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One Dimensional Motion Essay Sample

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One Dimensional Motion Essay Sample

Introduction

Motion is everywhere: friendly and threatening, horrible and beautiful. It is fundamental to our human existence; we need motion for learning, for thinking, for growing, and for enjoying life. Like all animals, we rely on motion to get food, to survive dangers, and to reproduce; like all living beings we need motion to breathe and to digest.

Motion is the most fundamental observation about nature at large. It turns out that everything, which happens in the world, is some type of motion. This lab looks at one-dimensional motion namely kinematics. This is when an object moves in relation to something else. It is the most basic of motions and a great starting point in researching motion. In looking at motion in a more scientific manner rather than just observing this lab will be taking measurements to look at relationships of distance, velocity and time. These measurements should agree with the known Galilean theories of motion.

Method Part A

A CBL unit was used with a motion sensor that could determine distance. The apparatus was placed on top of a table facing a long hallway with no obstructions. The CBL unit was then attached to a Ti-83 plus calculator to gather the data from the experiments. The HIKER program on the calculator was performed, which took distance measurements every 0.1 seconds for 6 seconds. Each test was collected then the results were inputted into the Graphical Analysis program for regression analysis. The first test was that of a person walking away as shown in figure 1. The second test was that of a person walking away at a faster pace as shown in figure 2. The third test was that of a person walking towards the detector as shown in figure 3. The fourth test was that of a person standing still with no movement, which is shown in figure 4 and the last test was that of someone walking away and coming back, which is shown in figure 5. Each graph has the corresponding regression curve of best fit that was calculated using Graphical Analysis.

Figure 1. Walking away

Figure 2. Walking quickly away

Figure 3. Walking towards

Figure 4. Standing still

These are basic motional movements that a regression curve or line and be placed over. The resulting regression analysis put forth equations for each test. These equations can be further analyzed to see what took place in each test.

Figure 5. Walking away and coming back

Next the same CBL motion detector was taken outside to allow for enough room for the test and placed on a table. Foam was packed around the sensor to ensure that the device wouldn’t be damaged during the test. The sensor was placed facing up. Again, like before, the CBL unit was attached to the Ti-83 plus calculator for data collection and the BALLDROP program was executed. The program took readings of distance at 0.02 seconds for approximately 1.6 seconds. After the program executed a basketball was thrown in the air above the sensor and caught after 1.6 seconds. The test was repeated many times because the tester’s hands would get in the way of the reading. When there was no unwanted obstruction influencing the results then the data was saved and imported in the Graphical Analysis software to ensure the accuracy of the results by minimizing the systematic error. Figure 6 is the resulting graph from the data and table 1 has the raw data collected.

Figure 6. Ball thrown in the air

Table 1. Raw data collected of time and distance

Time (sec)

Distance (feet)

Time (sec)

Distance (feet)

Time (sec)

Distance (feet)

Time (sec)

Distance (feet)

0.00920

1.491

0.38922

1.448

0.78922

3.121

1.18921

6.367

0.02920

1.484

0.40922

1.448

0.80922

3.376

1.20921

6.385

0.04920

1.484

0.42923

1.440

0.82922

3.755

1.22921

6.392

0.06920

1.484

0.44923

1.444

0.84923

4.056

1.24921

6.388

0.08919

1.480

0.46922

1.440

0.86923

4.263

1.26920

6.367

0.10919

1.476

0.48922

1.440

0.88923

4.480

1.28920

6.338

0.12919

1.469

0.50922

1.440

0.90923

4.689

1.30920

6.291

0.14919

1.469

0.52922

1.444

0.92922

4.894

1.32920

6.237

0.16920

1.466

0.54922

1.444

0.94922

5.106

1.34920

6.169

0.18920

1.462

0.56922

1.448

0.96922

5.286

1.36920

6.086

0.00920

1.491

0.58922

1.469

0.98923

5.448

1.38919

5.992

0.20921

1.455

0.60922

1.448

1.00923

5.600

1.40919

5.884

0.22920

1.448

0.62922

1.444

1.02923

5.736

1.42919

5.769

0.24921

1.444

0.64923

1.437

1.04923

5.863

1.44918

5.636

0.26921

1.444

0.66923

1.469

1.06922

5.974

1.46917

5.492

0.28922

1.444

0.68923

1.671

1.08921

6.071

1.48917

5.333

0.30922

1.440

0.70923

1.905

1.10921

6.158

1.50917

5.164

0.32922

1.444

0.72923

2.175

1.12921

6.226

1.52916

4.984

0.34922

1.444

0.74923

2.478

1.14921

6.284

1.54916

4.793

0.36922

1.440

0.76923

2.802

1.16921

6.334

1.56916

4.588

Analysis

As mentioned before, the results were all matched with a regression curve or line. Not all of the data was used to do this fit. Only the relevant data was used. For example, in figure 2 there is a sudden horizontal line that appears. This was due to the walking subject walking out of the range of the sensor. This part was not counted when performing the regression analysis on that particular data set as well as anything else out of the ordinary. In all of the cases these anomalies appeared at the beginning and end of the test.

The first part of the lab looked at linear motion, which produced a y = mx + b equation to explain what happened. To break it down the m corresponds to the average velocity, b corresponds to the beginning distance, x corresponds to the time and y corresponds to the distance traveled. Figure 3 shows a negative for m, this means that the test subject was moving toward the sensor at approximately 2.3 feet / second. Figure 4 basically had zero for average velocity which means the person stood still.

The last tests of figures 5 and 6 are more complicated. Figure 5 is a parabola so hence its regression brought a quadratic function. The resulting equation is y = -1.86 + 7.20X – 1.17X2. This was a situation in which the test subject walked away and then walked back. The 7.20 coefficient refers to the average velocity that was traveled for the test, which is 7.20 feet / second. The top of the curve, where the slope = 0, is the point at which the test subject turned around, which was 9.16 meters away. This was discovered by finding where the apex of the curve -b / 2a = 3.08 seconds. The 3.08 seconds was substituted into the equation to find the distance of 9.16 meters. The slope at any point of the curve would give the instantaneous velocity. The positive numbers would be when the test subject was walking away and the negative slopes would be when the subject was walking towards the measuring device.

The last test, which is represented by figure 6 and table 1, was that of a ball being thrown and falling back. The resulting regression produced the following equation y = -15.80X2 + 39.01X – 17.70. The units are in feet per second and will be translated into meters per second for clarification. According to the equation the gravitational pull against the ball was -9.64 m/s. This is arrived at by (-15.80 * 2) / 3.28 = -9.64 m/s. This is a little slower than the average of -9.80 m/s but it is expected because Calgary is at a higher altitude. Also, the equation states that the initial velocity of the ball was 39.01 feet / second, which translates to 11.89 m/s = 39.01 / 3.28. The initial position of the ball is listed as -17.70 feet but that would be false. The initial in reality was 1.5 feet because that is where the sensor begins to make its readings. Along the curve it is completely symmetrical, therefore at the same position on one side of the curve it has the same velocity but opposite sign than the other side. The apex of the curve occurs at 1.23 seconds (-b / 2a), which correlates to the height of the call reaching 6.37 feet above the measuring device.

Conclusion

The tests clearly demonstrate the Galilean theories of motion. The equations answer much as to what happened during all the tests and a better understanding of one-dimensional motion was achieved about velocity, distance and time. The final test showed that Calgary possibly has less of a gravitational pull than the average. All the tests demonstrated expected outcomes.

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