Kinematics Of Human Motion.docx

Experiment 2: Kinematics of Human Motion

Department of Math and Physics College of Science, University of Santo Tomas España, Manila, Philippines

Abstract The purpose of this experiment is to study the kinematics of human motion by drawing the displacement versus time graphs and velocity versus time graphs for uniform motion and uniformly accelerated motion. In addition, the normal reaction time was also examined in contrast with the reaction time while using a cell phone. The results showed that the graph of a displacement versus time graph with a constant velocity is a straight line that points upwards; while the graph of a displacement versus time with an increasing speed is a curve. On the other hand, the graph of a velocity versus time with a constant velocity is a straight horizontal line, whereas the graph of a velocity versus time with an increasing speed is a straight line that points upwards. Furthermore, the normal reaction time of a person is faster than the reaction time while using a cell phone.

relationship with force that causes the motion. Kinematics is the study of concepts involved in describing motion but not including the force or the cause of the motion. These concepts are displacement, velocity and acceleration. Displacement is the distance between an object moving in a straight line from its initial to its final position with a stated direction. Velocity is the speed of change of position of an object over time. Acceleration is the change in velocity per unit time. The data of the experiment will be obtained through a series of activities that will be applied to the concepts of Kinematics. Since kinematics is a quantitative description of motion, this experiment aims for the students to learn to draw the displacement versus time graphs and velocity versus time graphs for uniform motion and uniformly accelerated motion. The experiment also aims to determine one’s normal reaction time.

1. Introduction We live in a world wherein everything is in motion: the cars on the street, a dog chasing after a ball or a girl jogging in the park. Motion can also be observed in the environment itself like raindrops falling, the clouds moving and the never-ending cycle of water flowing in the rivers. In Physics, motion is the change of position of an object over time. The study of motion along with force and energy is under the branch of Physics called Mechanics. Mechanics is divided into two which are dynamics and kinematics. Dynamics is centered on the study of motion and its

2. Theory Kinematics studies the concepts of motion without considering the products of forces. It essentially deals with the acceleration and velocity of an object or person. It also deals with the displacement and distance of a moving object in a particular time frame. In this experiment, total displacement, average velocity, instantaneous velocity and rate of reaction were figured. The total displacement in this experiment refers to the vector quantity and

the person’s overall change in position. It conveys both magnitude and direction. Thus, displacement is a vector that starts from initial position to the final position. △x=x1-x2 where △x (displacement) is equal to x1 (initial position) minus x2 (final position). The average velocity is simply the change in displacement divided by change in time. →= 𝑣

𝑥−𝑥0 △→ = 𝑥 𝑡−𝑡0 △t

where → (average velocity) is equal to the 𝑣

quotient of x (initial displacement) minus x0 (final displacement) and t (initial time) minus t0 (final time). Average velocity can be simplified as △ → (change in displacement) divided by △ t 𝑥

(change in time). Meanwhile, instantaneous velocity indicates how fast an object moves. It defines the direction of the motion at each instant of time. Instantaneous velocity is simply twice of the average velocity.

In the first activity, the graphical analysis of human motion was predicted and compared using Vernier Logger Pro. The graphs of the displacement versus time and velocity versus time with a constant velocity from a chosen starting point and towards a starting point for a period of 10 seconds was predicted and sketched. Afterwards, the graphs of the displacement versus time and velocity versus time with an increasing speed along a straight line for a period of 10 seconds was also predicted and sketched. These graphs were then compared with the graph of motions produced by Vernier Logger Pro. In the second activity, a meter stick and timer was used. One student from the group walked in a straight line for 10 seconds while the remaining groupmates measured the distance he covered every second. The average velocity was computed by dividing the displacement over the total time. The total displacement was then graphed against the total time. The instantaneous velocity was also calculated by multiplying the average velocity by two. Lastly, the instantaneous velocity against time was plotted and analyzed.

Vins = 2(vav) Lastly, reaction time or rate of reaction time was also computed. It refers to the time between stimulus and response. The formula used in finding the reaction time was:

ℎ

t = √2 𝑔

Figure 1 Experimental set-up for graphical analysis of motion

where t (reaction time) is equal to the square root of 2 times h (the distance dropped) divided by g (acceleration due to gravity) which is equivalent to 9.80 𝑚⁄𝑠2. The value 9.80 𝑚⁄𝑠2 is used when an object falls under the influence of gravity. Acceleration of a free falling body is directed towards the center of the earth.

