Conservation of Momentum In Two Dimensions Lab - Dickey Physics

Name: ______________________________
Partner(s): __________________________
Conservation of Momentum In
Two Dimensions Lab
(2013)
Object:
The object of this experiment is to study the conservation of momentum in two
dimensions.
Date: ___________
Period: __________
Materials:
Grooved Plastic Ruler Plastic Ruler Support C-Clamp Electronic Balance
Two Steel Marbles Glass Marble White Paper Protractor
Carbon Paper Meter Stick Tape
Theory:
Previously, we investigated the momenta of colliding bodies moving along a single
straight line. What happens when two bodies go off in different directions after colliding To
find out, we shall roll one steel sphere down an incline so that it makes a glancing collision with
another steel sphere of the same size, knocking it off a support near the edge of the table (Part I).
In Part II of the lab, we will roll the steel sphere into a glass sphere. We shall then find the
momentum of each from their masses and velocities. We will be using a setup similar to Figure
1, below. In our setup, however, we will be placing the carbon paper on top of our white paper.
Also, our setup will have the plumb line hanging from the set screw where the struck sphere is
placed.

Theory: (cont.)
To find the velocities of the spheres, we shall use what we learned about projectile
motion. We know that objects projected with different horizontal velocities from the edge of a
table take the same time to fall to the floor. If we neglect air resistance, the horizontal
component of their velocity remains unchanged and therefore the distance they go horizontally is
proportional to their horizontal velocity. We can use this fact to measure the velocities of the
spheres after they have collided.
In Part I of the lab, the masses of the spheres are equal. Their distances traveled are
indicative of both the velocity and momentum vectors. You will add the two momentum vectors
graphically on your paper, placing the tail of the momentum vector of the target ball at the head
of the momentum vector of the incident sphere.
In Part II of the lab, the masses of the spheres are unequal. As a result, the distances
traveled are still indicative of velocity vectors, but not of momentum vectors. The easiest way to
make the distance vectors represent momentum vectors is to find the relative masses of the
spheres. For example, if the mass of the marble is one-third that of the incident steel sphere, you
can convert the distance vectors to momentum vectors by making the distance vector of the
marble one-third as long and leaving the initial and final distance vectors of the steel sphere
unchanged. Since momentum equals mass times velocity, these vectors now represent
momentum vectors.
Procedure:
1. Mass the steel sphere and marble.
2. Obtain four pieces of plain white paper. Tape the pages together as shown below to
form a "quad-sheet".
3. Secure the plastic ruler support to the lab table using the C-clamp.
4. Unwrap the plumb line, which is a line (as of cord) that has at one end a weight (as a
plumb bob) and is used especially to determine verticality, from the ruler support and
check to see that the plumb bob is not resting on the ground. The bob should hang
just above the floor. (Figure 1)
5. Place the quad-sheet on the floor so that the short edge is about two centimeters
behind the plumb line. Tape the paper to the floor.

Procedure: (cont.)
6. The ruler support contains a set screw. This functions as a holder for the target
sphere. The angle of the set screw can be varied relative to the groove on the ruler.
Check to see that the set screw on your ruler support is at an angle (not straight in
line) with the ruler groove. If it is not at an angle to the ruler groove, then move the
set screw to some angle. Just take care not to create an angle so large that the
incident sphere will not come into contact with the target sphere.
7. The plumb line is attached to the set screw. Mark the location of the bob on your
quad-sheet with a pencil. Label this mark, B. This mark will represent the location of
the target ball upon collision.
8. The position of the incident sphere can be found by using the diameter of the steel
marble. Place one of the steel marbles on the quad-sheet where you made the mark
labeled B. Position one end of the marble at B and make a mark at a diagonal in the
direction of the groove of the ruler. This second mark will be labeled A.
A
One Ball
Diameter
B
9. Place the carbon paper face-down over the white paper. Do not tape the carbon
paper down.
10. For the first set of five runs, you will only use one metal ball. Using a ruler, release
the steel ball from the top of the ramp. Repeat 5X. (Make sure that the ball does not
hit the C-clamp or the set screw.)

