11e-Conservation of Momentum 1-17-09 - 1 - THE CONSERVATION OF LINEAR MOMENTUM Introduction In this experiment you will test the validity of the Law of Conservation of Linear Momentum in one dimension utilizing elastic and inelastic collisions on an air track. Apparatus Computer with Logger Pro software Air Track Accessory kit - bumpers for the elastic collision Right angle clamps (2) or integral photogate clamps Vernier Lab Pro box Air Track Gliders (2) Laboratory Balance Pasco Air Track Vernier Photogate (2) Air supply Ring Stands (2) Figure 0: Elastic Near Collision Theory If two objects collide, and are subject to no net external forces, then it can be shown by application of Newton's 2nd and 3rd Laws that the total linear momentum of the system of masses will not be altered by the collision. The linear momentum of an object of mass m1 and velocity v1 is given by p1 = m1v1. In a system consisting of two objects of momentum p1 and p2, the total linear momentum is the vector sum of their individual momenta: p1 + p2 = m1v1 + m2v2 The total linear momentum before collision is m1v1 + m2v211e-Conservation of Momentum 1-17-09 - 2 - Figure 1 (Before the collision) If the two masses collide, in general, their velocities will be altered to v1' and v2', respectively. The total linear momentum after collision is m1v’1 + m2v’2 Figure 2 (After the collision) According to the conservation of linear momentum principle, the total linear momentum will not be altered by the collision, or p1 + p2 = p1' + p2' (1) that is: m1v1 + m2v2 = m1v’1 + m2v’2 (2) Procedure Conventions: Glider #2 is always the glider that is launched. Glider #1 is always the glider that starts out at rest between the two photogates. Ensure that the photogate that Glider #2 initially passes through is labeled Photogate #2 and that it is plugged into Digital Input #2 in the Vernier Lab Pro box. Ensure that the photogate that Glider #1 passes through is labeled Photogate #1 and that it is plugged into Digital Input #1 in the Vernier Lab Pro box. 1. Start the computer. 2. Turn on the air supply and increase the flow volume until the gliders are floating on a cushion of air. Level the air track by placing a glider in the center of the track and adjusting the leveling screws until the glider will remain at rest. 3. Clearly label the Gliders as #1 and #2 using a small piece of masking tape. 4. Plug the photogate timers into the Digital Inputs #1 and #2 in the Vernier Lab Pro box according to the convention above. Place the photogates symmetrically about the center of the track, leaving about 70 cm of open space between them. 5. Place one of the unused cylindrical track accessories on the top of each glider. These will be used as “flags.” Adjust height of photogates so that the flags will interrupt the beams when the gliders pass through the photogates. (Test to see if photogate timers work properly – when the beam is blocked the Red LED will light up.)11e-Conservation of Momentum 1-17-09 - 3 - 6. Open the Collision Timer file: Under the File menu click on the Open menu item. The Experiments folder will open, double click on the Probes and Sensors folder, double click on the Photogates folder and then double click on the Collisions Timer file. 7. Enter “Flag Lengths” - one for each photogate (to 4 significant figures). Measure the diameter of the flags using the calipers in the laboratory. To enter the numbers into the computer: Click on the Experiment menu and click on the Set Up Sensors menu item. Then select Show All Interfaces. Click on the first Photogate icon and select “Set Distance or Length.” Then enter “Flag Length” or “Photogate Distance” and click OK. Repeat for the second photogate. PART 1: Elastic Collision Figure 3: Elastic Near Collision 1. Affix a spring bumper to Glider #1 and a knife-edge to Glider #2. These must go in the lower holes - center of mass. Balance the gliders with another fixture on the other end. All parts weigh about the same. Weigh both gliders (with the bumpers and flags). Enter the masses of each glider and the width of the flags in Table 1. 2. Place Glider #1 between the two gates and carefully bring it to rest. Start the timer by clicking on the Collect button and launch Glider #2 toward Glider #1. If the two gliders are of identical mass then Glider #1 should move in the same direction as the incident Glider #2 at the same initial velocity of Glider #2 and Glider #2 would be at rest. In this case all the momentum was transferred from Glider #2 to Glider #1. If Glider #1 is more massive than Glider #2 then Glider #2 will rebound. If Glider #1 is less massive than Glider #2 then Glider #2 will not come to rest but will follow Glider #1. Catch the glider before it bounces off the end air track bumper. 3. The computer records all times and calculates velocities. Record these velocities (to 4 significant figures) in Table 1 Calculate the momentum and enter the results in Table 1. Compare total momentum prior to the collision to total momentum after. [Don't forget that momentum is a vector quantity! It has a direction (+ or – in this case) as well as a magnitude. Calculate % difference – the quantity (PT’ - PT) divided by PT and then multiplied by 100. Repeat 3 more times for a total of 4 data sets.11e-Conservation of Momentum 1-17-09 - 4 - PART 2: Inelastic Collision Figure 4: Inelastic at launch 4. Rotate the gliders by 180o so that the straight pin and a clay cup will be facing each other. Remove the safety cork from the straight pin. NOTE: It is essential that the clay in the clay cup be repacked after each run to fill in the hole. 5. Weigh both gliders and enter the data in Table 2. Ensure that the masses are the same to within 1.0 gram. If necessary, add a couple 1.0 gram disks to the lighter glider to make them as close to equal, in mass, as possible. 6. Place Glider #1 between the two gates, and bring it to rest. Start the timer by clicking on the Collect button, and launch Glider #2 toward Glider #1. 7. Go to step #3 and repeat that Procedure. 8. You have finished taking data. In Part 3, you will use the data that was taken in Part 1 and Part 2, for the Kinetic Energy calculations. PART 3: Energy Calculations 1. In the elastic cases the value of the total kinetic energy should be the same after the collision as it was before the collision. • Compare the kinetic