Physics Lab 1 - Exp. 3 2h736i

Vectors Ronald Patrick Pascual, Whaynne Joi Pegollo, Nikko Jay Perez, Beverly Pilapil, Adah Rachel Solante, Mark Ivan Rivera – Group 5 Physics Department, Adamson University, Ermita, Manila Abstract The experiment focused on studying vectors and determining its equilibrant and resultant using component method, graphical method and force table. Magnitude in of dynes and direction were given and were then used by the experimenters in graphical and component method. Furthermore, the magnitudes were converted to mass for the force table and the equilibrant was then adjusted so that the ring perfectly fits the center of the force table. Percent error was then computed by the experimenters considering component method results to be the standard value. The experimenters used the result of component method as the standard value and observed that the force table result was more accurate than the result of graphical method. 1. Introduction Vector's concepts and calculation methods lie at the heart of the physics curriculum, underlying most topics covered in introductory courses at the university level. In physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. Velocity and acceleration of a moving object and forces acting on it are all described by vectors. Several measurement methods were used namely: the force table, component method and graphical method. This experiment focuses on the vector quantities. It aims to study vectors the graphical method of determining the resultant of several forces, as well as to determine the equilibrant of two or three given forces using the component method or the force table. The results gathered were then compared in of percent error. 2. Theory

A physical quantity is a physical property that can be quantified by measurement. Physical quantity can be measured by either scalar quantity or vector quantity. A scalar quantity is a measurement medium strictly in magnitude only. Time, volume, speed and temperature are examples of scalar quantity. A vector quantity is a measurement that refers to the magnitude with direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity’s magnitude. Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector. The magnitude defines as how much or how strong. The direction tells where it lies. Some of its examples are velocity, displacement, and force. The addition of scalar quantities is to simply add the magnitudes algebraically. The addition of vectors is produce by two or more vectors. Vector quantities are measured with direction.

Graphical method is a simple way to measure a vector. It has two kinds: parallelogram and polygon method. A parallelogram method is translated to a common origin. The method involves drawing the vectors to scale in the indicated direction, sketching a parallelogram around the vectors such that the resultant is the diagonal of the parallelogram. A polygon method also called tip to tail method. It is a method to find the resultant of two or more than two vectors. Once all vectors are chained together, the resultant vector is simply a vector chained from tail of the first vector to the tip of the last vector. This was used by the experimenters to find the resultant of the given forces. In of component method, the resultant is the sum of all vectors with respect to the angle. It is drawn from the Pythagorean Theorem. The resultant lies on the formula, (1) where

is the summation of all x

components

and

is

the

summation of y components. Force components are solved using the equation,

Equilibrant Equilibrant is a force capable of balancing forces to equilibrium. The equilibrant must be equal in magnitude but opposite in direction of the resultant. Force formula was used by the experimeters to find the value of masses used on the force table. It is given by, (5) where F is the force or weight, m is the magnitude in dynes and g is the gravitational force equal to 980m/s. Percent Error Percent error is important in solving a problem. It is the difference between experimental and standard value, as a percentage of the standard. To determine the percent error, the experimenters used the formula,

(6) where the standard value is the magnitude of the resultant from component method and the experimental value was either the magnitude of the resultant from graphical method or the magnitude of the resultant from the force table.

(2) 3. Methodology

(3) Finding an angle The formula in finding an angle is given by (4)

Force table, weight holders, set of masses, graphical paper, ruler, pencil and protractor were the materials used by the experimenters throughout the experiment.

The given forces F1, F2 and F3 were used by the experimenters to find the masses for the force table. Fifteen (15) grams, twenty (20) grams and twenty-five (25) grams were the computed values and were then placed on their specified direction deducting five (5) grams (weight of weight holders). The equilibrant, the fourth vector, was then estimated until suspended in such a way that the ring exactly fits the center of the force table. Polygon method or tip-tail method was used by the 4. Data and Results Table 1 presents the magnitudes of forces with its direction. The datum was used by the experimenters to calculate and analyze resultant and equilibrant. Table 1.

Table 2 presents the resultants and equilibrant observed

experimeters for graphical method. The forces were graphed in a 1:3000 centimeter scale. The magnitude of the resultant was then measured by a ruler and the angle by a protractor. In component method, the experimenters directly substituted the values for component x and component y. The resultant was then computed by the use of Pythagorean Theorem and the angle using tangent function.

and measured by the experimenters. Both of the results were accurate having a little difference compared to the standard value. Table 2. Table 3 presents the standard value calculated by the use of analytical method or

component method. The percent error of both A and B were very little though, the force table was more accurate with 0.46130% error compared to graphical method with 0.90979% error. Table 3. 5. Conclusion The objective of determining the equilibrant and resultant of the

given forces was satisfied by the experimenters after they have studied the vectors and graphical methods during the methodology. In calculating the resultant and equilibrant using component method, geometric sum was used by the experimenters, since, the vectors does not have the same line of action. It produced the standard measurement for the computed force. Component method, thus, produce the real value because it undergoes statistical computations. In determining the equilibrant and resultant of the given forces using the force table and graphical method, the experimenters observed that the results of the force table were more accurate compared to the results of the graph. References: 1. Physics Education. 2003. "Initial understanding of vector concepts among students in introductory physics course, from http://physicseducation.net/ docs/AJP-71-630-638.pdf 2. Apostol, T. (1967). Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra. John Wiley and Sons. From,

http://en.wikipedia.org/wiki/E uclidean_vector 3. Apostol, T. (1969). Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications. John Wiley and Sons. From, http://en.wikipedia.org/wiki/E uclidean_vector 4. CC-BY-SA. Physical Quantity. From, http://www.princeton.edu/~a chaney/tmve/wiki100k/docs/ Physical_quantity.html 5. Anonymous. Vectors. From, http://global.britannica.com/ EBchecked/topic/1240588/v ector 6. Anonymous. Examples of Vector and Scalar Quantity in Physics. From,http://examples.yourdi ctionary.com/examplesvector-scalar-quantityphysics.html 7. Anonymous. VectorsFundamentals and Operations. From, http://www.physicsclassroom .com/Class/vectors/u3l1e.cf m 8. Fendt, Walter. The University of Oklahoma. From http://www.nhn.ou.edu/walk up/demonstrations/WebTutor ials/HeadToTailMethod.htm