1 Lab 8 -Ballistic Pendulum Since you will be designing your own procedure you will have two class periods to take the required data. The goal of this lab is to measure the speed of a ball that is fired from a projectile launcher using two different methods. The Projectile launcher has three different settings, “Short Range,” “Medium Range” and “Long Range,” however you will only need to determine the speed for any ONE of these Range settings. Method 1 involves firing the ball directly into the “Ballistic Pendulum” shown below in Figure 2 for which limited instructions will be provided. Method 2 is entirely up to your group. While you have significant freedom to design your own procedure, you will need to worry about the random and systematic uncertainties you are introducing based on your procedure. This manual will provide a few hints to help reduce a few of those uncertainties. The ballistic pendulum pictured in Figure 2 is important canonical problem students study to explore the conservation of momentum and energy. The ball is fired by the projectile launcher into a “perfectly inelastic collision” with the pendulum. The pendulum then swings to some maximum angle which is measured by an Angle Indicator. Caution: The pendulum has a plastic hinge and Angle Indicator which are both fragile. Be gentle. Study the ballistic pendulum carefully. Before we begin, here are a few things to consider and be aware of in Figure 2: Projectile launcher Angle indicator (curved black bar) Clamp Pendulum (can be removed for measurements) Figure 2: Ballistic Pendulum Plumb bob Firing string Release point Figure 1: Projectile Launcher Bolt for removing pendulum 2 A. Clamping the ballistic pendulum to the table will reduce random uncertainties in the speed with which the projectile launcher releases the ball. Similarly, you should check that the various bolts are snug and that the ball is always fully inside the launcher (not rolling around inside the barrel of launcher). B. If the lab bench is not perfectly horizontal the plumb bob and angle indicator will not read zero degrees before you begin your experiment. You should fix AND/OR account for these discrepancies. C. In Figure 3 you will notice a tiny gap between the launcher and the pendulum. This important gap prevents the launcher from contacting the pendulum directly as the ball is fired. Without this gap an unknown amount of momentum is transferred from the launcher directly to the pendulum (in addition to the momentum transferred by the ball) significantly complicating our experiment. Figure 3: Important gap between Launcher and Pendulum Equipment 1 Ballistic Pendulum (shown in Figure 2) A bag with three balls 1 loading rod 1 Clamp 1 triple beam balance scale Safety goggles for each group member Any equipment found in your equipment drawer. Reasonable equipment reque.

1. 1
Lab 8 -Ballistic Pendulum
Since you will be designing your own procedure you will have
two
class periods to take the required data.
The goal of this lab is to measure the speed of a ball that is
fired
from a projectile launcher using two different methods. The
Projectile launcher has three different settings, “Short Range,”
“Medium Range” and “Long Range,” however you will only
need to
determine the speed for any ONE of these Range settings.
Method 1 involves firing the ball directly into the “Ballistic
Pendulum” shown below in Figure 2 for which limited
instructions will be provided. Method 2
is entirely up to your group. While you have significant
freedom to design your own procedure,
you will need to worry about the random and systematic
uncertainties you are introducing

2. based on your procedure. This manual will provide a few hints
to help reduce a few of those
uncertainties.
The ballistic pendulum pictured in Figure 2 is important
canonical problem students study to
explore the conservation of momentum and energy. The ball is
fired by the projectile launcher
into a “perfectly inelastic collision” with the pendulum. The
pendulum then swings to some
maximum angle which is measured by an Angle Indicator.
Caution: The pendulum has a plastic hinge and Angle Indicator
which are both fragile. Be
gentle.
Study the ballistic pendulum carefully. Before we begin, here
are a few things to consider and
be aware of in Figure 2:
Projectile launcher
Angle indicator (curved
black bar)

3. Clamp
Pendulum (can be removed
for measurements)
Figure 2: Ballistic Pendulum
Plumb bob
Firing string
Release
point
Figure 1: Projectile Launcher
Bolt for removing pendulum
2
A. Clamping the ballistic pendulum to the table will reduce
random uncertainties in the
speed with which the projectile launcher releases the ball.
Similarly, you should check
that the various bolts are snug and that the ball is always fully
inside the launcher (not
rolling around inside the barrel of launcher).

