Experiment 3: Kinematics of Human Motion Laboratory Report

Charles Sanchez, Geminesse Sianghio, Ferguie Solis

Department of ChemistryCollege of Science, University of Santo Tomas

España Street, Manila Philippines

Abstract

In this experiment of Kinematics of Human Motion, the part of mechanics that enables us to describe motion. The Kinematics of humans in this experiment is defined by making use of graphs that depict the velocity and time based on the member’s movements. The instantenous velocity was also calculated based from the distance displaced per second by one of the member in 10 seconds. One’s reaction time was also obtained by the use of a meter stick.

Introduction

Kinematics is a branch of physics that deals in describing motion, to describe it from its graph and together with the use of placing x and y components of a graph can the motion done be described. [1] Also it is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Kinematics is a branch of mechanics. The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.

[2] For Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings. Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. Acceleration however is another type of vector quantity that is the rate from which velocity increases over time. This

experiment is divided into four activities: The graphic analysis of human motion, graph matching, graphical analysis of motion and reaction time.

In this experiment the group should be able to draw displacement versus time graphs and velocity versus time graphs for uniform motion and uniformly accelerated motion. And to also determine one’s normal reaction time

Theory

Kinematics is the study of motion that defines an objects motion through the use of words or diagrams. In this experiment, kinematics is motion of an object that varies with displacement, acceleration and velocity. The equations or formulas used in this experiment are:

lim∆t →0

¿2¿) Eq. (1)

Eq. 1 shows the formula for computing the instantaneous velocity of an object where instantaneous velocity is equal to (2)(average velocity) where ∆ x is the change in displacement and ∆ t is the change in time.

t=√2 hg

Eq. (2)

Eq.3 is used as a formula for computing one’s reaction time, where h is the distance the meter stick has fallen measured from the 50 cm mark to where the meter stick was caught.

Methodology

The materials used in the experiment were the following: meter stick, timer, Vernier Logger Pro and ultrasonic range finder

In the first activity the predicted and sketched the appearance of a 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 10s, moving toward a chosen starting point with constant velocity for a period of 10s and moving away from a chosen starting point along a straight lone with increasing speed for a period of 10s. With the use of Logger pro, the researchers produced a graph of the three different motions

In the second activity two files were opened on the software Vernier Logger Pro: “01b Graph Matching” where a postion versus time graph appeared and “01d Graph Matching” where a velocity versus time graph appeared. The researchers then moved in a way that their motion matched the motion based from the graph

In the third acitivity a member was asked to walk in a straight line for 10s starting from rest and his distance is measured every second. The total displacement versus total time was plotted and also instantaneous velocity was determined after each time interval and is also plotted in the format instantaneous velocity versus time. The motion of the member was also analyzed.

In the last activity a member was asked to hold a meter stick vertically at the zero mark while the thumb and index finger is placed in the 50cm mark without touching it. The reaction time is then computed. The procedure is then repeated for the other members of the group and also the procedure is repeated again with the addition of a distraction (talking to a friend on a smart phone)

Results and Discussion

In this experiment the kinematics of human motion are observed by the use of a motion detector, this experiment also is divided into four activities: The graphic analysis of human motion, graph matching, graphical analysis of motion and reaction time. The first two activities makes use of graphs being depicted in a computer.

Figure 1. Moving away with constant veloctiy

Figure 2. Moving towards with constant velocity

Figure 3. Moving away with increasing speed

The second activity is mainly matching graphs that are saved on the computer based in the member’s movements. The graphs involved are position versus time graph and velocity versus time graph.

Figure 4. Position vs. Time

Firgure 5. Velocity vs. Time

The third and fourth activity however requires computations. In activity 3 a member of the group was asked to walk in a straight line for 10 seconds.

Table 1. Activity 3 results

Time (s)

Total Displacment

(m)

Average Velocity

(m/s)

Instantaneous Velocity

(m/s)1 0.51 0.510 1.022 1.21 0.605 1.213 2.16 0.720 1.444 2.98 0.745 1.485 3.55 0.710 1.426 4.27 0.712 1.457 5.09 0.727 1.458 6.06 0.758 1.529 6.88 0.764 1.53

10 7.86 0.786 1.57

Graph1. Instantaneous Velocity versus Time

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

Series 1

In the last activity one’s reaction time is measure by grasping a meter stick vertically without telling and by being distracted.

Time Reaction time (s)

Reaction time while

1 1.6 2.52 2.1 2.63 1.7 2.1

Conclusion

Kinematics is the study of motion and the analysis of classical mechanics whereas regardless and independent on the causes of motion. It includes properties such as position, velocity and acceleration which are all geometrically and time-related properties of motion. With this, graphs are highly recommended to describe their mathematical models and relationships. The characteristics of motion can be further analyzed by its shape and slope of the lines in their respective graphs. This experiment mainly focuses on the principles of the displacement vs. time graphs and the velocity vs. time graphs to further delineate motion. Every graph in the displacement-time relationship represents the nature of motion of the body. A stationary body represents a straight line parallel to the x- axis and a body withholding a constant velocity represents an inclined straight line, which concludes that displacement is directly proportional to time. As for the velocity vs. time graphs, having a constant velocity is a having zero acceleration as

well. While having an increasing velocity or accelerating velocity will represent a graph with an inclined slope. A change in motion will result in a positive velocity when plotted in a velocity-time graph, The principle behind the slope of the line on a velocity-time graph is that it is proportional to its acceleration in a way that, if the acceleration is positive the slope is positive , if the acceleration is negative the slope is negative as well.

6. Application1.) Device a way to determine the height of a building using only a stopwatch.

To be able to determine the height of the building, you need an object which you can drop at the top of the building. There you can measure the time of the rock dropped at the top of the building up to the ground. Now you can determine the height of the building by using the formula gravity.

Formula: d= 12>¿2

Where d is the distance or the height, g is the acceleration due to gravity which is -9.80 m/s2

2.) From the point of view of physics, is there a basis to the law banning the use of cell phone while driving?

Yes. Because by using a cell phone or any kind of device is associated with the concept of reaction time. With a given example, when a person is driving any kind of vehicle and focuses on the road itself, the reaction of time is much more faster than a person driving a vehicle and suddenly uses his cell phone. Similarly with activity 4 in experiment 3 which the researchers performed where the reaction time is more faster when you are focused, and slower when you’re not paying attention to the meter stick.

3.) Draw your displacement versus time graph and velocity versus time graph from your home on your way to UST and back.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.51.3

1.5

1.7

Velocity vs. Time

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

20406080

100120

Displacement vs. Time

4.) Under what circumstances is a short reaction time ideal? Under what circumstances is long reaction time ideal?

Reaction time is the amount of time that passes between the introduction of a stimulus and the reaction by the subject to that stimulus. It takes to respond to a stimulus. One of the factors affecting a response is the number of possible stimuli. Where each stimuli has their own response which are presented. Having one possible response is having a short reaction time. When several possible response it is having a long reaction time. [3]

References

[1]http://www.physicsclassroom.co m/class/1D Kin/Lesson-1/Introduction

[2]http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

[3]www.psychologydictionary.org/reaction-time-rt/ Page Last Modified- 6th November, 2012