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CONSERVATION OF MOMENTUM

In order to test the conservation of momentum we will conduct an experiment with air hockey pucks. We will use two pucks to create an elastic collision. One puck is stationary, while the other is launched directly at it using a rubber band. In order to find momentum, we need to find the velocity of both pucks before and after the collision. To find the velocity of the first puck, we will launch it without the second puck there and record the time it takes for the puck to hit the side of the air hockey table and measure the distance from its starting position to the edge of the table. To find the velocity of the second puck, we will launch the first puck into the second and record the time it took for the puck to reach the end of the table from the collision. After recording and analyzing all data we will determine whether momentum was conserved or not.

Materials: Air Hockey Table 1 octogonal hockey puck 1 circular hockey puck Meter Stick Rubber Band Stopwatch

Safety Precautions: We will take care to set up the launcher to ensure that it does not stray from the intended path and hit anyone. We will make sure no one is standing at the edge of the table, where fingers could get hit by the pucks.

media type="file" key="Kyle.mov" width="383" height="383" Mr. Eddy Approves

Procedure: || ** FORCE APPLIED TO M1 ** || ||  7.5 N   || ||  7.6 N   || ||  7.4 N   || || ** 7.5 N ** || || ** WEIGHT OF M1 & M2 ** || ||  0.035 lbs || ||  0.034 lbs || ||  0.036 lbs || || ** 0.035 lbs ** || || ** DISTANCE M2 TRAVELED ** || ||  1.5 m   || ||  1.6 m   || ||  1.4 m   || || ** 1.6 m ** || || ** TIME ELAPSED OF M2 ** || ||  0.542 s   || ||  0.535 s   || ||  0.536 s   || || ** 0.535 s ** ||
 * We decided to conduct an experiment using an a rubber band to launch an air hockey puck on an air hockey table to create an elastic collision with another air hockey puck.
 * By conducting this experiment we hope to prove that momentum is conserved in an elastic collision.
 * In order to collect data, we took the mass of the two different air hockey pucks. We also measured the distance between the stationary puck and the other puck before it was launched. We used a meter stick to measure the length of the pucks. We used a spring scale to measure the force that the rubber band had on the puck. A meter stick was also used to measure the distance that the puck traveled after the collision.
 * We had a problem finding the velocities because the length of the table was relatively short so the distance and time, which was recorded using a stopwatch, made the results inaccurate.
 * To correct this, we modeled the experiment to have the maximum distance from where the collision occurs to the table edge to increase distance and therefore time, which would be less affected by reaction time.
 * We also videotaped the collision and by using a feature on the camcorder called "frame advance" we were able to calculate the velocity of the second puck even more accurately.
 * Frame advance shows the movement from one frame to the next, so we were able to pinpoint the exact frame in which the puck hit the edge of the table. To find out how much time passed in each frame, we videotaped a stopwatch with milliseconds and recorded how much time passed between each of the frames. By finding the time in each frame and counting the number of frames from the collision until the puck hit the edge and multiplying, we were able to find the full time elapsed in a more accurate way.
 * Data Collection:
 * ** TRIAL **
 * ** 1 **
 * ** 2 **
 * ** 3 **
 * ** AVERAGE **
 * ** TRIAL **
 * ** 1 **
 * ** 2 **
 * ** 3 **
 * ** AVERAGE **
 * ** TRIAL **
 * ** 1 **
 * ** 2 **
 * ** 3 **
 * ** AVERAGE **
 * ** TRIAL **
 * ** 1 **
 * ** 2 **
 * ** 3 **
 * ** AVERAGE **



