Glancing Collisions and Conservation of Momentum

Transcription

1 Bob Somers 12/16/04 Per. 4 Daniel Lau, Patrick Noland Glancing Collisions and Conservation of Momentum Purpose In this lab we set out to prove that momentum is conserved in the real world, even in glancing, two-dimensional situations. Using concepts from previous chapters we were able to set up an environment to effectively measure the necessary information to compute the momentums before and after the collision. This was a key step in being able to prove that the momentum is conserved. Theory There was a lot of theoretical reasoning behind this lab. Much of it used concepts from previous knowledge to set up a situation in which momentum could be effectively and accurately measured. We know that projectiles move on their axis independently of one another. For example, we know that the horizontal velocity of an object does not affect the rate at which it falls vertically, however the time remains the same for both. We could then use this fact coupled with the tool of carbon paper to measure the distance that the large ball covered after leaving the edge of the ramp. After computing the time it took for an object to fall the distance of the table we were able to link the horizontal distance and vertical fall time to obtain horizontal takeoff velocity.

2 We then could use the horizontal velocity of the ball and the measured mass of the ball to obtain our starting momentum. This gave us a number to compare to once we had finished the glancing collision calculations. We then began dropping the ball down the ramp with a smaller ball at an offset as to create a two-dimensional collision. We repeated the process of the first ball, by measuring the horizontal distance and using the vertical drop time link to find the velocity of each ball after the collision. Using the mass measurements of the balls and the measured impact angles we were then able to deduce the momentum after the collision, which was surprising close to our original value. This made it quite easy to prove that momentum was conserved in glancing collisions. Procedure 1. Tape together four sheets of paper and tape them to the floor in the landing zone of the ramp. Be sure that the hanging bob is just over the edge of the landing zone paper. 2. Lay the carbon paper gently on top of the landing zone paper. 3. Make sure that the peg is swung off to the side and drop the large ball down the ramp. Run this a few times to obtain a cluster of dots on your target paper. 4. Place the small ball on the peg. Slide it back just far enough so that the large ball will clip it as it comes down the ramp. 5. Drop the large ball down the ramp and watch the two balls collide. Run this a few more times to obtain a cluster of dots. 6. Make sure to mark the position of the hanging bob on your landing paper. This will later be used for data collection. Data Ramp height from ground: cm = m Large ball distance w/o collision: cm = m Large ball distance w/ collision: cm = m Small ball distance w/ collision: cm = m Large ball mass: 28.1 g = kg Small ball mass: 16.3 g = kg Collision spread: 52.4 Observations The ball made noise as it rolled down the ramp. Both balls made noise when they collided with each other and the floor. Both balls were made out of metal and had a similar physical makeup except for the difference in masses. The ramp wobbles slightly after the ball travels down the ramp. Both balls hit the ground at the same time. Without the collision, the large ball lands in line with the ramp. When a collision occurs, the balls spread in opposite directions.

3 Calculations First we calculate the time it takes the large ball to fall to the ground from the ramp height. x = ½at = ½(-9.80)t 2 t = s Next we use the time and the large ball s (w/o collision) horizontal distance to find a takeoff velocity = v(0.3896) v = m/s Next we use the vertical fall time and the large ball s (w/ collision) horizontal distance to find an after collision velocity = v(0.3896) v = m/s Next we use the vertical fall time and the small ball s (w/ collision) horizontal distance to determine its after collision velocity = v(0.3896) v = m/s Now we compute our momentum value before the collision by using the large ball s mass and its w/o collision takeoff velocity. p = mv p before = (0.0281)(1.005) p before = kgm/s Now we compute the momentum value of the collided large ball using its mass and its collision velocity. p = mv p large = (0.0281)(0.5587) p large = Now we compute the momentum value of the collided small ball using its mass and its collision velocity.

4 p = mv p small = (0.0163)(0.9701) p small = Now we set up our glancing collision triangle with two sides being the momentum values of the collision balls and the included angle being 180 minus the spread angle of We use the law of cosines to find the momentum on the third side. c 2 = a 2 + b 2 2ab cos C c 2 = (0.0157) 2 + (0.0158) 2 2(0.0157)(0.0158)(cos ) c = kgm/s Finally we do a percent difference calculation to find our how far off we were. (accepted experimental) x 100 = % difference accepted ( ) x 100 = % difference Error Analysis There were a couple minute factors that could cause a slight amount of error in this lab. However, for the most part this lab was pretty safe from any major sources of error, provided that it was conducted correctly. One small source of error is the lack factoring in air resistance. This would slow down the ball traveling after the collision very slightly causing it to cover less distance. This in turn would translate into a slower velocity, which would give us a slower momentum value. This would ultimately result in negative error. The wobbling of the ramp is something else that could have minutely affected the results. If the ramp were to wobble in one direction when the ball leaves the ramp, it could have a slight horizontal component that we weren t anticipating. We assumed that the ball left the ramp with a completely linear component. If, however, not all of its velocity was concentrated in the linear direction, it would translate into slower velocities after collision. This would in turn give it less momentum and negative error. The wobble in the ramp could also cause the ball to leave the ramp in a perfectly linear path like we anticipated, but not with all the velocity we had calculated. This would have the same effect as the source of error previously described. Conclusion As witnessed by the results of the lab, we were able to conduct an experiment with glancing collisions and be quite accurate with our conservation of momentum. Glancing collisions are difficult to measure in real life because you must measure the spread angle and the velocities of each object before and after the collision. By conducting the experiment for the most part in the air we were able to keep (relatively) constant velocity until the balls reached a point where we could physically measure their distance accurately. Not only did we end up finding a solution to the glancing collision experiment dilemma, but we also got to use and practice our projectile calculations as we found necessary data to link all of the pieces together. In this lab I gained great insight on how

5 to solve problems in different ways, ones which may not be readily apparent. I learned how to analyze a problem and look for a unique and workable solution to the problem without keeping myself restricted to the usual way of doing things.