Experiment Ballistic Pendulum

Experiment: Ballistic Pendulum Purpose The purpose of this experiment was to use a ballistic pendulum to determine the speed of a projectile by utilizing the conservation of momentum, conservation of energy, and kinematics. Theory A ballistic pendulum is a device that can be used to measure the speed of projectiles by using both conservation of momentum and conservation of energy. It contains a swinging pendulum and a spring gun. The gun shoots out the projectile (ball bearing) into the pendulum’s bob, creating an inelastic collision. There is a measuring bar that moves when the bob and ball collide. This bar moves to a certain angle, allowing us to obtain quantitative information about the collision. The angle can be used to determine the change in the height from the bottom of the pendulum to the final height of the ball and bob. The height can be used to find the speed of the pendulum and projectile by using conservation of energy. Conservation of momentum can then be used to find the speed of the projectile itself. The first part of our experiment served as an inelastic collision, a collision in which the objects’ shape is deformed or they stick together. In an inelastic collision, the momentum is conserved, but the kinetic energy is not. The momentum of the first step (the ball being shot from the gun), the second step (the ball entering the bob), and the conservation of the momentum between steps 1 and 2 can be seen in the following equations: The next two stages for the motion of the ball and pendulum do not involve conservation of momentum, but involve conservation of energy. No other collision occurs after the ball enters the bob; the two bodies simply swing upward together, which is why energy will be conserved between these steps of the experiment. In step 2 (the ball swinging in the bob), there is kinetic energy and potential energy, while in step 3 (the pendulum swinging to its max height), there is only potential energy, because velocity is 0 m/s at the max height. All the above can be seen in the following equations: As mentioned above, the bob will swing to a max height, which gives an angle (theta), that is recorded in order to determine the change in height. This value can be used, along with the conservation of energy equation of steps 2 and 3, to determine the velocity of the pendulum and bob. After the velocity of the pendulum and bob in step 2 is found, then that velocity, along with the conservation of momentum equation of steps 1 and 2, can be used to find the velocity of the projectile itself. A ballistic pendulum can also be used to determine the speed of a projectile by using projecile motion and 2D kinematic equations. For this to work, a ballistic pendulum will be place on the edge of a bench (with the pendulum part removed). When the ball is fired, it will exhibit free fall, and a change in distance in both the x and y directions will occur. The change in these distances can be used to determine the speed of the projectile by using the following kinematic equations: The percent difference can be found for these two portions of the experiment. A percent error can not be determined, as there is no GAV, but we will compare the two velocities using the following equation: Procedure For the first half of the experiment, we placed the ballistic pendulum on a level surface, pointed away from group members and breakables. We measured the mass of the projectile (ball bearing) using a triple beam balance. The mass of the pendulum was given to us by our lab instructor. I was responsible for this part. We placed the ball into the spring gun, pulled the spring back to the first notch, and then released the gun. Upon firing into the bob, the ball pushed the measuring bar to a certain angle, which was used in our calculations. We repeated this process for four more trials. I was responsible for reloading the ball into the gun after each trial. For the second experiment, we placed the ballistic pendulum at the edge of the table. We disconnected the bar portion of the apparatus so that the ball could land onto the floor upon firing. On the floor, we placed three sets of computer paper and transfer graphite paper in the range of the projectile. These papers were arranged so that the ball would mark its landing location upon landing. We layers the papers in this order: computer paper, graphite paper, and another computer sheet on top. We placed the ball into the spring gun as before, pulled back the spring to the first notch again, and released the gun. Someone was responsible for noticing on which of the three sheets the ball landed, and another tracked and retrieved the ball. We measured the height of the ballistic pendulum’s barrel from the floor as well as the range of the projectile for each trial (5 trials total) using a meterstick. Data (attached) Analysis (attached) Diagrams: Here are pictures of some of the equipment we used to obtain our measurements. Diagrams (continued): Conclusion The results of the first part of one of this experiment gave us an average angle of 27.8 degrees and average change in height of 0.0265 m. Using this change in height and the conservation of energy between steps 2 and 3, we were able to find the velocity of the ball and bob in step 2, which equaled 0.7211 m/s. By plugging this velocity into the equation for the conservation of momentum of steps 1 and 2, we were able to find the velocity of the projectile itself, which was 8.858 m/s. In the second part of the experiment, we used the measured values for the change in distance, along with kinematic equations, to determine the time it took the ball to fall. The average vertical displacement measured was 0.85 m, and the average horizontal displacement measured was 2.1545 m. We were able to use kinematic equations because the acceleration in the y direction of a free falling body is just due to gravity. The time we found (0.416 s) was then plugged into another kinematic equation, along with the change in distance in the x direction, to determine the velocity of the ball, which equaled 5.179 m/s. When comparing these two values using the percent difference formula, we calculated a percent difference of 52.42%. This shows that our results were not very alike, meaning that our results lacked precision. Some sources of error for these experiments may have been that the mass of the ball bearing was measured improperly, different people released the gun at different speeds, or an inaccurate reading of the angle on the ballistic pendulum. There also could have been friction at the top of the pendulum (the fulcrum of the arm that suspended the bob). This would have altered the maximum heights reached after the collisions. We also noticed that the measuring bar on the ballistic pendulum did not tend to stay still after the collision. Instead, it often bounced back to a smaller angle. This could have altered our measurements for the angles.