Experiment 2: Kinematics of Human Motion
Monica Policina, Marie Pamela Celestine Pua Phee, Maria Charmella Relopez, Anna Paula San Pedro Department of Biological Sciences College of Science, University of Santo Tomas España, Manila Philippines Abstract acceleration. Speed is a scalar quantity that Kinematics is a branch of classical concerns with the rate of an object when it mechanics concerned with the motion of covers distance. On the other hand, velocity, points, objects, and groups of objects a vector quantity, is the rate of the change in without considering the causes behind the position. The experiment is consists of four event. Four activities were conducted in this parts which involves graphical analysis of experiment. First is the graphical analysis of human motion, graph matching, graphical human motion, which involved graphs of analysis of motion and reaction time. displacement versus time and velocity versus 2. Theory time. Second is graph matching, where This experiment deals with the members attempted to copy the pattern given concept of kinematics , the study of the by the computer-generated graph. Third is quantitative description of motion. [1] It is a graphical analysis of motion, where in a 101 0 branch of dynamics that deals with aspects second duration the total displacement of motion apart from considerations of mass measured is 5.55 m, average velocity is and force. [2] The concepts that are involved 0.556 m/s and the instantaneous velocity is in Kinematics are Displacement and 1.11 m/s2. Last is the reaction time. Normal Velocity. Displacement is a vector quantity reaction time of each member was that refers to the straight line distance from calculated ranging from 0.1512-0.2914 s. the starting point to the end point. The displacement of an object also refers to its 1. Introduction change of position. [1] To calculate for the Kinematics , the study of motion that aims to explain the motion of objects or displacement, the formula used is given as: particles without considering the cause of D = Xf -Xi movement. It is often called the geometry of motion. It is usually associated with the where Xf is the final position of the object concept of displacement, acceleration, speed and Xi is the initial or first position of the and velocity. Displacement, a vector object. The unit for displacement is usually quantity, is the overall change in position of in meters (m). an object including the distance and the Another vector quantity is Velocity. direction it travels. Acceleration is another It is the rate at which an object moves in a vector quantity that deals with the change of given direction. [1] Generally, speed and velocity in a particular rate of time. Thus, velocity are sometimes interchangeable, when a velocity changes, there is
however, there is a clear distinction between these two quantities. The former has a magnitude only and makes use of distance while the latter has both magnitude and direction and it makes use of displacement. Hence, if the distance and displacement are the same in magnitude, speed and velocity will be also the same in the magnitude. [1] There are two kinds of velocity, Average velocity and Instantaneous velocity. Average velocity of an object is equal to the total displacement divided by the elapsed time. It is calculated over a time interval. To compute for the average velocity of an object, the equation used is:
where Δx is the displacement and Δt is the difference between the initial and final time. On the other hand, instantaneous velocity is the velocity at any particular instant or time. It may be considered as the average velocity of an object over a very short period of time. [1] It is described as:
The equation above presents that the ratio of
indicates that as the time decreases or
slows down until it reaches the value of 0. However, the equation used is Where Vav is the average velocity of the object. Also, the instantaneous velocity is equal to the instantaneous speed. These concepts are then applied and depicted in the Graphical Analysis of Motion. Using a graph to give a representation of the motion of an object is
very crucial and useful in analysis of the motion of a body. [1] The Displacement vs. Time graph shows the if the objects is either moving toward or away from a reference point. [5] The x-axis represents the time and the y-axis represents the displacement of an object. The slope of the line in this graph represents the velocity of that object. [6] Another one is the Velocity vs. Time graph. It shows the velocity of an object in a certain period of time. The slope of the line in this graph is now the o bject’s acceleration, which is the change in velocity. The slope is given by the formula:
source:khanacademy.org Since acceleration is defined as
∆
, it can be
inferred that the slope is equal to the acceleration of the object. Hence, if the slope is upward, the object is accelerating and the acceleration is positive and if the slope is downward or negative, it is decelerating and the acceleration becomes negative. [7] Another concept is the Reaction time. It is the amount of time elapsed in response to a stimulus. To determine the reaction time, the formula used is:
=√ ℎ
2
Where h is the distance the meter stick from the 50 cm mark to where it was held by the participant and g is the acceleration due to gravity which is 9.8 m/s2. 3. Methodology
