Experiment 2 Kinematics of Human Motion

Experiment 2: Kinematics of Human Motion Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila, Philippines Abstract Kinematics is a branch of classical mechanics describing the motion of bodies and systems without considering the mass of an object and the force behind an event. There are four activities in this experiment, first is graphical analysis of human motion and it involves displacement vs. time and velocity vs. time with a graph given. Second graph matching where experimenters will copy the pattern given by the file in the computer. Third, graphical analysis of motion where in a span of 10 seconds the total displacement is 2.49 m, average velocity is 2.49 m/s and the instantaneous velocity is 4.98 m/s2. Last would be the reaction time, members of the group measured their normal reaction time from 0.0186-0.243

motion and uniformly accelerated motion, and to determine one’s normal reaction time and his reaction time while being distracted. 2. Theory Kinematics is a branch of mechanics which deals with the idea necessary to define an event or motion regardless of the cause. The moving object is the center of the experiment noting the details of the action using velocity and acceleration. There are formulas relevant and essential in the experiment of kinematics of human motion: �= √2ℎ� t = time h = distance in meter stick g = 9.8m/s2

1. Introduction

Average velocity = ∆�∆�

Life is in constant motion. Mastery of motion has been critical to our survival and success as a species. Kinematics is a topic under Dynamics that describes motion without regard to its causes. In this experiment, kinematics focuses in one dimension: a motion along a straight line. This kind of motion, actually any kind of motion, involves velocity, displacement, and acceleration with regards to time. The objectives of the experiment are to draw the displacement versus time graphs and velocity versus time graphs for uniform

Instantaneous velocity = ∆�lim�→0∆�∆� Where ∆x = change in distance ∆t = change in time 3. Methodology The instrument that was used to determine the graphs for uniform motion

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines and the uniform accelerated motion in the first activity (Graphical Analysis of Human motion.) The outcomes were predicted through sketching the displacement versus time graph and velocity versus time graph in different conditions. With the use of the Logger Pro (Figure.1) a graph of motions was produced with variable conditions.

The fourth activity, was a test the reaction time of each of the members, each were supposed to catch a meter stick (Figure.2) suspended by another person with their thumb and index finger starting at the 50 cm mark, while the other person drops the meter stick without warning. The same procedure was performed but this time, while being distracted, by talking to the other person. 4. Results and discussion

Figure.1 The logger pro sensor used in the first and second activity

On the second activity titled Graph matching we were presented with two graphs in the computer screen we were to mimic the graphs by accomplishing certain kinds of motions. The devise used to sense the different motions was also the Logger Pro. The third activity, Graphical analysis of motion, required one of our group mates to walk in a straight line for 10 seconds starting form rest. The distance travelled every second was measured and used in computing the instantaneous velocity and average velocity. The results were then plotted.

Figure.2 A meter stick that was used to measure the reaction time in the fourth activity

For activity 1, graphical analysis of human motion, the experimenters were first asked to predict and sketch (Figure.3), and produce, using the Vernier Logger Pro program, (Figure.4) the appearance of the displacement vs. time and the velocity vs. time graph for a person moving away with constant velocity from a chosen starting point for a period of 10 seconds.

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines

Figure.3: Predicted Displacement vs. Time (top) and Velocity vs. Time (bottom) graphs of a person moving away from the origin with constant velocity

Figure.4: Produced Displacement vs. Time (top) and Velocity vs. Time (bottom) graphs of a person moving away from the origin with constant velocity.

From the displacement vs. time graph, it can be observed that the line is moving positively since what was asked for was a person moving away. Naturally, the displacement of the person will increase as he steps away from the origin as time goes by. From the velocity vs. time graph, it can also be seen that it is in a straight line with the same x values since what was asked for was a constant velocity. This was done by walking in a constant speed as time goes by. It would be in a position higher than zero (positive) since the

person is moving away (positively) from the origin. Second was for a person moving toward a chosen starting point with constant velocity for a period of 10 seconds.

Figure.5: Predicted Displacement vs. Time (top) and Velocity vs. Time (bottom, red line) graphs of a person moving toward the origin with constant velocity.

Figure.6: Produced Displacement vs. Time (top) and Velocity vs. Time (bottom) graphs of a person moving toward the origin with constant velocity.

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines

From the displacement vs. time graph, it can be seen that it moves negatively, from a high displacement at 0 sec to an almost 0 displacement at 10 sec. This is because the starting point of the person is at a point away from the origin, ending at the origin where the

displacement is at zero. Once again, the velocity is constant having the same x values but this time, instead of them being positive, the x values are negative since the person is moving toward (negative) the origin. Third was for a person moving away from a chosen starting point along a straight line with increasing speed for 10 seconds.

Figure.7: Predicted Displacement vs. Time (top) and Velocity vs. Time (bottom) graphs of a person moving away from the origin along a straight line with increasing speed

Figure.8: Produced Displacement vs. Time (top) and Velocity vs. Time (bottom) graphs of a person moving away from the origin along a straight line with increasing speed

Here, the displacement is gradually moving upward over time because the speed also needed to increase at the same time. To accomplish this, the steps taken must be larger as time passes. This is why the displacement gradually increases. The velocity on the other hand, is moving positively in a straight line since the speed is increasing constantly over time. It is not clearly seen in the produced graph since getting higher values of velocity would need higher displacement as well but this cannot be done due to limited space. For activity 2, graph matching, a displacement vs. time graph and a velocity vs. time graph needed to be reproduced.

