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### Ballistic Pendulum Lab

Purpose:  Develop a description of the ballistic pendulum collision by applying conservation of momentum to determine changes in velocity of the ball and pendulum and evaluating changes in energy of the system.

Equipment:
Triple Beam Balance
TI-84 Calculator
Photo Gate
Vernier Caliper
Ruler
Ballistic Launcher (see illustration below)

Procedure: Please see video to experience firsthand our procedure.

#### Pendulum Lab

Data:
Mass Ball: 59.0 grams= .059 kg
Change in Height: 10.5 cm= .105 m
Change in Time: 0.010148 sec
Diameter of Ball: 25.4 mm= .0254 m

Data Analysis/ Calculations:
Velocity(ball) : Diameter/ Change in Time = .0254 m/ .010148 sec= 2.50 m/s

Velocity(take-off)=(2gh)^(1/2)= (2 x 9.8 m/s^2 x .105 m)^(1/2)= 1.43 m/s

Mass of Pendulum:
m(ball) x v(ball) = v(final) x (m(ball) + m(pendulum))
(.059 kg x 2.5 m/s) = 1.43 m/s (.059 kg + m(pendulum))= .044 kg

Initial Kinetic Energy of Ball: (1/2)(.059 kg)(2.50 m/s)^2= .184 J
Initial Kinetic Energy of Ball and Pendulum: (1/2)(.103 kg)(1.43 m/s)^2= .105 J
Change in Kinetic Energy: .105 J-.184 J= -.079 J
Fraction of Kinetic Energy Lost: .079 J/ .184 J= .429 J

Change is Potential Energy: mgh= (.103 kg)(9.81 m/s^2)(.105 m)= .106 J

Conclusion:
By completing this open-ended lab, we learned to evaluate a ballistic pendulum collision by applying conservation of momentum to determine changes in velocity of the ball and pendulum and evaluating changes in energy of the system. In a completely inelastic collision like that of a ballistic pendulum, both bodies stick together and move with the same velocity. This process absorbs some of the system's kinetic energy. The system can also dissipate kinetic energy in producing sound or heat. Our system dissipated approximately .079 J.  This small change in kinetic energy was most likely the result of heat that the ball gave off when it collided with the catcher pendulum (see illustration.) Since there are no external forces acting on the system at the time of the collision, we can assume that linear momentum was conserved; however, we can not use The Law of Conservation of Energy because the total kinetic energy was not conserved.  Possible sources of error could have included air resistance and rounding of the measurements.