11-2-05 Physics Lab Purpose: The purpose of this experiment was to conduct a series of ramp experiments to determine how a collision with a marble affects the velocity of a ball rolling down a ramp system. Procedure: In this experiment we set up a ramp system that we would conduct a series of experiments with a steel ball and a glass marble. The ramp system was 5.6 cm in the vertical position from the table with an elevation of `dy of 5.5 cm since the track is 1 cm tall on the other end. The ramp also has a piece that is level with the table that is approx. 3 cm from the end of the table. There a piece of drinking straw is cut and supports a glass marble, that will be used in the experiment to conduct a collision. First we set up the ramp, and put paper on the floor to mark the exact position of the balls travel in the horizontal positioning. We dropped the steel ball off of the edge of the table to get a point to measure from the see exactly how far the ball will travel horizontally. For an exact mark we used carbon paper to mark the place of impact on each trial. After we conducted the vertical drop we ran the steel ball down the ramp with no collision to take place. The ball had a velocity coming off of the ramp in the horizontal direction so the ball went off of the table and traveled horizontally in the direction that it left the table. The ball traveled a distance and then was marked again using carbon paper to get a location of impact. The same ball was then used in the experiment to collide with the glass marble that was being supported by the drinking straw. There was great detain in the experiment to make sure the ball and the marble met at an angle the promoted 90 degree angles in both the vertical and horizontal positioning, so it would hit flush and there would be an even and exact collision. The experiment was conducted and the positioning of the ball and the marble were noted by the use of carbon paper. We had data to show us the position of vertical fall off of the table, the position of horizontal travel by the ball with no collision and the ball in collision as well as the marble in the collision. Data: Distance from the ramp system to the floor 92 cm Time it took the ball to reach the floor .43 sec Determined using the equation Vf^2 = V0^2 + 2 a `ds. Which equals vf = sort( 2( 9.8 m/s^2( .92 m )). Which gives us a final velocity of 4.24 m/s^s which can be divided by the acceleration of gravity to give us the `dt. Since the ball was traveling in the horizontal direction, the acceleration of gravity plays no part in the calculations of velocity, and since it has no acceleration the V0, Vf and Vave are all equal to each other. The ball alone had a `ds of 32 cm, so the Vave is determined using `ds/`dt = 32 cm /.43 sec= 74.4 cm/sec The ball in the collision with the marble had a `ds of 30 cm so its Vave was 30cm/.43 sec= 69.8 cm/sec. The marble used in the collision had a `ds of 60 cm so it Vave was 60cm/.43 sec = 139.5 cm/sec. The velocity change of the steel ball was from the collision minus the undisturbed roll which is 69.8 cm/sec- 74.4 cm/sec, which gives a `dv of -4.6 cm/sec. The velocity change of the marble can be conducted by using the final velocity of impact with the floor minus the initial which is zero since it was sitting still during collision. 139.5 cm/sec - 0 cm/sec = 139.5 cm/sec for the `dv of the marble. Therefore the steel ball is more massive since it had the least change in magnitude of velocity change, since it was bigger it was less affected by the collision. By using a ratio the steel ball is 30:1 times more massive than the marble. Since it is more massive then it must have a greater volume, but how much greater is the volume. If the radius of the steel ball is 25 mm and the radius of the marble is 18mm, the volume can be conducted by using ( D2 / D1) ^3 = ( 25mm/18mm) ^3 = 12500/ 5800 = 2.1 Therefore the steel ball has a volume 2.1 times greater than that of the glass marble. Since the volume of the steel ball is about 2.1 times as much and about 30 times as massive then the density can be determined by using m/v. Conclusion: In conclusion I feel that we conducted the experiment correctly and observed a promising result with creditable data.