There were four activities conducted in the experiment. These involved the construction of different graphical analysis of human motion, graph matching, and the measurement of the reaction time. The first and the third activity are similar, however, the graph for the third activity was recorded from actual human motion whereas the first activity were based from assumptions and ideal graphs. The materials used in the experiment were a timer, a meter stick and, Vernier Logger Pro. For the first activity, the group was asked to construct different graphical analyses of human motion. These graphs were based from different instances. It includes a person moving away with constant velocity from a starting point for 10 seconds, and a person going back to the starting point, or origin, with the same conditions. Furthermore, for the last task of the activity, the person was asked to move away with increasing speed from the starting point (logger pro) in a straight line for a duration of 10 seconds. All instances for the first activity were graphed according to its respective results Next, in the second activity, Vernier Logger pro was used as a detector of motion and an illustration board as the object in motion. One member was tasked to operate the computer, and another member was assigned to hold and control the movement of the board. The member who was assigned to operate the computer was asked to click the “collect” button, cuing the start of the activity. On the other hand, the motion of the member
manipulating the movement of the illustration board was detected by an apparatus and plotted it as a graph that can be observed in the computer screen. Moving forward, backward, no movement at all, and its corresponding speeds affected the results in the graphs. In the third activity, a member was asked to walk straight for 10 seconds that begins in their desired reference point. When the member begins to walk for the activity, the distance traveled for every second was marked. Afterwards, the marks were measured from 0 to 1s, 0 to 2s, and so on until 0 to 10s. Instantaneous velocity and average velocity were determined in this activity. Lastly, for the fourth activity, the reaction time of each member was determined. One member was asked to hold a meter stick vertically at zero mark, and the member (or the subject) was to position his thumb and index finger at the 50 cm mark without touching the meter stick. Two recorded measurements were to be acquired for each member. First measurement was for catching the meter stick without doing anything else, and the second was the measurement upon catching the stick while the subject was distracted. 4. Results and Discussion Activity 1: Graphical Analysis of Human Motion The first activity involves sketching a displacement vs. time graph given the following conditions: moving away with constant velocity in a period of 10 seconds. Figure 1 shows the sketch of the displacement vs. time graph while figure 2
shows the sketch for the velocity vs. time graph. Figure 1. Prediction graph for displacement vs. time of a person moving Figure 2. Prediction graph for velocity vs. time of a person moving away.
away.
As shown in figure 1, the sketch shows a positive slope, indicating that as the person moves away, his/her displacement increases. [5] Figure 2 depicts a horizontal line, indicating the given condition that the person moves in constant velocity (slope=0). The motion was also graphed using the Vernier Logger Pro. Figure 3 shows the displacement vs. time and velocity vs. time graphs generated by the software, Figure 3. Displacement vs. time and velocity vs. time graphs of a person moving away at constant velocity using Vernier Logger Pro. The figure shows that the actual graph is identical as the prediction graph, with a positive slope for displacement versus time and a zero slope for the velocity vs. time, showing constant velocity. This also infers that the motion is in positive direction. The following motion is a prediction graph of a person moving toward a point with constant velocity. The succeeding figures show the prediction graphs of the given conditions.
Figure 4. Prediction graph for displacement vs. time of a person moving
The prediction graph for displacement vs. time shows a negative slope because it is estimated that as the person moves toward the point, the displacement decreases. On the other hand, the velocity vs. time graph matches that of figure 2, since the velocity is constant. Figure 6. Displacement vs. time and velocity vs. time graphs of a person moving away at constant velocity using Vernier Logger Pro.
The generated graph matches the prediction graphs for a person moving towards a point with constant velocity. The negative slope indicates the decrease in displacement, and the zero slope indicates the constant velocity of the person. [6]
toward a chosen point.
Figure 5. Prediction graph for velocity vs. time of a person moving toward a chosen point.
The last motion is a prediction graph of the displacement vs. time and velocity vs. time of a person moving away moving away from a point with an increasing speed for 10 seconds. Figures 7 and 8 shows the prediction graphs of the motion. Figure 7. Prediction graph for displacement vs. time of a person moving away from a chosen point at increasing velocity.
Figure 8. Prediction graph for velocity vs. time of a person moving away from a chosen point at increasi ng velocity.