BEFORE THE COLLISION **M1** .035 lbs X __1 kg__ = **0.0159 kg** 2.2 lbs F = ma 7.5 = (.0159)(a) Vf**2** = Vi**2** + 2aΔX Vf**2** = 0 + 2(471.7)(0.067) This final velocity found in the previous step is the initial velocity for this problem. The acceleration in the x-direction is 0 m/s. The distance the puck travels before the collision is 0.33m. Vf**2** = Vi**2** + 2aΔX Vf**2** = (5.622)**2** + 2(0)(0.33) .035 lbs X __1 kg__ = **0.0159 kg** 2.2 lbs Object is at rest AFTER THE COLLISION .035 lbs X __1 kg__ = **0.0159 kg** 2.2 lbs Object is at rest .035 lbs X __1 kg__ = **0.0159 kg** 2.2 lbs __ Using stopwatch: __ Distance traveled: 1.6 m Time Elapsed: 0.535 s  V = d/t V = 1.6/0.535 __ Using frame advance: __ Distance traveled: 1.6 m Time Elapsed: 0.81 s  V = d/t V = 1.6/0.81 || M  ||  V  ||  P  || || 0.0159 kg  ||  2.371 m/s || 0.0377 W  || || 0.0159 kg  ||  0 m/s || 0 W  || ||  ||   || ** 0.0377 W ** || __ Using stopwatch: __ || ** M ** || ** V ** || ** P ** || ||  0.0159 kg   ||   0 m/s ||  0 W   || ||  0.0159 kg   ||   2.99 m/s ||  0.0475 W   || ||    ||     ||  ** 0.0475 W ** || __ Using frame advance: __ || ** M ** || ** V ** || ** P ** || ||  0.0159 kg   ||   0 m/s ||  0 W   || ||  0.0159 kg   ||   1.97531 m/s ||  0.0314 W   || ||    ||     ||  ** 0.0314 W ** || % ERROR % error = __(B-A)__ X100 (B+A)/2 __ Using stopwatch: __ % error = __(0.0377-0.0475)__ X100 = **23% ERROR** (0.0377+0.0475)/2 __ Using frame advance: __ % error = __(0.0377-0.0314)__ X100 = **18.2% ERROR** (0.0377+0.0314)/2  MOMENTUM || M  ||  V  ||  P  || || 0.0159 kg  ||  2.371 m/s || 0.0377 W  || || 0.0159 kg  ||  0 m/s || 0 W  || ||  ||   || ** 0.0377 W ** || || ** M ** || ** V ** || ** P ** || ||  0.0159 kg   ||   0 m/s ||  0 W   || ||  0.0159 kg   ||   1.97531 m/s ||  0.0314 W   || ||    ||     ||  ** 0.0314 W ** ||
 * 1)  Find the mass:
 * 1)  Find the acceleration of the puck:
 * a = 471.7 m/s2 **
 * 1)  Using Part 1 of the diagram, find the velocity of the puck right after the force acts on it:
 * Vf = 5.622 m/s **
 * 1)  Using Part 2 of the diagram, find the velocity of the puck right before the collision:
 * Vf = 2.371 m/s **
 * M2 **
 * 1)  Find the mass:
 * 1)  Find the velocity right before the collision:
 * V = 0 m/s **
 * M1 **
 * 1)  Find the mass:
 * 1)  Find the velocity right after the collision:
 * V = 0 m/s **
 * M2 **
 * 1)  Find the mass:
 * 1)  Find the velocity of the object right after to collision:
 * V = 2.99 m/s **
 * V = 1.97531 m/s **
 * BEFORE: **
 * ** M1 **
 * ** M2 **
 * ** TOTAL **
 * AFTER: **
 * ** M1 **
 * ** M2 **
 * ** TOTAL **
 * ** M1 **
 * ** M2 **
 * ** TOTAL **
 * BEFORE: **
 * ** M1 **
 * ** M2 **
 * ** TOTAL **
 * AFTER: **
 * ** M1 **
 * ** M2 **
 * ** TOTAL **

Conclusions:
 * After analyzing our data we found that our momentum was not completely conserved. This could be due to various different errors that may have occurred during our experiment.
 * Sources of Error
 * One error we encountered was while we were solving the equations to find the final velocity. At first we found 400% error because we only split the experiment up into two separate equations instead of three. The three separate problems needed to be parts 1, 2 and 3 as seen in the picture.
 * Another source of error that influenced our results was that our launcher had differences between the trials due to movement of fingers and the rubber band being stretched out.
 * Error could have also occurred between finding the velocity of the first puck and second puck because two different people launched the puck, and because of differences in steadiness and finger placement, our results could have been effected.
 * Kelsey did the data section, but I just uploaded it for her.