What the Puck? …an exploration of Two-Dimensional collisions 1) Have you ever played 8-Ball pool and lost the game because you scratched while attempting to sink the 8-Ball in a corner pocket? Sketch the shot below: Each figure below shows a cue ball hitting an 8-ball at different impact points. Rank, from greatest to least, the angle between the balls after collision A B C D E F Greatest 1_______ 2________ 3________ 4________ 5________ 6________ Least Or, all of the angles between the balls after collision will be the same. _______ 2) Please carefully explain your reasoning. ATE Workshop for Physics Faculty, 2013
Transcript
What the Puck? …an exploration of Two-Dimensional collisions
1) Have you ever played 8-Ball pool and lost the game because you scratched
while attempting to sink the 8-Ball in a corner pocket? Sketch the shot below:
Each figure below shows a cue ball hitting an 8-ball at different impact points. Rank, from greatest to least, the angle between the balls after collision A
B
C
D
E
F
Greatest 1_______ 2________ 3________ 4________ 5________ 6________ Least Or, all of the angles between the balls after collision will be the same. _______ 2) Please carefully explain your reasoning.
How sure were you of your ranking? (circle one) Basically Guessed Sure Very Sure 1 2 3 4 5 6 7 8 9 10 3) If you’re close to a pool hall, you may want to convince your instructor to
move the lab there. If not, you can do similar analysis with a pair of hover pucks.
Obtain 3 overhead movies of puck collisions that have one puck initially stationary, and the colliding puck hitting at different impact points on the stationary one. Play each movie multiple times and estimate the angle of motion between the pucks after collision.
4) Explain your observation: Since this is Physics and we have the tools, we won’t stop with estimates. You will use video analysis to quantify the motion and explore the role that momentum plays in two-dimensional collisions. Use one or more of the following analysis approaches:
1) Open up Logger Pro. Under “Insert”, go to “Movie”. Locate the movie file you want to open and open it. You should have the movie opened in front of the LoggerPro graph.
• Click on to open the toolbar for video analysis. Click on and setup your scale for a known object’s dimension on the screen.
2) Click the position locator, , and start marking one of the pucks before, during and after collision with the 2nd puck. Make sure you have at least 8-10 points just before collision and right after collision.
3) Click the add data set button, , and mark the 2nd puck before, during and after collision. Again, make sure you have at least 8-10 points just before and right after collision. 4) To better view your data, go under “Page” and click on “Auto Arrange”. Now you should have a window with the movie, data table, and graph in its own place. 5) If your two pucks have the same mass, you don’t really need to create momenta columns. If, however, your masses are not the same, then you need to create “New Calculated Columns” under the “Data” menu for the momenta of each puck in the x and y-directions. 6) On your graphs, find the slope of the x graphs before (initial) and after (final) collision. Find the slope of the y graphs before (initial) and after (final) collision. Fill in the table below with your calculated values. p1x initial p2x initial ptotalx initial p1x final p2x final ptotalx final
p1y initial p2y initial ptotaly initial p1y final p2y final ptotaly final
7. Was momentum “conserved” in each direction?
ATE Workshop for Physics Faculty, 2013
8. Also calculate the angles of each puck before and after collision. Angle puck 1before
Angle puck 1 after Angle puck 2 before
Angle puck 2 after
9. What was the angle between the two pucks after collision?
ATE Workshop for Physics Faculty, 2013
Objective:
• To determine what happens to the momentum of a system as two friction-free pucks collide.