Procedure: (cont.)
A
B
11. For each of next five runs, place the second ball on the dimpled screw prior to
releasing the first ball. Once again, use a ruler to release the first ball from the top of
the ramp. Be sure that both balls are marking the quad-sheet. This will complete Part
I of the lab.
A
B
12. In Part II of the lab, you will repeat all the steps in Part I with the exception that you
will roll the steel sphere into the glass marble instead of a second steel sphere. You
will need to use a new quad-sheet. Be sure to make your A and B marks.
Data:
1. Mass of either steel sphere __________________________ kg.
2. Mass of the marble _______________________________ kg.
3. The rest of the data will be collected on your two quad sheets.
Analysis and Questions: (Answer in the space provided. Be sure to show your
calculations.)
1. Because your quad-sheets contain your data, make sure one member of your group
turns in the quad-sheets with their lab.
2. Take out the quad-sheet you used in Part I of the lab. This is the one in which you ran
a steel sphere into another steel sphere.

Analysis and Questions: (cont.)
3. Draw circles around the three sets of five data points.
A
B
4. Mark a small X in the center in each of the circles you just drew.
5. Draw a vector representing the incident sphere's velocity before collision. Label the
vector (v A1 ), and measure its length in centimeters. Write both the label and the
measurement next to the vector on the quad-sheet.
x
A
B
v A1
x
x
6. Draw a vector representing the incident sphere's velocity after collision. Label the
vector (v A2 ), and measure its length in centimeters. Write both the label and the
measurement next to the vector on the quad-sheet.
x
v A2
A
B
v A1
x
x

Analysis and Questions: (cont.)
7. Draw a vector representing the target sphere's velocity after collision. Label the vector
(v B2 ), and measure its length in centimeters. Write both the label and the
measurement next to the vector on the quad-sheet.
x
v A2
A
B
v A1
x
v B2
x
8. Using your Part I quad-sheet, intersect vectors (v A2 ) and (v B2 ). You will need to
trace lines backwards from these two vectors until they intersect.
x
v A2
A
B
v A1
x
v B2
x
9. Using a protractor, measure the angle formed between the vectors (v A2 ) and (v B2 ).
Write this angle on your Part I quad-sheet.
x
v A2
A
B
v A1
x
v B2
x

Analysis and Questions: (cont.)
10. Take the angle you just measured, along with the length of vector (v B2 ) you
measured earlier and add (v B2 ) to (v A2 ). You will need to use your protractor and
meter stick for this step.
x
v A2
v B2
A
B
v A1
x
v B2
x
11. Theoretically, the two velocity vectors after collision (v A2 ) and (v B2 ), which added
together represent the final momentum of the system, should add up to the incident
velocity vector (v A1 ), which represents the initial momentum of the system. If the
vectors (v A2 ) and (v B2 ) did not add up perfectly, then you will calculate the percent
error. To accomplish this, draw a dashed line from the tip of the (v B2 ) vector you
just drew to the end of (v A1 ). Measure the length of this dashed line and write it on
the quad-sheet.
x
v A2
v B2
A
x
B
v A1
v B2
x
% Difference =
12. Take the distance of the dashed line, divide it by the length of vector (v A1 ) and
multiply by 100. This will be your percent difference. Write these calculations on
your Part I quad-sheet.

Analysis and Questions: (cont.)
13. We will follow a very similar process with your quad-sheet from Part II of the lab.
We will need to change a few things, however, because this section of the lab deals
with spheres of unequal mass.
14. Take your quad-sheet from Part II and follow Analysis and Questions steps three
through nine.
15. Instead of directly adding vector (v B2 ) to (v A2 ), as in Part I of the lab, we will need
to take into account the smaller mass of the glass marble. To do this, you multiply
the length of (v B2 ) by the ratio of the mass of the glass marble to the mass of the
steel marble. The equation is written below.
Length of v
B2
Mass
Mass
Glass Marble
Steel Sphere
Draw the converted (v B2 ) vector on top of the old one. It will be shorter than the
original. Be sure to write the conversion calculations on your Part II quad-sheet.
x
v A2
A
B
v A1
x
v B2
x
16. Follow Analysis and Questions steps ten through twelve in adding the converted
(v B2 ) vector to (v A2 ) and calculating the % Difference. Be sure to include all
necessary calculations, vectors, etc... on your Part II quad-sheet.
17. Using the information in the table above, do you think we had a closed system in our
experiment Justify your answer.
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