Initial Velocity Of The Second Experiment example essay topic

Measuring the Velocity of an Object Using the Ballistic Galvanometer ABSTRACT: The objective of this lab is to prove the conservation of energy and momentum by comparing initial velocities of two different experiments using the Ballistic Pendulum method. To conduct this method, a ballistic galvanometer was used to measure the velocity of a metal ball in an inelastic collision and in projectile motion. The ballistic galvanometer consists of pendulum with a holding chamber at the bottom of the pendulum arm. Across from the arm is a metal holder where the ball is positioned, pushed back, and launched from. Once the ball is launched, it shoots directly into the chamber of the pendulum with an initial velocity (V), and swings back to the top of the galvanometer at a higher position. The pendulum is stopped from coming back down when it swings back by a grooved, rubber padding that catches onto the chamber.

This method described above is a demonstration of inelastic collision. Three trials of this experiment were conducted to record the change in height (h) of the pendulum arm after each trial. The mass of the arm / pendulum (M), mass of the ball (m), the acceleration of gravity (g), and the measured heights are known and from this data, the initial velocity can be calculated using the equation shown below. The second part of the lab was to measure the initial velocity of the same metal ball using the same ballistic galvanometer. Except, instead of the ball shooting into the chamber of the pendulum, it was launched from the top of the table, where the galvanometer was positioned, to the floor. One trial was done where the height of the table (h) and the distance on the floor where the ball landed (x) was measured.

From this data and the acceleration of gravity (g), the time (t) was calculated using the equation shown below. Once the time (t) was calculated, the initial velocity (v) can be calculated using another equation given below. By comparing the two initial velocities of the two different experiments, the conservation of energy and momentum can be confirmed by how close the values of the two velocities were to each other. METHODS: The figures below demonstrate set up of the two different experiments using the same galvanometer. To measure the change in height in the first experiment of the pendulum arm from the start position to the final position, the initial height was measured in centimeters from the tabletop to the middle of the chamber of the pendulum before the collision.

Then the final height position was also measured in centimeters from the table top to the middle of the chamber as it sat on the rubber padding after the collision. For the second experiment, the height from the tabletop to the floor was measured in centimeters using a two-meter ruler. The distance on the floor from the table to the position where the ball landed (x) was measured in centimeters using a two-meter ruler as well. Formulas: Experiment 1: Inelastic Collision Experiment 2: Projectile Motion V = (M+m) x 2 g h t = 2 h V = X m g t RESULTS: CONCLUSION: The initial velocity of the first experiment was not equal to the initial velocity the second experiment with a difference of 78.8 cm / 's. The initial velocity of the second experiment where the ball was projected to the floor had a lower velocity. This is because the velocity of the ball was measured over a longer distance than the velocity of the ball when it entered the chamber of the pendulum.

The ball must have slowed down over the longer distance rather than having the faster velocity when shot in a short distance. However, since the initial velocities of both experiments were close in value to each other, the law of conservation of energy and momentum still hold true. The potential energies of both experiments were equal to the kinetic energies and that was how the initial velocities for both experiments were calculated. In terms of momentum, the inelastic collision of the first experiment shows that energy was not conserved before and after the collision because the momentum is changed. The momentum of the ball by itself is changed once it enters the chamber of the pendulum because the masses are added together after the collision as opposed to each mass by itself. The errors that occurred in the experiments can be due to the swinging of the pendulum arm before launching the ball in experiment one.

Also, human errors could have been made in experiment 2 when observing the spot where the ball landed on the floor and gave an incorrect distance for x..