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OVERVIEW
The laws of Physics are expressed as mathematical relationships among physical quantities. Most of these quantities are derived quantities, in that they can be expressed as combinations of a small number of basic quantities. In Mechanics, the three basic quantities are length, mass, and time. All other quantities can be expressed in terms of these three.
The laws of Physics are expressed as mathematical relationships among physical quantities. Most of these quantities are derived quantities, in that they can be expressed as combinations of a small number of basic quantities. In Mechanics, the three basic quantities are length, mass, and time. All other quantities can be expressed in terms of these three.
LEARNING OBJECTIVES:
At the end of this module, you should be able to:1. Calculate your resultant displacement.2. Compare the resultant displacement obtained in the experiment with the Polygon and the Component Method.
At the end of this module, you should be able to:1. Calculate your resultant displacement.2. Compare the resultant displacement obtained in the experiment with the Polygon and the Component Method.
SCALAR AND VECTOR QUANTITIES
The three fundamental quantities in mechanics are length, mass, and time. The other quantities are expressed in terms of these three such as the quantities that describe the motion of an object. Scalar and vector quantities are used to describe the motion of an object. Scalar quantities are the physical quantities that have magnitude only such as distance, speed, mass, and density; whereas, vector quantities are the physical quantities that have both magnitude and direction such as displacement, velocity, acceleration, and force. Scalar exists in one dimension only while vector can exist in one, two, or even three dimensions. Henceforth, vector quantities are significant in the study of motion as stated in the image.
The three fundamental quantities in mechanics are length, mass, and time. The other quantities are expressed in terms of these three such as the quantities that describe the motion of an object. Scalar and vector quantities are used to describe the motion of an object. Scalar quantities are the physical quantities that have magnitude only such as distance, speed, mass, and density; whereas, vector quantities are the physical quantities that have both magnitude and direction such as displacement, velocity, acceleration, and force. Scalar exists in one dimension only while vector can exist in one, two, or even three dimensions. Henceforth, vector quantities are significant in the study of motion as stated in the image.
VERTICAL AND HORIZONTAL COMPONENTS
Meanwhile, the first laboratory experiment is mainly focused on vectors. In one-dimensional or straight-line motion, a simple plus or minus sign can be used to indicate a vector's direction. Positive or plus motion is typically seen to be forward, to the right, or upward, while negative or minus motion is generally thought to be backward, to the left, or downward. Furthermore, in two dimensions, a vector describes motion in two perpendicular directions, such as vertical and horizontal. For vertical and horizontal motion, each vector is made up of vertical and horizontal components. For instance, the Vector A shown on the image in the right has vertical component represented by the blue arrow and horizontal component represented by the red arrow. The direction is represented by the theta (θ) or simply the angle that the vector makes with the horizontal.
Meanwhile, the first laboratory experiment is mainly focused on vectors. In one-dimensional or straight-line motion, a simple plus or minus sign can be used to indicate a vector's direction. Positive or plus motion is typically seen to be forward, to the right, or upward, while negative or minus motion is generally thought to be backward, to the left, or downward. Furthermore, in two dimensions, a vector describes motion in two perpendicular directions, such as vertical and horizontal. For vertical and horizontal motion, each vector is made up of vertical and horizontal components. For instance, the Vector A shown on the image in the right has vertical component represented by the blue arrow and horizontal component represented by the red arrow. The direction is represented by the theta (θ) or simply the angle that the vector makes with the horizontal.
WHAT IS A RESULTANT?
A resultant is the vector sum of two or more vectors (physicsclassroom.com). In other words, it is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R as shown in the diagram on the left. Vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram. This method is also called the graphical or polygon method which literally needs a protractor and a ruler to graphically calculate the resultant. Another method is analytical or polygon method which involves calculations in determining the magnitude and direction of the resultant. These two methods were utilized in the laboratory experiment to calculate the resultant displacement of the vectors. Shown below is the submitted laboratory report for this experiment.
A resultant is the vector sum of two or more vectors (physicsclassroom.com). In other words, it is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R as shown in the diagram on the left. Vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram. This method is also called the graphical or polygon method which literally needs a protractor and a ruler to graphically calculate the resultant. Another method is analytical or polygon method which involves calculations in determining the magnitude and direction of the resultant. These two methods were utilized in the laboratory experiment to calculate the resultant displacement of the vectors. Shown below is the submitted laboratory report for this experiment.