4. B. If the lab bench is not perfectly horizontal the plumb bob and
angle indicator will not
read zero degrees before you begin your experiment. You
should fix AND/OR account
for these discrepancies.
C. In Figure 3 you will notice a tiny gap between the launcher
and the pendulum. This
important gap prevents the launcher from contacting the
pendulum directly as the ball
is fired. Without this gap an unknown amount of momentum is
transferred from the
launcher directly to the pendulum (in addition to the momentum
transferred by the
ball) significantly complicating our experiment.
Figure 3: Important gap between Launcher and Pendulum
Equipment
1 Ballistic Pendulum (shown in Figure 2)
A bag with three balls
1 loading rod
1 Clamp

5. 1 triple beam balance scale
Safety goggles for each group member
Any equipment found in your equipment drawer.
Reasonable equipment requests will be honored by your
instructor.
Procedure- Measure the speed of the ball
1. Wear safety goggles during this experiment as projectiles
will be coming from your
apparatus as well as other groups.
Tiny gap
3
2. Select a ball and a power setting for your experiments. You
will not need to change
these decisions through this experiment.
3. Your task is to measure the speed of the ball as it leaves the
projectile launcher.
Method 1- Ballistic Pendulum
4. The sequence of events for the ballistic pendulum can be
broken down into 4 important
points:
P1) The ball at rest in the projectile launcher with the spring

6. compressed, pendulum at rest.
P2) The ball leaving the projectile launcher at speed �1 before
the collision, pendulum at
rest.
P3) The ball stuck in the pendulum after the collision where
everything is moving at speed
�2. The pendulum is (almost) completely downward.
P4) The ball stuck in the pendulum after they have swung to
the maximum angle � and
momentarily have a speed of zero.
Take advantage of these four snapshots to ask yourself
questions like:
“Where does the momentum at point B come from?”
“By the time we get to point D, where did that momentum go?”
“Does all of the energy of the spring at point A, remain in the
system at point D?”
5. We learned back in Lab 2 that the important length for a
pendulum is from pivot point
to Center of mass. Locate the Center of Mass of the pendulum
by balancing the
pendulum on a ruler as shown in Figure 4. (Group 1: Should the

7. ball be inside the
pendulum during this measurement?)
6. Consider Figure 5, the schematic diagram below of the
pendulum swing. Create a
procedure for measuring Δℎ, the height change of the center of
mass during a swing,
from other quantities you can measure.
Figure 4
Center of mass must be
somewhere over the ruler if
balanced. Group 2: How
much systematic
uncertainty could this
introduce in your
measurement of Δℎ?

8. Radius of the pendulum.
ruler
4
7. Use conservation of energy and conservation of momentum as
appropriate to
determine the velocity of the ball based on the maximum angle
of swing. Make sure
you record multiple identical trials so you have a measure of the
random uncertainty
inherent in your equipment.
8. Before you move on to Method 2, make sure you measure the
“zero offset” in the angle
indicator of your ballistic pendulum so you can account for this
systematic error in your
data.
9. Group 3: Do we expect all of the kinetic energy of the ball
(just after it is fired, but

9. before the collision) to be turned into gravitational potential
energy when the
pendulum-ball system is at maximum swing? If no, where did
the majority of the lost
energy go?
10. Group 4: Do we expect all of the momentum of the ball (just
after it is fired, but before
the collision) to be found in the pendulum-ball system when it
is at maximum swing? If
no, where did the majority of the lost momentum go?
(Removing the clamp and placing
the ballistic pendulum on a rolling cart is an interesting way to
investigate this question.)
The answer to these group questions can be included in the
report wherever the group
deems most appropriate. Make sure you use footnotes so the
TA can find your answer.
Figure 5
Δℎ

