Conversation of Momentum in Collisions PDF

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This is a Lab report for a physics experiment on conservation of momentum in collisions....

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Lab Report: Experiment 6 Conversation of Momentum in Collisions

Shivam Agarwal TA: Peter Adam Mistark Lab Partners: Chris Risley March 9th, 2016 Abstract: In this experiment, we used an air table and a puck to study the momentum of elastic and inelastic collisions. We also used the dots created by the pucks on the other side of the paper to find the angle formed by the lines which we drew to connect the dots that indicated to the collision of the pucks. This experiment also helped us in finding out the changes of velocity in elastic and inelastic collisions and to trace the motion of the center of mass of a two body system.

Introduction: In this experiment we used an air table and a puck to take the readings of the movement of the puck in elastic, inelastic and a spiral collision. We were given an air table, a pair of Velcro rings (pucks), 3 large plain sheets, 2 identical clear plastic triangles, a clear plastic protractor and a clear plastic ruler. In investigation 1, we use the dots formed by the pucks on the back of the paper and then connected them with lines to calculate the distance and the change of velocity after the collision. In investigation 2, we do the same thing except that we us Velcro rings on the puck this time so that they stick to each other and we have an elastic collision. In investigation 3, instead of colliding the pucks to each other, we spin them together, so that we have a spiral motion and we can calculate the angles between them to calculate the center of massof the two bodies.

Investigation 1: Procedure: First we setup the air table in a completely straight position to prevent the pucks to move due to an unwanted force. Then we place the sheet of paper on the table on which we will be colliding the pucks to take the readings of the momentum. Then we switch the power of the air table on and bang both the pucks to each other. The pucks do not have a Velcro band, so there will be an inelastic collision. The pucks will then take a different direction. We then rotate the paper to look at the dots formed by puck. After adjoining the dots of the two pucks, we form

lines and measure the distance travelled which helps us find out the velocity and hence we calculate the momentum of the inelastic collision.

Data Processing: Before collision After collision

Velocity of puck 1 0.31 0.127

Velocity of puck 2 0.285 0.38

Change in kinetic energy: 9.65% Investigation 2: Procedure: We setup the air table in the same position as in investigation 1 to prevent the pucks to move due to an unwanted force. Then we place the second sheet of paper on the table on which we will be colliding the pucks to take the readings of the momentum. Then we switch the power of the air table on and bang both the pucks to each other. This time the pucks have the Velcro band due to which they stick to each other and we have an elastic collision. Then rotate the paper to look at the dots formed by puck. After adjoining the dots of the two pucks, we form lines and measure the distance travelled which helps us find out the velocity and hence we calculate the momentum of the elastic collision.

Data Processing: Before collision After collision

Velocity of puck 1 0.618 0.378

Velocity of puck 2 0.570 0.456

Change in kinetic energy: 50.37% Investigation 3: Procedure: We setup the air table in the same position as in the first two investigations to prevent the pucks to move due to an unwanted force. Then we place the third sheet of paper on the table on which we will be spinning the two pucks together to take the readings of the center of mass and the angle. Then we switch the power of the air table on and spin both the pucks together. This time the pucks have the Velcro band due to which they stick to each other and we have both the pucks spinning together. Then rotate the paper to look at the dots formed by puck.

After adjoining the dots of the two pucks, we form lines and measure the angles formed between the lines and the best fit line which was passed through the midpoint of the lines.

Data Processing: Angular Velocity 300 200

f(x) = − 353.99 x + 234.67

100 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-100 -200 -300 -400

Slope = -353.99 Y intercept = 234.67

Conclusion: The percentage change in kinetic energy in inelastic collision is 9.65% The percentage change in kinetic energy in elastic collision is 50.37% The slope in investigation 3 is -353.99 and the y intercept is 234.67 The angle vs. time ratio is: Angles (degrees)

Time (s) 205 163 70 57 -5 -75 -220 -300

0 0.2 0.4 0.6 0.8 1 1.2 1.4

1.6

Questions: 1. Compare the energy loss in the completely inelastic case to the approximately elastic case? Which collision demonstrated a greater energy loss? Do your results agree with theory?  The energy loss in the elastic case was higher because there was a higher decrease in the velocity due to which there was a higher decrease in the force it was applying. Resulting in a higher energy loss. The energy loss in investigation 2 is about 50% whereas the in investigation 1 is around 10%.

2. Do the centers of mass in investigation 3 lie on a straight line? Explain why they do or do not. Are the distances between adjacent points constant? Explain!  The center of mass in investigation 3 is not on a straight line but is very close to the line of the best fit. The distances between the adjacent points are not constant because the center of mass is not constant at every point because of the spiral position.

3. Do the points on your plot of angle vs. time in investigation 3 lie among a straight line? Explain.  The points on the angle vs. time graph are not on the same line but are very close to the line of best fit. They are not on the same line because the pucks were in a spiral position and did not have a constant center of mass at every point.

4. If there were no external forces acting on the two pucks, their complex motion could be described as the combination of the uniform linear motion of the center of mass and a uniform circular motion of the pucks about the center of mass. Describe how well your results agree with this explanation, and explain any deviations that you observe from the predicted behavior.  My results agree with this explanation because the points formed in my graph are very close to the line of the best fit. There are a few deviations but they are caused because of the changing center of mass of the pucks due to circular motion.

5. In investigation 3, are the momenta of each puck conserved? Explain.  The momenta of each puck are conserved because there is no change in the initial kinetic energy and he final kinetic energy will be the same due to no collision.

Acknowledgements: I would like to thank my T.A. – Mr. Peter Mistark and my lab partner Chris Risley who helped me in the lab.

References: O.Batishchev and A.Hyde, Introductory Physics Laboratory, Hayden-McNeil, 2016...