Salazar_BSCE2B_LR#1_Measurements and Vectors.pdfIn this experiment, we simply created three connected vectors, with different displacement or length, and a resultant vector just like the figure previously shown but by following the specific directions instructed in the study guide. Note that the resultant vector is always the vector that connects to the starting point of the first vector. The length or distance as well as the direction or angle of all the vectors, including the resultant vector, were measured physically. Then, we used the gathered data to determine which among the methods, graphical/polygon method or analytical/component method, is better in determining the resultant displacement of the vectors. In using the graphical/polygon method, the sketch or graph should be properly scaled and made as accurate as possible to obtain little or no discrepancy at all. The accuracy of the magnitude and direction of the resultant displacement will depend on the accuracy and precision of the sketch. Meanwhile, the analytical/component method only requires simple computation which can be calculated within five minutes. In order to compute the vertical and horizontal components of each of the vectors, I used y = rsinθ and x = rcosθ, respectively, where r is the displacement and θ is the direction or angle of the vector. To determine the magnitude of the resultant displacement, use the formula R = √(x2 + y2), where x and y are the previously computed horizontal and vertical component. Furthermore, to compute the direction of the resultant, use tan θ = y/x.
The result showed that in the analytical/component method, percent differences of 0.01 and 0.0083 were obtained for the magnitude and direction of the resultant, respectively; whereas, 0.04 and 0.03 were the obtained percent differences for the magnitude and direction of the resultant, respectively using the graphical/polygon method. Meaning, the obtained magnitude and direction of the resultant using the analytical/component was the closest to the actual measured quantities. For instance, the actual measured magnitude was 2.3 meters with a direction of 60° North of West, while the computed quantities using the analytical/component method were 2.27 meters and a direction of 60.5° North of West. This only means that the analytical/component method is more reliable than the graphical/polygon method in determining the resultant displacement. It has the most accurate result. One reason for this is a thorough calculation can obtain perfection on the measurements or results. Mistakes are seldom committed in computations since the formula is very simple. Henceforth, accuracy and precision is the strength of the analytical/component method. On the other hand, the strength of the graphical/polygon method is having a graphical representation of the vectors. It creates a visual understanding of the measurements obtained in the field. However, its accuracy depend on the drawing itself. Note that any misalignment of the ruler or protractor used might yield an error in the result.
REFLECTION
This laboratory experiment made me realize that a resultant is just the vector sum of two or more vectors. Adding two or more vectors means determining first the vertical and horizontal components of each vector, then getting the summation of each component, to finally determine the magnitude of the resultant vector by getting the square root of the sum of the squares of the summation of each component. Furthermore, the direction of the resultant can be obtained using the tangent function which says that tangent theta is equal to the ratio of the opposite side to the adjacent side or simply y/x. This method pertains to the analytical/component method in which the magnitude and direction of the resultant displacement will be obtained through calculations. Another method is through a vector addition diagram or the graphical/polygon method. In this method, the vectors will be drawn and scaled accurately to obtain an accurate resultant displacement. However, this laboratory experiment showed that the former method yields the most accurate resultant displacement with a very little percent difference from the field result. The analytical/component method's strength is accuracy and precision whilst for the graphical/polygon method is having a visual representation of the vectors. Nonetheless, both methods can be used to determine the resultant displacement of some given vectors.
This laboratory experiment made me realize that a resultant is just the vector sum of two or more vectors. Adding two or more vectors means determining first the vertical and horizontal components of each vector, then getting the summation of each component, to finally determine the magnitude of the resultant vector by getting the square root of the sum of the squares of the summation of each component. Furthermore, the direction of the resultant can be obtained using the tangent function which says that tangent theta is equal to the ratio of the opposite side to the adjacent side or simply y/x. This method pertains to the analytical/component method in which the magnitude and direction of the resultant displacement will be obtained through calculations. Another method is through a vector addition diagram or the graphical/polygon method. In this method, the vectors will be drawn and scaled accurately to obtain an accurate resultant displacement. However, this laboratory experiment showed that the former method yields the most accurate resultant displacement with a very little percent difference from the field result. The analytical/component method's strength is accuracy and precision whilst for the graphical/polygon method is having a visual representation of the vectors. Nonetheless, both methods can be used to determine the resultant displacement of some given vectors.
REFERENCES:
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