In this experiment you will analyze the momentum of two pucks in such a way that you will be looking at the horizontal and vertical components of each puck’s momentum before, during and after the two collide. Option 1: Perform your own collision and gather video evidence of the collision. Option 2: Analyze the data from a movie that has already been produced. 2A: Analysis from scratch. 2B: Analysis of momentum with pre-made columns. Experiment: Option 1 If you are choosing option one, your first mission will be to create a movie watching an overhead view of a collision between two “Air Pucks”. The collision should be one in which a moving puck approaches and collides with a stationary puck. Once the movie is produced import it into LoggerPro to prepare for analysis. Then follow the guide for Option 2A beginning at the second step. Option 2A: 1) Open the LoggerPro File entitled “Scratch 2-D Puck Analysis” 2) Begin the analysis by tracking the position of both pucks. 3) Be sure to include data from before as well after the collision. LoggerPro will keep track of both the X and Y positions and velocities. 4) Set an origin at the beginning of the analysis 5) Set a “Scale” to convert into metric position (width of puck is 19 cm) 6) Create a PuckMass parameter, find and enter the actual mass of the puck. 7) Create Calculated Columns by selecting “New Data Column” in the Data menu
What the Puck? Component – Calculated Columns
ATE Workshop for Physics Faculty, 2013
• Create X-Momentum columns for both pucks 1 and 2 • Create a “Total X Momentum” Column by adding the two above. • Create Y-Momentum columns for both pucks 1 and 2 • Create a “Total Y Momentum” Column by adding the two above.
Option 2B: 1) Open “Student Analysis 2-D Puck” LoggerPro Lab 2) Begin the analysis by tracking the position of both pucks. 3) Be sure to include data from before as well after the collision. LoggerPro will keep track of both the X and Y positions and velocities. 4) LoggerPro will also keep track of the X, Y and Total Momentums of the pucks 5) This information will be plotted and displayed on the two graphs Data Analysis: Option 1 and 2A: (The next step has already been done for Option 2B) Create and Display two graphs each one displaying three lines The first graph should display the X momentum of puck 1, puck 2, and total. The second graph should display the Y momentum of puck 1, puck 2, and total. Interpretation: What does your data suggest is happening to the Horizontal (X) momentum? What does your data suggest is happening to the Vertical (Y) momentum? What do you suppose this suggests about the total momentum of the system throughout the video?
ATE Workshop for Physics Faculty, 2013
Follow-up Questions 1) It has been said that in an elastic collision like the one we performed, the angle made between the paths of the pucks after the collision should be 90°. The picture to the right represents a collision similar to the one you studied. Does it support or refute the statement above? (Carefully measure to support your answer) 2) Now use the X and Y components of the post collision vectors from your data
to determine the angle of deflection from the original path for each puck. Then calculate the angle between the two paths. How well does this data agree with the statement made in number 1?
3) In the pool trick shown in the picture at the
right the cue ball is intended to push the yellow ball directly into the side pocket and then travel down to hit the yellow striped ball in the corner pocket. Discuss the physical possibility of successful completion of this trick based on the physics displayed in this lab.
ATE Workshop for Physics Faculty, 2013
What the Puck? Vector
In this exploration you are going to cause a collision between two air pucks, with one sitting still and one moving that hits the first. You want to have them hit so that it is not a head on collision.
1) Determine how you are going to take the data. You will need to clean off your table and use it to take the data as the floor will not work well. You will need to take a video of the collision making sure you have data before and after the collision.
2) You will likely need to stand on the table to hold the camera above the
motion to get a good video. You will need to use good video practices when taking you video. You can use the pucks as your scale.
3) Once you have your video in logger pro, analyze the video, remembering you
will need to track two objects. Once you have done the analysis, you will need to create a calculated column for the magnitude of the total velocity of the puck for each time.
4) Once you have the velocity data, use this and the mass to create a vector
triangle showing the momentum before and after the collision. Does the triangle close if drawn to scale? To find out, measure the angles the pucks are moving after the collision and draw a scale “triangle” and see if the initial momentum of the moving puck is the equal to the vector sum of the two puck after. Make your drawing on a whiteboard.
5) If you triangle did not fully close, describe one or more possible reasons since
we know momentum should have been conserved.
6) What is the angle between the velocity vectors after collision? What should they be? Explain any differences.