When a body moves at increasing velocity, it is expected that the graph would indicate a positive slope. The displacement vs. time graph would also be a positive slope, since the displacement would increase as the person moves away from the chosen point. [10] The next figure shows the graph generated by the Vernier Logger Pro given
the conditions. Figure 9. Displacement vs. time and velocity vs. time graphs of a person moving away at constant velocity using Vernier Logger Pro. The generated graph was not identical with the predicted graph, With the displacement vs. time graph consistent with the previous graph while the velocity vs. time graph showing a zero slope, which is erroneous. It may be caused by systematic errors such as inconsistent position of the Vernier Logger Pro sensor, inaccurate movement of the person, and mismatched coordination of the person moving away and the person operating the software. Activity 2: Graph Matching In this activity, the Vernier Logger Pro software was used in which a graph pattern was given and the students are tasked to move in a way that the graph of motion matches the graph. 2 graphs were given, with varying difficulty. The first graph shows a position versus time graph. The student must follow the match the graph, initially 1 meter away from the sensor for half a second, then move further at increasing speed up till it reaches approximately 2.5 meters at 2 seconds, stopping at that position for 3 seconds, then returning to the sensor when it reaches a distance of 1.8 meters for approximately 1 second and remaining in that position. The whole activity has a period of 10 seconds. As shown in the figure, the black graph shows the provided graph while the graph in red shows the student’s matched graph.
Figure 10. Position versus time graph of the motion using Vernier Logger Pro.
Figure 11. Velocity versus time graph of motion using Vernier Logger Pro.
The second graph shows a velocity versus time graph. This graph is more difficult than the previous as the graph requires the student to move at a certain velocity at a short period of time. As shown in the figure below, the graph of motion starts at 0 m/s for 2 seconds, then immediately changing velocity to 0.5 m/s away from the sensor and maintaining that speed for 3 seconds, then moving toward the sensor, returning at a velocity of 0 m/s for 2 seconds, moving towards the sensor again at a velocity of -0.5 m/s for 3 seconds. The activity has a total duration of 10 seconds. In contrast to the former graph, this graph is much more difficult to match given that the movements must be done in a matter of seconds.
In general, the x-axis of the graph represents the time while the y-axis represents either the position or velocity, depending on the given graph. A positive slope indicates an increase in speed or a change in position. A movement toward the sensor would represent a downward/ negative slope, which may also indicate a negative displacement. Horizontal lines indicate that the board is at constant velocity. [6] Factors that may affect the desired result of the activity include: distractions from the environment, such as random objects placed near the area of the activity, unsteady handling while moving the board, and failure to match the graph due to the short period of time given (10 seconds). Activity 3: Graphical Analysis of Motion For this activity, a member of the group walks in a straight line while another member marks the distance she travels each second. The distance is then measured using a meter stick, and values are expressed in meter or m/s. The displacement versus time graph is illustrated in the figure below. The graph
show a positive slope, indicating that the longer the time, there is an increase in the
displacement. The average velocity is computed by dividing the displacement by the time, given by the formula:
Where v is the velocity, d is the displacement, and t is the time. The instantaneous velocity is determined by multiplying the average velocity by 2. Table 1 shows the data for the total displacement, average velocity, and instantaneous velocity at each second. Table 1. Collated data for the total displacement, average velocity, and instantaneous velocity of a person walking in a straight line for 10 seconds.
ime
Total Average placement Velocity (m) (m/s)
antaneous elocity (m/s)
3
1.626
0.542
1.084
4
2.294
0.574
1.147
5
2.989
0.598
1.196
6
3.576
0.596
1.192
7
3.794
0.542
1.084
8
4.249
0.531
1.062
9
5.142
0.571
1.143
10
5.555
0.556
1.111
Activity 4: Reaction Time
Reaction time is the length of time for a system to respond to a stimulus. There is also a concept to consider here which is free fall. Objects in the absence of air resistance would fall with the same constant acceleration due to gravity which is equal to 9.8 m/s2. Also, objects falling at a longer period of time goes faster as it goes [1] Table 2 shows the data for the reaction times of each member of the group, as well as the reaction times while calling. Table 2. Reaction Times of each group member. Student
Reaction Time (s)
Reaction Time while Calling (s)
1
0.2104
0.2152
2
0.1512
0.2595
1
0.735
0.735
1.470
3
0.2900
0.2347
2
1.276
0.638
1.276
4
0.2347
0.2914
Based from the results, a longer reaction time is observed while calling or being distracted by other people. It can be inferred that common distractions such as mobile phone can affect the reaction time of a person. [8] The average reaction time of the group was 0.2216 seconds, while the average reaction of the group while calling was 0.2502 seconds. 5. Conclusion The displacement versus time graph and velocity versus time graph for uniform motion and uniformly accelerated motion were drawn and the results showed that at constant velocity, an increase in displacement would yield a positive slope while a decrease in displacement would have a negative slope. The graph for velocity would be a zero slope, since it is constant. For uniformly accelerated motion, the velocity vs. time graph would be a positive slope. The normal reaction time and the reaction time while there are interference like talking or using the cellphone was also determined. It was showed in the gathered results that there were different effects of the interference with respect to the reaction time. Thus, explaining the reason behind the banning of cellphone while driving. With all the activities done, the objectives were completed.