10. 5
Method 2- Your choice on how to measure the ball’s speed.
11. For method 2, you have much more freedom in how you
determine
the speed of the ball. Here is a list of possibly useful items
available to
you.
A) A clipboard with paper, placed on the floor will record the
location
a ball strikes it.
B) The foam inserts attached to the collision carts will catch
a ball if it is shot into the foam.
C) Most cell phones can take slow motion video. Don’t
forget to place reference objects in your frame to
establish the scale ratios you will need for calculations.
12. Group 5: What systematic uncertainty is inherent in your
procedure for method 2?

11. Explicitly estimate the size of each uncertainty.
13. Make sure the group records multiple trials, so you have an
estimate of the random
uncertainty of method 2.
Writing the report
14. Researcher 1- Explain how your group determined the speed
of the ball using the
ballistic pendulum. When exactly was conservation of Energy
used? When exactly was
conservation of momentum used?
15. Researcher 2- Fully explain the procedure your group used
to complete Method 2.
Make sure you spend significant time discussing how your raw
data was transformed
into a measurement of the ball’s speed. You cannot assume the
grader knows your
procedure as every group could be using different equipment.
An annotated
sketch/picture is very helpful, but not strictly required.

12. 6
16. DA 1- Organize the data for Method 1 and Method 2 adding
units and descriptive titles
to the headers for your data. These data headers should match
up to the steps
mentioned by the Researcher in the procedure. In the report,
include a data table with
at least a sample of the data showing all the major
steps/calculations the group needed
to perform to ultimately determine the speed of the ball in each
method.
17. DA 2- Create a plot to show your measurement of the speed
of the ball using both
methods. Find a way to represent the systematic uncertainties
you measured in
questions Group 2 and Group 5.
18. PI 1- We want to think carefully about the momentum and
the energy in the
ball/pendulum system at the four points outlined in step 4
above.

13. From P1 to P2 does the momentum of the system change? If so
what force is
responsible for that change in momentum?
From P2 to P3 does the momentum …
From P3 to P4 does the momentum …
From P1 to P2 does the Energy of the system change? If so
what force is responsible for
that change in energy?
From P2 to P3 does the Energy …
From P3 to P4 does the Energy …
In your discussion make sure you address the fact that in some
of the cases above a
force is changing the energy without changing the momentum
(or changing the
momentum without changing the energy). How is this possible?
19. PI- Summarize. What is the speed of the ball as it is fired
from the projectile launcher?
(Report your results with proper rounding.) How do you
account for any differences

14. between the two different experimental methods?
20. Before leaving the classroom, make sure you email the data
out to the entire group and the
Teaching Assistant. Please use the subject “Lab 8 data- Section
###, Group ###.”
Sheet1~~~~~~~~~~~~~~~~~~~~Mass of ball (kg)Mass of
pendulum(kg)Radius of pendulum(m)Starting angleh
initial~0.0220.230.25500~~~Method 1~TrialAngleΔhvelocity
final?????????v
ball~1150.00868891430.41288799754.7294443352~2170.01114
228720.46755927485.3556789658~318.50.01317746790.508470
17675.8242947518~4180.01248058830.4948425445.668196412
8~518.50.01317746790.50847017675.8242947518~~~~~~~~Met
hod 2~Trial Distance(m)Time(s)v
ball~12.650.584.5689655172~22.590.465.6304347826~32.630.5
34.9622641509~42.6260.495.3591836735~52.6240.574.6035087
719~~~~~~
Method 1 4.7294443351886812 5.3556789657664012
5.8242947517925403 5.6681964127590332
5.8242947517925403 Metho d 2
4.5689655172413799 5.6304347826086953
4.9622641509433958 5.3591836734693876
4.6035087719298255