Experiment 3: Kinematics of TranslationLaboratory Report

Rafael David, Pamela de Leon, Katrina de Vera, Manette Dejelo

Department of Sports ScienceCollege of Rehabilitation Sciences, University of Santo Tomas

España Street, Manila Philippines

Abstract

Kinematics is a branch of mechanics that describes the motion of objects and systems without consideration of the forces that causes the motion. In this experiment, the displacement vs. time graphs and velocity vs. time graphs were plotted, and a graphical analysis was made. The reaction time of each member of the group was computed.

1. Introduction

There are two aspects to any motion. In a purely descriptive sense, there is the movement itself. Then, there is the issue of what causes the motion to change, which requires the forces to be considered. Kinematics deals with the concepts that are needed to describe motion without reference to its forces. To describe the motion of an object, we must be able to specify the location of the object at all times. Displacement is a vector quantity for it conveys both magnitude and a direction. The magnitude of the displacement vector is the shortest distance between the initial and final positions of the object.

Average velocity is displacement over elapsed time.

This equation indicates that the unit for average velocity is the unit for length

divided by the unit for time (ms

). Average

velocity is a vector that points in the same direction as the displacement in the equation. If the displacement points in the positive direction, the average velocity is positive. If the displacement point in the negative direction, the average velocity is negative.

Reaction time is the interval of time between application of a stimulus and detection of a response. It is the ability to respond quickly to a stimulus.

In this experiment, the group should be able to achieve the following objectives: (1) to draw the displacement versus time graphs and velocity versus time graphs for uniform motion and uniformly accelerated motion (2) and to determine one’s reaction time.

2. Theory

Graphical analysis of motion is defined as a detailed study of the motions used in a work task or at a given work area. The average speed of an object in the interval of time is the distance traveled by

1

the object divided by the duration of the interval the instantaneous speed is the limit of the average speed of the duration of the time interval approaches zero. Like velocity, speed also has the dimensions of a length divided by a time. The SI unit of speed is the meter per second, but the most usual unit of speed in everyday usage is the kilometer per hour.

Average Speed= distanceelapsed time

Velocity is defined as the distance covered by a moving object in a particular direction in unit time or speed in a particular direction. The SI unit of velocity is m/s (meters per second). Velocity is defined as the distance travelled in a specified direction in unit time. The distance travelled in a specified direction is displacement.

AverageVelocity=displacementelapsed time

Acceleration is defined as the rate of change of velocity of a moving body with time. This change could be a change in the speed of the object or its direction of motion or both. Acceleration = Rate of change of velocity with time. If the velocity of an object increases then the object is said to be moving with positive acceleration. If the velocity of an object decreases then the object is said to be moving with negative acceleration. Negative acceleration is also known as retardation or deceleration. If the change in velocity is zero, example either the object is at rest or moving with uniform velocity, then the object is said to have zero acceleration. If the change in velocity in equal intervals of time is always the same, then the object is said to be moving with uniform acceleration. If the change in velocity in equal intervals of time is not the same, then the object is said to be moving with variable acceleration.

a=∆ v∆ t

A body falling straight down moves only under the influence of gravity and air resistance, for fairly short falls by massive objects, the effect of air resistance is negligible. Gravity is equal to 9.8 m/s2

Kinematic Equations:

1

2

3*

4*

5*

* Requires constant Acceleration

The slope of a line characterizes the general direction in which a line points.  To find the slope, you divide the difference of the y-coordinates of a point on a line by the difference of the x-coordinates. One of the most important properties of a straight line is in how it angles away from the horizontal. This concept is reflected in something called the "slope" of the line. Vertical lines have no slope. In particular, the concept of slope simply does not work for vertical lines. Formula to find the slope of a line:

2

A direct relation is of the form a = b. This means that if one goes up, the other must go up with it. If one is doubled, the other must also be doubled. An inverse relation is of the form a = 1/b. This means that if one is doubled, the other is halved, thus maintaining equality.

3. Methodology

The materials that were used for this experiment were battery operated toy car, meter stick, and a timer.

In the first activity (uniform motion), the distance traveled by a battery operated car every 2s interval for 20 seconds was measured. The total displacement versus total time using was plotted. The best fit line was drawn, and the slope of the line was determined.

In the second activity (graphical analysis), a motion detector was used along with a board made of Styrofoam. A student was tasked to control the computer while the other student held the board. The icon collect was clicked by the student in the computer signaling the start of the experiment. The movement of the student who held the board was determined by the graph that was presented on the computer. The student moved either forward or backward depending on the interval of the graph.