ATE Workshop for Physics Faculty, 2013
What the Puck? …using simulations to check your knowledge
1) A nifty EJS simulation will allow you to explore the collision of virtual pucks in
the absence of all that messy reality (friction, rotation, etc.). When you run the simulation (linked below), you will see this:
2) You will want to set V2 = 0 m/s, and adjust the position of puck 1 upward:
3) Click the start button and hit pause immediately after the collision:
Look at the angle between the two momentum arrows. Measure with a protractor for grins and giggles. To set up for another test, click the reset button, reset V2 = 0 m/s, and position puck 1 to another vertical location. 4) Use this simulation to check your answers to the ranking task exercise you
completed earlier: Each figure below shows a cue ball hitting an 8-ball at different impact points. Rank, from greatest to least, the angle between the balls after collision A
B
C
D
E
F
Greatest 1_______ 2________ 3________ 4________ 5________ 6________ Least You can also mess around with uneven masses, both with initial velocities, etc. Have fun!
1) Below are bird’s-eye views of six automobile crashes an instant before they
occur. The automobiles have different masses and velocities. All automobiles will remain joined together after the impact and skid to rest. Rank these automobile crashes on the basis of the angle at which the wreckage skids. Let 00 be the angle oriented directly toward the right and measure angles counterclockwise from 00.
_____ The ranking can not be determined based on the information provided.
2) Explain the reason for your ranking:
ATE Workshop for Physics Faculty, 2013
3) Below are bird’s-eye views of six automobile crashes an instant before they occur. The automobiles have different masses and velocities. All automobiles will remain joined together after the impact and skid to rest at the same angle, as measured from a line oriented directly toward the right. Rank these scenarios on the basis of the initial velocity of the auto traveling toward the top of the page.
_____ The ranking can not be determined based on the information provided.
4) Explain the reason for your ranking:
ATE Workshop for Physics Faculty, 2013
5) For each of the collisions illustrated below, sketch a graph of the momentum of asteroid A, the momentum of asteroid B, and the total momentum in the system of the two asteroids. Sketch the horizontal and vertical momentum separately. Begin your graph before the collision takes place and continue it after the collision is over. Use a consistent scale on all graphs.
a. The two asteroids remain joined together after the collision.
t
Py
t
Px
b. The two asteroids remain joined together after the collision.
700 kg
70 m/s
1000 kg
100 m/s
B
A
t
Py
t
Px
ATE Workshop for Physics Faculty, 2013
6) For each of the collisions illustrated below, sketch a graph of the momentum of asteroid A, the momentum of asteroid B, and the total momentum in the system of the two asteroids. Sketch the horizontal and vertical momentum separately. Begin your graph before the collision takes place and continue it after the collision is over. The asteroids’ initial velocities are both oriented at the same angle from horizontal. Use a consistent scale on all graphs.
a. The two asteroids remain joined together after the collision.
t
Py
t
Px
b. The two asteroids remain joined together after the collision.
700 kg
70 m/s
1000 kg
100 m/s
B
A
t
Py
t
Px
ATE Workshop for Physics Faculty, 2013
7) For each of the collisions illustrated below, sketch a graph of the momentum of asteroid A, the momentum of asteroid B, and the total momentum in the system of the two asteroids. Sketch the horizontal and vertical momentum separately. Begin your graph before the collision takes place and continue it after the collision is over.
a. The two asteroids remain joined together after the collision and move directly toward the top of the page.
700 kg
100 m/s
1000 kg
vB
B
A
t
Py
t
Px
b. The two asteroids remain joined together after the collision and move directly toward the right. The asteroids’ initial velocities are both oriented at the same angle from horizontal.
1000 kg
vB B
700 kg 70 m/s
A
t
Py
t
Px
ATE Workshop for Physics Faculty, 2013
8) For each of the explosions illustrated below, sketch a graph of the momentum of fragment A, B, and C, and the total momentum in the system of the three asteroids. Sketch the horizontal and vertical momentum separately. Begin your graph before the explosion takes place and continue it as the fragments move apart. The exploding egg is initially at rest.
a. Fragment A moves horizontally and fragments B and C move at the same angle from horizontal after the explosion.
C
20 kg
A
B
10 kg
10 kg
t
Py
t
Px
b. Fragment B moves vertically and fragments A and C move at the same angle from vertical after the explosion.
