Investigation 5.3.1: Analyzing Two-Dimensional Collisions
This investigation explores two-dimensional collisions to determine whether total momentum and total kinetic energy are conserved.
The vector nature of momentum is crucial in performing calculations involving collisions in two dimensions. Although vector scale
diagrams are recommended for the analysis of the collisions you will study, you may choose components or trigonometry to analyze
the collisions.
Question
What can be learned by comparing the total momentums and total kinetic energies of objects colliding in two dimensions before and
after the collision?
Prediction
Examine Figure 1 on pg. 263 and answer the following:
(a) For the Category I collisions, predict how the total momentum and total kinetic energy of the system before the collision will
compare with the total values after the collision.
Hypothesis
(b) Write a hypothesis to explain what you anticipate you will observe in the collision in Category III.
(c) Describe how you will find the unknown mass in the Category IV collision.
Figure 1 Possible collisions to analyze in Investigation 5.3.1
Category I: The total momentum before the collision is compared to the total momentum after the collision; this analysis involves a
vector addition.
Category II: The change in momentum of one puck is compared to the change in momentum of the other puck
Category III: Two colliding pucks of equal mass stick together after colliding; this analysis involves learning as much as possible
about the collision.
Category IV: Determining an unknown mass: you must choose between vector addition and vector subtraction to solve this problem.
Procedure
1. Open the 2D Air Table applet located at http://www.shs.d211.org/physicsd211/vphysics.htm
2. In a group of two students, practice creating Category I and Category II collisions with pucks of common mass (ie. 1kg). When
you have developed an appropriate level of skill, proceed to the next step.
3. Set the spark frequency to an appropriate period for the velocity you choose and have each member of your group create a
Category I collision and a Category II collision. After each collision, create a screen shot of the initial conditions and post
collision results and save the file appropriately. Format the images to fit on a single page and print the two images.
4. Practice the Category III collision so that the pucks have a common velocity after the collision. Have each member of your group
create a Category III collision. After each collision, create a screen shot of the initial conditions and post collision results and save
the file appropriately. Format the images to fit on a single page and print the two images.
5. After all the groups have completed step 4. Add an extra mass to one of the pucks and imagine that this is an unknown
quantity. Have each member of your group create a Category IV collision. After each collision, create a screen shot of the
initial conditions and post collision results and save the file appropriately. Format the images to fit on a single page and print the
two images.
Analysis
(e) Write out the conservation-of-momentum equation you intend to use for each of the four categories of collision. Ask your
teacher to check the equation before you apply it to the data images obtained.
(f) Starting with the Category I collision, mark off four appropriate displacement vectors, one sample of which is shown in
Figure 4. In this sample, the time interval during which the displacement occurred is 5  20 ms = 100 ms, or 0.10 s,
assuming two significant digits. Working directly on the printed images, draw all the vectors and use them to determine
whether total momentum and kinetic energy are conserved.
(g) Repeat (f) for the Category II collision.
(h) Analyze the Category III collision showing as much as you can about momentum and kinetic energy.
Figure 4 Sample displacement vector for the Category I collision
(i) You know the mass of one puck in the Category IV collision. Perform the measurements and calculations needed to
determine the total unknown mass of the second puck. Since you know what that mass is, calculate your percent error. Show
all your work.
(j) Classify each collision you analyzed as elastic, inelastic, or completely inelastic. For each type of collision, describe what
happened to the kinetic energy.
Evaluation
(k) Comment on the accuracy of your predictions and hypotheses.
(l) List the sources of random, systematic, and human errors in this investigation, and describe ways you tried to minimize them.