions. This is because net momentum will never change (m1v1i+m2v2i = m1v1f+m2v2f).

PROCEDURE
  1. Place two pucks away from each other on one axis, and use tape to mark starting positions.
  2. Use two timers to record how long it takes for A and B each to go from rest to the collision.
  3. Stop both A and B after they move away from the collision, while simultaneously using the other two timers to record how the time from the collision to when they are stopped (at rest).
  4. Tape the collision point and the final positions of A and B.
  5. Use a meterstick to measure the distances from the starting points of A and B to the collision, and the distances from the collision to the final points of A and B.
  6. Use a protractor to measure the angles that A and B create after the collision.
  7. Repeat steps 1-6 above for the different trials and different types of collisions. Adjust velocities and positions of the hover pucks to match the different types of collisions.


COLLISION DIAGRAMS
drawn to scale
-faded is before collision & darker is after collision
EB2P3_PUCK1.png
EB2P3_PUCK2.png
EB2P3_PUCK3.png
DATA

EB2P3_hover_data1.png
EB2P3_hover_data2.png
CALCULATIONS
EB2P3_calc1.png
EB2P3_calc2.png
EB2P3_calc3.png
EB2P3_calc4.png
EB2P3_calc6.png
EB2P3_calc7.png
EB2P3calc8.png
EB2P3_calc9.png
EB2P3_calc10.png

CONCLUSION
Although we had an extremely high percent difference, qualitatively our lab was correct. We had the right set up and our hypothesis was on target. The only problem was the amount of human error that came into play. There were so many things that could have been done to make our lab better. With timing we could have stopped it a couple of seconds early or late. There was also some trouble with finding exact positions of the hover pucks because they kept moving. Also, the fact that the hover puck rotated made it loose KE which took away from the velocity. We could have easily fixed these issues if we filmed the collision from a bird's eye view. If we filmed the collision from up above we could get the exact times by using the timer on the film and we could get the exact distances where the collision happened and where we stopped the hover pucks. Also if we put in photogate times we would have gotten the exact velocity of the hover pucks. In conclusion we found our hypothesis true. Momentum was conserved both on the x and y axis no matter how big the percent difference was.

Lab: Elastic and Inelastic Collisions

Date: March 25th, 2011
Members: Roshni, Allison, Emily
Honors Physics, Period 2

PROBLEM
What is the relationship between the initial momentum and final momentum of a system?

OBJECTIVE
To determine if the Law of Conservation of Momentum holds true, if total momentum is always conserved before and after a collision.

MATERIALS
- 2 carts
- masses
- dynamic track
- 2 motion detectors
- 2 USB links

SETUP
SETUProshniallisonericaemilyaaronevan_.jpg

HYPOTHESIS
Because the Law of Conservation of Momentum states that momentum must always be conserved in a collision and explosion, the final and initial momentums of our experiment should be very similar, if not exactly the same.

PROCEDURE
For this lab, we are testing out different types of explosions and collisions, and measuring the absolute difference between their momentums before and after.
  • Collision 1: The carts were moving together and then they bounced off each other and separated.
  • Collision 2: The two carts were moving together and they stayed stuck to each other (did not separate).
  • Explosion 1: We attach the two carts together, turn on the motion sensor, and use a weight to hit the plunger that is holding them together. The carts come apart (explode) and we measure the final momentum of this system (and compare it to the initial momentum).
  • Collision 3: One cart was at rest, and one was moving. The moving cart bounced off of the at-rest one and then set it in motion.
  • Collision 4: One cart was at rest and one was moving. Instead of bouncing off, the moving cart stuck to the at rest one but still set it in motion (they moved together, as one object).
  • Collision 5: The two carts were moving in the same direction and they bounced off each other.
  • Collision 6: The two carts were moving in the same direction and they stuck together and moved together.

