LabLab

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 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 compressed, pendulum at rest. P2) The ball leaving the projectile launcher at speed 𝑣1 before the collision, pendulum at rest.

P3) The ball stuck in the pendulum after the collision where everything is moving at speed 𝑣2. The pendulum is (almost) completely downward.

P4) The ball stuck in the pendulum after they have swung to the maximum angle 𝜃 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 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?

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

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

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?

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.

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.

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

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 ###.”