In the third activity (reaction time), a group mate was asked to hold a meter stick vertically at the zero mark while the other group mate positioned her thumb and index finger at the 50cm mark. The group mate was told to drop the meter stick without telling the other group mate. It was caught with the thumb and index finger. The reaction time from the formula is: t=√2 ;

where h is the distance the meter stick has fallen measured from the 50cm mark to where the meter stick was caught. The other group members also determined their reaction time.

4. Results and Discussion

Table 1. Uniform Motion

Time(s)

Displacement (cm)

Ave. Velocity (cm/s)

2s 63 cm 31.5 cm/s4s 162 cm 40.5 cm/s6s 359 cm 59.8 cm/s8s 425 cm 53.1 cm/s10s 512 cm 51.2 cm/s12s 584 cm 48.7 cm/s14s 663 cm 47.4 cm/s16s 732 cm 45.6 cm/s18s 797 cm 44.3 cm/s20s 869 cm 43.45 cm/s

Table 1 shows the time, displacement, and average velocity of the battery operated car. The distance travelled by the car was measured every 2s for 20 seconds.

Figure 1. Displacement vs. Time

3

Figure 2. Average Velocity vs. Time

Figure 1 and Figure 2 show the plotted displacement versus time and average versus time, respectively. The slope

was determined with the formula slope=∆ y∆ x

.

For figure 1, the slope is . For figure 2, the slope is .

Figure 3.1 Graphical Analysis

Figure 3.2 Graphical Analysis

Figure 3 shows the graph matching by using the motion detector and board made of Styrofoam. This shows the movement of the member.

Table 2. Reaction Time

StudentRT(s)

RT while talking (s)

Raffy 0.24s 0.25sPamela 0.24s 0.22sKatrina 0.22s 0.17sManette 0.24s 0.17s

Table 2 shows the reaction time of the group members while dropping a meter stick without any signal, and another while the other members were distracting the particular student. Katrina had the fastest reaction time. While talking, Manette and Katrina had the fastest reaction time.

5. Conclusion

Determining the velocity and displacement in objects is a hard task to do. But with the help of graphs, you can come to understand and apply what the things you learned are there for. You have to have patience for you to be able to analyze what motion is all about. There are many different ways. Just like in this activity, a toy car’s velocity was measured by carefully taking note of its distance in every 2 second interval. It wasn’t easy; you might have to repeat it to be accurate. Another way to determine velocity is what happened with Activity number 4. It can be very unpredictable but still you can measure one’s reaction time. In any way that you try to figure out how velocity and displacement works, it is going to need time and patience for you to be successful with your goal.

4

6. Applications

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 one must do the following. First, get a rock or any object that would not break if dropped. Then drop the rock and with the use of a stopwatch measure the time it took for the rock to reach the ground from the building. For the calculations, we will use this formula y = Vot + 1/2at 2. Y will be the measurement of the building, Vo will be the initial velocity which is 0 and a will be the acceleration which is -9.8m/s2, or gravity and t will be the time. Let’s assume the time for example would be 6.00 seconds. The equation will look like this: y = (0m/s) (6.00s) + ½(-9.8m/s2) (6.00s)2. y = -176.4m or simple 176 meters. We could therefore calculate the height of the building using a stopwatch and some math calculations.

2) If you drop a feather and a hammer from the same height here on earth, which will reach the ground first? Will you get the same result if you perform the experiment on the surface of the moon?

The hammer will reach the ground first than the feather if dropped from the same height here on earth. It is because of the weight difference of the two. The hammer is heavier than the feather thus resulting in a greater speed based on the formula s = m×a,

with acceleration being represented as gravity. On the other hand, you will not get the same result if this experiment was done on the moon. Both the hammer and the feather will drop at the same time. The reason behind this is that there is no gravity present in the moon thus enabling the hammer and the feather to drop at the same time.

7. References

[1] Cutnell, J.D. & Johnson, K.W. (2010). Introduction to physics. (8th ed.). USA: John Wiley & Sons.

[2] Reaction Time. Retrieved on December 9, 2010 from http://www.topendsports.com/testing/reactime.htm

[3] Graphical analysis of linear motion. Retrieved on December 9, 2010 from http://phy-061062.blogspot.com/2007/06/graphical-analysis-of-linear-motion.html

5