Work and Energy on an Air Track - Lab For Phys 1151 PDF

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This is a Lab report for a physics experiment on work and energy on an air track....

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Lab Report: Experiment 7 Work and Energy on an Air Track Shivam Agarwal TA: Peter Adam Mistark Lab Partners: Chris Risley March 25th, 2016 Abstract: In this experiment, we used a linear air track with glider and air pulley to verify the work-energy theorem. We did the experiment twice, once by inclining the air track and sing no masses and for the other time we kept the air track completely straight and hung a mass at one end to look at the change in kinetic energy and acceleration. The main purpose of this experiment was to measure the acceleration of gravity using precision instruments.

Introduction: In this experiment, we used an air track to measure the acceleration of gravity and the work energy theorem. We were given a linear air track with glider and air pulley, a computer o measure all of the data, a PASCO PASPort USB link, a motion sensor, a small block and a 1 ounce lead weight with clip and paper tape. There were two investigations in this experiment. In investigation 1, we had to keep the air track inclined and then switch the power of the apparatus and the motion sensor on, so that the PASCO Capstone could measure the motion and can print a graph representing the motion of the glider. As we had the graph, we had to then calculate the velocity and the average position of the glider to plot a graph of velocity^2 against the average position to find out the acceleration due to gravity and the percentage difference in the actual and he experimental value. For investigation 2, we had to repeat the same experiment with the some details changed. First of all, we had to keep the air track horizontal instead of inclined and we had to hang the 1 once lead with the clip on the other end of the glider. This experiment was conducted to understand the work-energy theorem and to measure the acceleration due to gravity.

Investigation 1: Procedure: In this investigation, first we had to keep the air track inclined so that we could measure the motion in an incline. Then we switched the power of the motion sensor and the apparatus on, so that the glider moves to the other end due to the force of gravity. The surface of the glider and the apparatus were smooth, so that the frictional force acting on the experiment is only on the upward direction due to which there are two slopes produced. As the glider, moved to the other

side it collided at the end three to 4 times, so that the computer could graph its movement and position as it had a changing kinetic energy. After we had all our data, we used the metrics known to us to calculate the velocity, velocity^2 and the average position in order to learn more about the work-energy theorem and then we plotted a graph of position against time and a graph of velocity’^2 against average position. The latter graph had two lines due to which we had two slopes which helped us the find the average acceleration due to gravity.

Data Processing: Chart Title 1.4 1.2

Positon(m)

1 0.8 0.6 0.4 0.2 0

0

2

4

6

8

Time(s)

10

12

14

16

18

0.7

Linear ()

0.6 f(x) = 0.48 x − 0.07

Velocity ^2 (m/s)

0.5

Linear () Linear ()

Linear () Linear ()

Linear ()

f(x) = 0.57 x − 0.23

0.4

0.3

0.2

0.1

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ave Positon (m)

0.5692 = 2gsin (1.78) 0.4817 = 2gsin (1.78) Acceleration = 9.1629 m/s^2 Percentage difference = 6.5%

Investigation 2: Procedure: This investigation was very similar to the first investigation. We had to mostly repeat the same steps but first we had to keep the air track straight so that there is no incline and we could measure the motion of the glider horizontally. Then we had to attach a 1 ounce lead weight with a paper clip on the other side of the glider so that it has a mass while it moves and the motion sensor catches the motion of the glider. The rest of the experiment was the exact same as we calculated the velocity, velocity^2 and the average position of the glider with the given metrics and then drew the same graphs to have two different slopes which then helped us to find out the acceleration due to gravity.

Data Processing:

Chart Title 1.4 1.2 1 0.8 0.6 0.4 0.2 0

0

1

2

3

4

5

6

7

8

9

1.2 f(x) = 1.29 x − 0.48

1

0.8

f(x) = 1.52 x − 1.16

0.6

0.4

0.2

0 0.2

0.4

0.6

0.8

2(.03)*g/ (0.03+.337) = 1.29 2(.03)*g/ (0.03+.337) = 1.5214 Acceleration = 8.59 m/s^2 Percent Difference = 12%

Conclusion: In investigation 1, Acceleration due to gravity = 9.1629 m/s^2 Percentage difference in actual value = 6.50% In investigation 2, Acceleration due to gravity = 8.59 m/s^2

1

1.2

1.4

Percentage difference in actual value = 12%

Evaluation: The different errors that could have possibly been made while calculating the acceleration could be: 1. Systematic errors = the errors that could have been made by us while conducting the experiment like not keeping the air track completely straight or taking the reading of the motion wrong. 2. Random errors = the errors that were not made by us but happened because the experiment was conducted once and so may have been there due to lack of precision like the lead weight moving because of the loose paper tape that made it stuck to the glider.

Questions: 1. For the configuration of investigation 1, what is the kinetic energy change over one full cycle of the motion?  Kinetic energy = 0.5 * m * v^2 = 0.5 * 0.337 * 0.0676 = 0.0113 m/s^2 2. For the configuration of investigation 2, what is the initial kinetic energy of the system as you release the glider? What is the final kinetic energy just before the glider crashes into the bumper?  0.5 * m * v^2 So, Initial KE = 0.5 * (0.337 +0.03) * 0.0004 = 7.34 * 10^-5 J Final KE = 0.5 * (0.337 + 0.03) * 0.2116 = 0.0388 J 3. For the configuration of investigation2, what is the change in potential energy from the moment of release to the moment of collision with the bumper? Considering the kinetic energy of the system just before it crashes into the bumper, what is the change in total energy of the system? Is the change in energy positive or negative? Explain whether your result makes sense.  4. For the configuration of investigation 1, for the upwards part of the motion, how does friction affect the total energy of the glider? How does it affect the total energy for the downwards part of the motion?

 For the upward part, the friction affects the total energy of the glider in a negative way whereas it does not affect the total energy in the downwards part. 5. For the configuration of investigation 1, draw force diagrams for all the forces on the glider including friction, for both the case of upwards and downwards motion.

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...