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines For the first graph, the following was shown along with the experimenter’s attempt at reproducing it.

For the second graph, the following was shown with the experimenter’s attempt.

Figure.9: Given Displacement vs. Time graph to be reproduced (black line) with attempted reproduction (red line)

Figure.10: Given Velocity vs. Time graph to be reproduced (black line) with attempted reproduction (red line)

To reproduce this, the person did not move from his position for approximately 1 second. This, in turn, gave a consistent zero displacement. Then, he had to move away from the origin for approximately 2 seconds (3second mark) and had to stop, once again for approximately 3 seconds (6-second mark). This produced the positive movement in the displacement as the person moved away from the origin, then since he stopped moving again a line with the same displacement was produced. After, he had to move closer to the origin for approximately 1.5 seconds (7.5second mark) and lastly, he had to stop for approximately 5 seconds (10-second mark), producing a line moving negatively as he was walking towards the origin and another line with the same displacement as he stopped moving, respectively.

To reproduce this, the experimenter had to stay still for approximately two seconds. This produces a line with zero velocity as there was zero speed. Then, he had to move consistently away from the origin for approximately 3 seconds (5-second mark). This produced an elevation in the velocity which turns into a plateau since the person consistently moves in that speed. He had to stay still for approximately 2 seconds (7-second mark), producing the depression at the velocity since there was, again, zero speed. Finally, he had to move towards the origin at a constant speed for the last 3 seconds (10-second mark) producing the negative line as he was moving towards the origin, and another plateau since he was moving constantly at that speed and direction. Total

Ave.

Inst.

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines Time (s)

Displac e ment (m) .90 1.47 1.23 1.87 1.59 1.06 1.16 1.60 2.18 2.49

1 2 3 4 5 6 7 8 9 10

Velocity (m/s)

Velocity (m/s)

0.90 1.47 1.23 1.87 1.59 1.06 1.16 1.60 2.18 2.49

1.80 2.94 2.46 3.74 3.18 2.12 2.32 2.20 4.36 4.98

Instantaneous Velocity (m) vs Time (s) 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

10

Ta ble 1. Measured and calculated data on the distance travelled every second Graph 1. Instantaneous Velocity vs Time Based on the results, the student was not able to achieve constant velocity. Although it can be seen that the student accelerated from second 1 to the 10th, human error came into place and gave inconsistent velocities every second.

Table 2 shows the obtained reaction time of each student while being idle and while calling.

Student

Reaction Time (s)

1 0.207 2 0.064 3 0.163 4 0.202 Table 2. Reaction Time

Reaction Time (s) while calling 0.243 0.186 0.202 0.202

The table shows the reaction time of the experimenters while dropping a meter stick without any signal and another while the other members are distracting the particular student conducting the experiment. Student 2 had the best reaction time with 0.064 seconds while being idle and 0.186 seconds while being distracted by the other students. 5. Conclusion From this experiment, the displacement vs. time and velocity vs. time graphs for uniform motion and uniformly accelerating motion of humans in given situations had been predicted, sketched, and compared to real time results. From here, it can be said that velocity can be constant while displacement is increasing in a straight line. It can also be said that at increasing velocity, displacement also gradually increases, showing a slightly curved line.

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines The displacement, average velocity, and instantaneous velocity per second was also determined for a person walking at constant acceleration. From the results, it can be seen that as velocity increases, so does the displacement since achieving constant acceleration would need larger steps thus having larger displacements. This can be seen as the increments of total displacement, average velocity, and instantaneous velocity increase every second. The group members’ normal reaction times and their reaction times while talking had also been determined. From the results, it can be said that, on average, the reaction times are slower when talking compared to when they are concentrated.

Displacement vs. Time from Home to UST 20 15

Displacement (km)

5 0

Time (min)

Figure 1: Displacement vs. Time graph from home to UST

Displacement vs. Time from UST to home 0 -2

6. Applications 1. Devise a way to determine the height of a building using only a stopwatch. 2. From the point of view of physics, is there a basis to the law banning the use of cellphone while driving? From the point of view of physics, just like in the reaction time experiment conducted, the students exhibited better reaction times when not distracted by anything. This can be related to driving while using a mobile phone which greatly reduces the drivers’ reaction time and could be a great danger to the safety of motorists. 3. Draw your displacement versus time graph and velocity versus time graph from your home on your way to ust and back.

10

-4 -6

Displacement (km)

-8 -10 -12 -14 -16

Time (min)

Figure 2: Displacement vs. Time graph from UST to home (origin)

Experiment 2: Errors, Uncertainties, and Measurements Laboratory Report Praiseus Acao, Aime Rose Alberto, Aldrin Agawin, Samuelle John Aquino Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines

Velocity vs. Time from Home to UST 60

0

50

-10

40

Velocity km/hr

Velocity vs. Time from Home to UST

30

-20

20

Velocity km/hr -30

10

-40

0

-50

Time (min)

-60

Time (min) Figure 3: Velocity vs. Time from Home to UST Figure 4: Velocity vs. Time from UST to Home (origin)