The purpose, of this experiment, was to prove that there is a relation between the magnitude of the resulting vector, and the angle between the vectors that are being added. The test was performed by creating a balance between three weights tied to strings on a pulley that transferred the string on top of a graduated disc, which made easy the measurement of the angles between them. After performing the experiment, my group concluded that there is a relation between the angle between the vectors and the magnitude of the resulting vector.

Introduction

Physics deals with the study of properties such as forces; these properties are represented not only by a magnitude, but by a direction as well. One of the tools that physics use to represent forces is the vector. In order to have a better understanding of the addition and subtraction of vectors, an experiment was performed. The experiment enabled us to see the relation between the angles and the magnitudes of vectors when they are added.

Procedure

The procedure was as follows:

1.First choose two weights and hag them from a string that was lied on a pulley and tied to a ring placed at the center of the graduated disc. Note: for this step the ring was secured with a pin. 2.The strings were placed in a desired angle.

3.A third weight was tied to a string going in an opposite direction from the two that had already been placed. 4.More weight was added to the third string until the forces are balanced. 5.Measure the angles and weights of the vectors.

6.Repeat the procedure five times to verify that it is reproducible. 7.Record the averages of the measurements, and calculate the resulting vectors with the formula. 8.Analyze and get a conclusion

...
Abstract
The experiment was about the resolution of vector quantities using different methods or techniques. Among those are the Parallelogram, Polygon, and the Analytical or Component methods. Using each method, it was found out that Component method is the most accurate as its approach is purely theoretical, that is, all other physical factors are neglected leaving only the appropriate ones to be calculated. In addition, properties of these quantities such as associativity and commutativity of the addition operation were also explored.
1. Introduction
Vectors play an important role in many aspects of our everyday lives or of one’s daily routine. It is a mathematical quantity that has both a magnitude and direction.
A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". The study of vectors had gone through a lot of revisions, starting from the 19th century where mathematicians used geometrical representations for complex numbers. Lots of changes and multiple varieties of altering were conducted to this study, which led to the discovery of the vector that we all know today. Operations on vectors are also made possible through time. Addition of vectors was clarified and can now be done in different ways. Vectoraddition in a...

...|Component of vectors |Resultant vectors by component method
28 July 2012
REDG 2011
1
The Right Triangle (c) (a)
(b)
c = a +b
2 2 2 2 2
Solve for a and b.
a2 = c2 -b2 b2 = c2 -a2
c = a +b
28 July 2012
REDG 2011
2
The Right Triangle
hypotenuse opposite
adjacent
28 July 2012 REDG 2011 3
The Right Triangle
adjacent
hypotenuse
opposite
28 July 2012 REDG 2011 4
The Right Triangle
The opposite always faces opposite to the reference angel
28 July 2012
REDG 2011
5
The Right Triangle
Identify the opposite, adjacent, and hypotenuse in each right triangle below.
z y 1 x a
28 July 2012
a 2 b b 4 c
REDG 2011
y c x p 5 s q
6
3
z
Trigonometric Functions
opposite sinθ= hypotenuse adjacent cosθ= hypotenuse opposite tanθ= adjacent
28 July 2012
REDG 2011
7
The Right Triangle
Write the equations to get the values of the unknown side (represented by letters in red color).
z y 1 x a
28 July 2012
a 2 b b 4 c
REDG 2011
y c x p 5 s q
8
3
z
Resultant Vectors
28 July 2012
REDG 2011
9
Resultant Vectors
Hint: Identify the adjacent and opposite
How do we determine for the x-component? What about for the y-component?
28 July 2012 REDG 2011 10
Resultant Vectors
Hint: The resultant vector is the hypotenuse of the triangle....

