# PHYSLAB 99

PALO ALTO, CALIFORNIA

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ttp://bn.k12.ma.us/

# Ballistic Pendulum

The ballistic pendulum is an example of both conservation of momentum and energy. A ballistic object, inthis case, a highly lethal suction cup dart, is fired at a pendulum bob. The dart which sticks to the bob transfers 100% of its momentum to the pendulum. However, energy is not conserved because it is an inelastic collision. Then, to calculate the amplitude of the pendulum, we do use conservation of energy, where the kinetic energy of the bob/dart system is converted into potential energy.

## Objectives

• Measure the amplitude of the ballistic pendulum as a function of bob mass
• Measure the amplitude of the ballistic pendulum as a function of length
• Calculate how much mechanical energy is conserved in the collision
• To determine the initial velocity of the dart.

## Materials

TI-82,83,86,89,92, or 92 Plus Ring Stand

CBL System Pendulum Rod

Vernier Motion Sensor Suction Cup Dart Gun

PHYSICS Program

Darts

Scale or Balance

## Procedure

1. Measure the mass of the pendulum bob, the dart separately and the length of the pendulum

2. Use the ring stand to hang the pendulum bob from a horizontal rod.

3. Set up the motion sensor 20 cm from the pendulum bob. You may need to attach large cards to the pendulum bob to reflect the ultrasonic waves and to shield the motion of the gun. Connect the motion sensor to the Sonic port on the CBL. Link the CBL to the calculator.

4. Turn on the CBL and the Calculator, and start the physics program.

5. Set up the calculator and the CBL by doing the following:

• Select SET UP PROBES from the MAIN MENU.
• Select ONE as the number of probes.
• Select MOTION from the SELECT PROBE Menu.
• Select COLLECT DATA from the MAIN menu.
• Select TIME GRAPH from the DATA COLLECTION Menu.
• Enter 0.05 Seconds between samples
• Enter 99 Samples
• Select USE TIME SETUP

6. Load the dart gun. Make sure the suction cup and target surface are clean.

7. Press ENTER on calculator to begin collecting data

8. Immediately fire the gun. Aim to hit the pendulum square on.

9. Display the distance vs. time graph from your calculator and read the maximum displacement of the pendulum. Record this in the data table.

10. Display the velocity vs. time graph from your calculator and read the maximum velocity of the pendulum. Record this in the data table.

## Data Table

Mass of dart (kg):

 Trial # Mass of Bob (kg) Max Velocity (m/s) Max Displacement (m) Length (m)

## Analysis Data Table

 Delta x (m) Delta h (m) PE (J) V final (m/s) KE (J) Final Momentum (kgm/s) Initial Momentum (kg m/s) V Initial (m/s)

## Analysis

1. Using your calculator, Graphical Analysis plot distance vs.time and record delta x.

2. Using your calculator or Graphical Analysis plot velocity vs. time and record your final velocity.

3. Using delta h = L - SQRT( L^2 - Delta x ^2 ) Calculate delta h and record it in the table above.

4. Determine the kinetic energy ( 1/2 m v^2 ). Enter this value in your data table.

5. Determine the potential energy (mg delta h). Enter this value in your data table.

6. If the total kinetic and potential energy are the same, we say the energy is conserved. Are these values the same? Explain.

7. The collision between the dart and the pendulum is perfectly inelastic. Write the conservation of momentum for the collision of the system.

8. Determine the final momentum (mv) using the final velocity obtained from your graph. Enter this value in your data table.

9. Using conservation of momentum mv(initial) = mv(final) calculate the initial velocity. Enter this value in your data table.

## TEACHER INFORMATION

1. Be sure that the motion detector is located at least 40 cm away from the pendulum to obtain better results.

2. Be sure that the sensor detects the pendulum and not the dart gun. Using clay or tape, "glue" an index card on one side of the pendulum so that the dart will stick to the index card and the pendulum will swing with the dart on it.

3. Remind your students that the kinetic and potential energy are calculated from the pendulum and dart system. The mass should be the sum of the pendulum and dart masses.

## SAMPLE DATA TABLE

Mass of dart (kg): 0.0015 kg

 Trial # Mass of Bob (kg) Max Velocity (m/s) Max Displacement (m) Length (m) 1 0.022 0.351 0.515 0.26

 Delta x (m) Delta h (m) PE (J) V final (m/s) KE (J) Final Momentum (kgm/s) V initial (m/s) Initial Momentum (kg m/s) 0.055 0.005 0.0011 0.34 0.0013 0.008 5.32 0.007

## Special Gracias

1. This lab was created with the help of my boyfriend Gary Garber. Thanks for helping make this lab a successful one!

2. Thanks Clarence Bakken for your daily support. You are THE MAESTRO! Gracias!

3. Also special thanks to Lettie, Dave, Mary Jane, Kristine and Jason for making this summer program a great/fun one!

4. Special GRACIAS to all the Physlab Participants for making me laugh so much.....and "Can you please stop talking about Casio!?"