DATA

EB2P3_cart_data.png


CALCULATIONS
EB2P3_P_EQNS.png












EB2P3_%diff.png
EB2P3_abs_diff.png


GRAPHS
emilyroshniallisonLABpics.png

ANALYSIS QUESTIONS
1. Is momentum conserved in this experiment? Explain, using actual data from the lab.
  • Yes, momentum is always conserved in this experiment. We know this because our percent difference between final and initial momentums were minimal, between 0% and 23.66%. (See data table above).

2. When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is.
  • During this explosion the lighter cart has a higher velocity. This is because of the equation Ft=mv. Since the impulse (Ft) is constant, (the force and the time are the same for both), the impulse divided by the mass equals the velocity. The smaller the mass is, the higher the velocity is.

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

4. Is the momentum dependent on which cart has its plunger cocked? Explain why or why not.
  • No because they are acting as one system with net momentum. Therefore, it does not make a difference which one has its plunger cocked.

CONCLUSION
In conclusion, we found our hypothesis to be correct. We found the momentum to be the same before and after the crash. Although we had some error, our calculations were mainly pretty good. By finding the initial and final velocities of the two carts and knowing the mass, we were able to use the momentum equation, p=mv, to prove our hypothesis correct. For our percent error we fluctuated in findings. Sometimes our error was 23.66% and other times we found no error at all. The error can be coming from the fact that our carts are being pushed by humans and there is no saying that they are going the same speed. Also there were times when the velocity was supposed to be a negative number but it went the opposite direction. We simply added or took away the negative and this could have given us false calculations. Overall the Law of Conservation of Momentum held true and we found our momentums to be almost equal.

Lab: Crush Energy

Date: March 21st, 2011
Members: Roshni, Allison, Emily
Honors Physics, Period 2

PROBLEM
What is the crush energy of the damage done by a metal ball on an aluminum can?

OBJECTIVE
To find out how much energy a metal ball takes to crush an aluminum can when dropped at various heights.

HYPOTHESIS
The greater the height the can is dropped from, the more energy it uses to damage the can. We made this assumption based off of our knowledge of gravitational potential energy (mgh). Because mass and gravity remain constant in these tests, the more we increase height, the more the crush energy should increase.

PROCEDURE
For this lab, we dropped a metal ball on an aluminum drink can, measured the depth and width of the intrusion zone, and used those measurements to determine the crush energy.

DATA

CRUSH_1.png
EB2P3CRUCHCALC3.png

CALCULATIONS
EB2P3CRUSHCALC1.png
EB2P3CRUCHCALC2.png
CONCLUSION
We satisfied our purpose by finding the crush energy and the velocity of the ball. While our experimental values differed slightly from our theoretical values, our percent difference is small enough that our values can be considered accurate. As we predicted, the crush energy and velocity increased the higher we dropped the ball from. When we dropped it from 5.5 in above, the total crush energy was 0.1329J and the velocity was the 2.006m/s. Then when we dropped it from 7.5 in above, the crush energy was 0.1639J and the velocity was 1.932 m/s. For example, while we found the velocity of the ball to be 2.006 m/s according to our crush energy calculations,according to our GPE calculations, the velocity was actually 1.655m/s. This represents a 19.17% difference between these velocities. This error probably comes from the inaccuracy of our measurements. Because we manually cut the index cards to mirror the crush zone, they were probably not very precise despite our best efforts. Further error could have been the result of our conversion factors. Because aluminum cans are different than cars, our conversion factors may not be perfectly accurate since they are different materials. An additional source of error is how the ball hit the can. Even though we tried to drop it straight down, the ball often went off course. It never perfectly hit the middle of the can as we intended. In order to improve this lab we would need to improve all of these factors. We would need more precise measurement tools and conversion factors, as well as a better way of creating the crush zone.

Reaction Time Activity

Date: March 18, 2011
Members: Roshni, Allison, Emily
Honors Physics, Period 2

Our Data:
rxntime1.png