6. Applications 6.1 Devise a way to determine the height of a building using only a stopwatch.
One way to determine the height of a building using stopwatch is to use the formula:
where y represent the measurement of the building, V0 is the initial velocity, a is the acceleration and t is the time. The value for initial velocity will be 0. The acceleration will be 9.8 m/s2 which is the constant acceleration due to gravity. To get the value for the time, a stopwatch will be used. For instance, given the time for the object to hit the ground from the top a building is 15 seconds, the equation with the substituted value will be:
= ( / )( . ) + (. / )( . ) = . 0
15 00 1
2
9 8 2
15 00
2
After computing the equation, the answer is:
1102 5
Thus, the height of the building is 1102.5. 6.2 From the point of view of physics, is there a basis to the law banning the use of cellphone while driving? Driving requires full attention to one’s surroundings, such as incoming cars, stop lights, road signs, and pedestrians. When a person uses a cellphone while driving (i.e. texting or calling), she/he is therefore not concentrated and would most likely encounter accidents. The physics behind this is that the driver’s reaction time is affected when she/he uses a phone while driving (Physics, 2016). Thus, there is a scientific basis through physics regarding the law on banning the use of cellphone while driving.
6.3 Draw your displacement versus time graph and velocity versus time graph from your home on your way to UST and back. *Refer to the last page for the graphs 7. References [1] Valdes, B.J. & Navaza D.C. (2011). YOU AND THE NATURAL WORLD Physics. Quezon City. Phoenix Publishing House Inc. [2]Tyson, H. N. (1966). Kinematics. New York: Wiley. [3] Displacement Formula. (n.d.). Retrieved February 06, 2017, from http://www.softschools.com/formula s/physics/displacement_formula/22/ [4] Physics. (n.d.). Retrieved February 06, 2017. [5]DISTANCE / DISPLACEMENT- TIME GRAPHS. (n.d.). Retrieved February 08, 2017, from https://www.pathwayz.org/Tree/Plai n/DISTANCE %2F DISPLACEMENT- TIME GRAPHS [6]Khan Academy. (n.d.). Retrieved February 08, 2017, from https://www.khanacademy.org/scien ce/physics/one-dimensionalmotion/displacement-velocitytime/a/position-vs-time-graphs [7] Khan Academy. (n.d.). Retrieved February 08, 2017, from https://www.khanacademy.org/scien ce/physics/one-dimensionalmotion/acceleration-tutorial/a/whatare-velocity-vs-time-graphs
[8] Physics. (n.d.). Retrieved February 08, 2017, from http://donttextonthego.weebly.com/p hysics.html [9] Kinematics. (n.d.). Retrieved February 08, 2017, from http://www.physicsplanet.com/article s/kinematics [10] BBC - Higher Bitesize Physics Analysing motion : Revision. (n.d.). Retrieved February 08, 2017, from http://www.bbc.co.uk/bitesize/higher /physics/mech_matt/analyse_motion/ revision/1/ Images: Vernier Logger Pro [10]Vernier Shield Hookup Guide. (n.d.). Retrieved February 08, 2017, from https://learn.sparkfun.com/tutorials/v ernier-shield-hookup-guide Meterstick [11] Yard stick. (n.d.). Retrieved February 08, 2017, from http://www.zeppy.io/discover/gb/yar d-stick
6.3.
