PHYS 211 Ballistic Pendulum Observations

Lab 12: Ballistic Pendulum The objective of this laboratory experiment is to use a steel ball and a projectile launcher in trails to determine the launch speed for short, medium, and long-range settings. This is to help us conceptualize gravitational potential energy (PE) and conservation of mechanical energy, as well as to explore relationships between the momentum and kinetic energy (KE). Relevant Equations: - To determine iniKal launch velocity and uncertainty: ࠵? ! = # "# ! $% - Measure mass of ball and determine iniKal momentums and uncertainKes: ࠵? = ࠵?࠵? - Find final velocity aOer collision: o ࠵?࠵? = (࠵? &’(()*+,-.(./ )࠵?∆ℎ = (࠵? &’(()*+,-.(./ )࠵?(࠵? − ࠵? cos ࠵?) o ࠵?࠵? = ࠵?࠵? = 0 $ ࠵? &’(()*+,-.(./ ࠵? 1 $ = ࠵? &’(()*+,-.(./ ࠵?(࠵? − ࠵? cos ࠵?) o ࠵? 1 = 62࠵?(࠵? − ࠵? cos ࠵?) - Find final momentum aOer collision: ࠵? 12,’( = (࠵? &’(()*+,-.(./ )࠵? 1 - ࠵? 2,232’( = ࠵? 12,’( - ࠵? &’(( ࠵? ! = ࠵? &’(()*+,-.(./ ࠵? 1 Lab Set-Up: To prepare for our experiment, we removed the pendulum from the launcher. We then put a piece of hard cardboard on the ground with a piece of regular paper taped on it. Then, we set a piece of carbon paper on top of that, shiny side up. This is so that when the steel ball hits the top of the carbon paper, it leaves a mark on the regular paper, and the whole setup does not move on impact. Part One: For the first part of our lab experiment, we removed the pendulum and launched the ball five times at our paper, each time recording the distance the steel ball travelled horizontally before

striking the ground. This was done for short, medium, and long-range settings of the launcher. We recorded this data in a table in excel and used it to calculate the momentum of the ball- pendulum system before the ball collides with the pendulum. Trials Short Medium Long Trial 1 0.845 1.5 2.085 Trial 2 0.86 1.5 2.095 Trial 3 0.875 1.505 2.105 Trial 4 0.89 1.51 2.115 Trial 5 0.9 1.515 2.13 Avg. 0.874 1.506 2.106 v0 2.080506 2.731026 3.229554 p 0.136897 0.179702 0.212505 Part Two: During this part of our lab experiment, we mounted the pendulum before launching the ball into the pendulum using short, medium, and long-range settings of the projectile launcher. We were careful to record the initial angle at rest, launch the ball twice, and then launched again for each trial. Using the data recorded in an excel table, we then calculated the speed of the pendulum and ball together just after the collision, and then multiplied by the mass to get momentum. Our table with observed and calculated values is attached below. This table is also important for part three of our experiment. Trials Short (θ) Medium (θ) Long (θ) Trial 1 16 25 35.5 Trial 2 16 25 36 Trial 3 16 25 35.5 Trial 4 16 25.5 35.5 Trial 5 15.5 24.5 35.5 Avg. 15.9 25 35.6 Vf 0.450099 0.7043598 0.994825 p 0.13719 0.2146889 0.303223 pfinal-pinitial 0.000293 0.0349874 0.090718 Uncertainty 0.0003 0.0003 0.0003

Summary In this experiment momentum is conserved, while kinetic energy is not. The fact kinetic energy is not conserved could be from many factors, such as not all the potential energy being transformed into kinetic energy, or the kinetic energy turning into other types of energy such as sound or heat. It could also be effected by friction from the tube, friction from the rotational assembly, and air resistance. Momentum, however, is different from energy, where it describes the amount of mass in motion, which is conserved across the two experiments.