PHYS 1111L - Introductory Physics Laboratory I

Laboratory Advanced Sheet
Ballistic Pendulum

1. Objective. The objective of this laboratory is to use the ballistic pendulum to predict the initial velocity of a projectile using the principles of conservation of linear momentum and conservation of total mechanical energy.

2. Theory. The initial velocity of the projectile will be measured by two independent methods. Those measurements will then be compared.

a. The first measurement method will use the range of a projectile launched horizontally from a given height above the lab table's surface to measure the initial velocity of the projectile. From the results of the projectile motion laboratory:

where v_1i is the initial velocity of the projectile,
g is the acceleration due to gravity near the Earth's surface,
x is the range of the projectile, and
y₀ is the initial height of the projectile above the surface of the lab table.

b. Derive the expression for the initial velocity of a projectile in a ballistic pendulum system (v_1i). Hint: Refer to Serway and Faughn's discussion of the ballistic pendulum (pages 160-1). The pendulum we use will be very similar to that shown Figure 6-11 of your text. Explain all assumptions and show all steps.

3. Apparatus and experimental procedures.

a. Equipment.

1) Ballistic pendulum apparatus

2) Meter stick.

3) Carbon paper.

4) Mass balance.

b. Experimental setup. The experimental setup is shown in Figure 1 (provided by the student).

c. Capabilities. To be provided by the student.

4. Requirements.

a. In the laboratory.

1) Using the techniques you learned in the projectile motion laboratory, determine the initial velocity of the launcher by measuring the initial height and range of the mass when projected horizontally. (Warning: Keep the pendulum portion of the apparatus out of the line of fire during this part of the laboratory.) Conduct five range trials.

2) Conduct five trials allowing the projectile and the pendulum to collide. Measure the change in height of the center of mass of the pendulum-ball combination before and after the collision.

3) Measure the masses of the projectile and the pendulum.

b. After the laboratory. The items listed below will be turned in at the beginning of the next laboratory period. A complete laboratory report is not required for this laboratory.

Para. 2. Theory.

Provide the portion of the theory section dealing with the development of the equation used to calculate the initial velocity (v_1i) of the projectile using the ballistic pendulum. Use the following symbols in your development:

1) The change in height of the center of mass of the ball and pendulum is h.

2) The mass of the ball is m₁; the mass of the pendulum is m₂.

Para. 3. Apparatus and experimental procedures.

1) Provide a figure showing the experimental setup.

2) Provide a description of the capabilities of the equipment used in the experiment.

Para. 4. Data.

1) Provide a copy of your data (Annex A contains tables for data).

2) Provide the following calculations in an Excel^TM spreadsheet:

a) The initial velocity of the projectile as determined by the range method.

b) The initial velocity of the projectile as determined using the ballistic pendulum.

c) The percent discrepancy between the two initial velocities. Use the initial velocity determined using the range method as the accepted value in this calculation.

Para 5. Results and Conclusions.

1) Provide a statement of the initial velocities determined by each method.

2) Provide a statement of the percent discrepancy in your results for the initial velocity determined using the ballistic pendulum.

3) Assess the accuracy of the experiment.

4) Describe sources of random error in the experiment.

5) Describe sources of systematic error in the experiment.

Annex A
Measurements

1. Initial height of projectile (use bottom of mass).

2. Range of projectile.

3. Mass measurements.

4. Change in height of center of mass of ball and pendulum system.

Last update: October 22, 2002