The third activity used a meter stick to determine the normal reaction time of each student versus the reaction time while using a cell phone. One member of the group held the meter stick vertically at the zero mark and another member situated his thumb and index finger at the 50 cm mark without touching the meter stick. The meter stick was dropped and the other member caught it with his thumb and index finger. The instructions were repeated while the other

3. Methodology

member used his phone. Afterwards, the reaction time for each set-ups was computed using the ℎ

formula 𝑡 = 2 𝑔 (where h is the distance the meter stick has fallen from the 50 cm mark to where the meter stick was caught and g is the measure of gravity). Lastly, the procedure was repeated and the reaction time of each member was determined.

The displacement versus time graph shows a line at a 45° angle, this is because from two points, start and finish, the person has covered a positive distance. While the velocity versus time graph shows a horizontal line because the speed at which the distance is covered is constant. Graph 2

Figure 2.1 Experimental set-up for reaction time

Graph 2 was done as a prediction of displacement versus time graph and velocity versus time graph of a person moving toward a chosen starting point with constant velocity for a period of 10 seconds. The displacement versus time graph shows a downward slope or a -45° angle because the person walked back to the starting area which causes the total displacement have a value of zero. The velocity versus time graph shows a horizontal line due to the speed is still constant. Figure 2.2 Close-up of the experimental set-up for reaction time

Graph 3

4. Results and Discussion: Graph 1

Graph 3 was done as a prediction of the displacement versus time graph and velocity versus time graph of a person moving away from a chosen starting point along a straight line with increasing speed for a period of 10 seconds. Graph 1 was done as a prediction of displacement versus time graph and velocity versus time graph of a person moving away with constant velocity from a chosen starting point for a period of 10 seconds.

The displacement versus time graph is a line that is increasing. This is due to having a speed that is increasing therefore the distance covered will be increasing. The velocity versus

time graph shows a 45° because the speed of motion is increasing. Table 1: Results for Graphical Analysis of Motion Time

Total Average Instantaneous Displacement Velocity Velocity

1

The rate of motion given for table one was not uniform as to the average velocity differing for every second. As well as the results for reaction time, each individual student has different recorded numbers. This is because different people have different reaction speeds from one another. There is, however, a problem with regards to accuracy during the experiment. The time given was not precise as to which a step is not taken at exactly a second.

2

Student

Reaction Time (s)

Reaction Time while calling

1

1.75 s

N/A

2

1.64 s

N/A

3

2.30 s

N/A

4

3.06 s

N/A

5

2.93 s

N/A

(s)

3 4 5 6 7 8 9 10

Table 1 was done with one of the researchers as the experimental unit in which the person was asked to walk in a straight line for 10 seconds and to measure the displacement achieved every second within the 10 second frame. Table 2: Results for Reaction Time Table 2 was done with a meter stick vertically held while one of the researchers places their thumb and index finger at the 50 cm mark. The meter stick is then released and the researcher catches it with their thumb and index finger.

5. Conclusion The experiment about kinematics was a successful in determining one’s normal reaction time with the use of a meter stick and a stopwatch. It is also successful in determining the relationship between displacement and time as well as velocity and time how one affects the other by drawing displacement over time graphs and velocity over time graphs. 6. Application 1.) Devise a way to determine the height of a building using only a stopwatch. To determine the height of a building using a stopwatch drop a ball from the top of the building and record the time it takes for the ball to reach the ground. Compute for the distance travelled by the ball using the formula 𝐻 = 1 2

𝑎𝑡 2 , Where 𝐻 is the height of the building, 𝑎 is

the constant gravitational acceleration of the ball which is 9.8𝑚/𝑠 2 , and 𝑡 is the time it takes for the ball to reach the ground. e.g.

Cutnell, J. D., & Johnson, K. W. (2015). Introduction to physics. London: John Wiley & Sons. Retrieved from http://fsinet.fsid.cvut.cz/en/U2052/Kinematics.p df Motion. (n.d.). Retrieved August 28, 2017, from https://www.britannica.com/science/motionmechanics 𝐻=

1 2 𝑎𝑡 2

1 𝐻 = ( )(9.8 𝑚/𝑠 2 )𝑥 (5.06𝑠)2 2 𝐻 = 125.46 𝑚 2.) From the point of view of physics, is there a basis to the law banning the use of cellphones while driving? The use of cellphones while driving increases the chance of getting a road accident, because the use of cellphones while driving increases the driver’s reaction time and the average driver’s reaction is 2.3 seconds and if they are using they are using their cellphones while driving it will hinder their focus on the road and more onto their cell phones thus it will increase their reaction time therefore furthering the time it will take for the driver to engage on the brakes resulting to an accident. 3.) Draw your displacement versus time graph and velocity versus time graph from your home on your way to UST and back. 7. References:

Silverio, A. A., & Bernas, G. D. (n.d.). Physics: exploring life through science. Quezon City: Phoenix Publishing House, Inc., 2012.