...Directed Line Segment:
VECTORS
• A line segment with direction is called a directed line
segment.
• If ‘A’ and ‘B’ are two distinct points in the space, then the
ordered pair (A, B) is called as a directed line segment and
is denoted by """""# .
!
• In """""# , ‘A’ is called initial point and ‘B’ is called terminal
!
point of """""# .
!
• The distance from ‘A’ to ‘B’ is called the length or magnitude of """""# . The length or magnitude of """""#
!
!
is denoted by '"""""# '. Thus '"""""# ' = ! .
!
!
• The direction of """""# is from ‘A’ to ‘B’ or towards ‘A’ to ‘B’.
!
• A line which is having the directed line segment is called the support of the directed line segment.
• The support of """""# is denoted by ,""""# .
!
!
• Thus every directed line segment has three attributes, namely, direction, magnitude and support.
• Two directed line segments are said to be they are having same direction if their supports are
parallel and the terminal points lie in the same half plane determined by the line passing through
the initial points.
• """""# and """""# are said to have the same direction if their supports are parallel and
!
./
1. A≠C and ‘B’ and ‘D’ are lies in the same half plane determined by the line ,""""# .
.
2. A=C and A, B, C and ‘D’ are collinear such that ‘B’ and ‘D’ lie on the same ray originating from
‘A’.
"""/
• """""# and .""# are said to have the opposite direction if their supports are parallel but not have...

...
Date _________
Addition and Resolution of Vectors
Equilibrium of a Particle
Overview
When a set of forces act on an object in such a way that the lines of action of the forces pass
through a common point, the forces are described as concurrent forces. When these forces lie
in the same geometric plane, the forces are also described as coplanar forces. A single
G
G
equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and
G
F2 , as shown. This resultant force is obtained by a process of vectoraddition of the original
forcevectors and produces the same effect as
the combined effect produced by all the
original forces. Conversely, a set of
concurrent forces can be balanced exactly by a
single force that acts at the common point of
concurrence of the forces. Such a force is
G
known as the equilibrant FE of that set of
forces and it is equal in magnitude but acts in
exactly opposite direction to the resultant of
the set of forces. A particle is considered to be
in (static) equilibrium under the action of a set
of forces when the vector sum of all the forces
is zero....

...Chapter 1 Vectors, Forces, and Equilibrium
1.1 Purpose
The purpose of this experiment is to give you a qualitative and quantitative feel for vectors and forces in equilibrium.
1.2
Introduction
An object that is not accelerating falls into one of three categories: • The object is static and is subjected to a number of diﬀerent forces which cancel each other out. • The object is static and is not being subjected to any forces. (This is unlikely since all objects are subject to the force of gravity of other objects.) • The object is moving with constant velocity. In this case, the object may be subject to a number of forces which cancel out or no force at all. This case is not considered in this lab. The category of physics problems that involve forces in static equilibrium is called statics. Physicists and engineers are subjected to static problems quite frequently. A few examples of these principles in use are seen in the design of bridges and the terminal velocity of a person falling through the air. Mathematically, forces in equilibrium are just a special case of Newton’s Second Law of Motion, which states that the sum of all forces is equal to the mass of the object multiplied by the acceleration of the object. The special case of forces in equilibrium (static), occurs when the...

..."The Force Table" is a simple tool for demonstrating Newton’s First Law and the vector nature of forces. This tool is based on the principle of “equilibrium”. An object is said to be in equilibrium when there is no net force acting on it. An object with no net force acting on it has no acceleration. By using simple weights, pulleys and strings placed around a circular table, several forces can be applied to an object located in the center of the table in such a way that the forces exactly cancel each other, leaving the object in equilibrium. (The object will appear to be at rest.) We will use the force table and Newton’s First Law to study the components of the forcevector.
we student , should be exposed more to these apparatus so that we will not find these things hard to use.
This lab was about constructing vectors graphically and being able to find the resultant of the vectors. Using a ruler to make the vectors and solving them graphically to find the resultants.
"The Force Table" is a simple tool for demonstrating Newton’s First Law and the vector nature of forces. This tool is based on the principle of “equilibrium”. An object is said to be in equilibrium when there is no net force acting on it. An object with no net...

...Addition of Vectors
Objectives:
The purpose of this experiment is to show that the magnitude and direction of the resultant of several forces acting on a particle may be determined by drawing the proper vector diagram, and that the particle is in equilibrium when the resultant force is zero.
Principles:
RABx = Ax + Bx
RABy = Ay + By
R2 = R2X + R2Y
R = Rx2+Ry2
Tanθ = RyRx
θ = Tan-1 RyRx
List of Equipment:
1. Force table
2. Four pulleys
3. Four weights
4. Slotted weights
5. Level
6. Protractor
7. Metric Ruler
8. Graph paper
Main Result:
After drawing a vector diagram to scale, using a scale of 20 grams per centimeter and determine graphically the direction and the magnitude of the resultant by using the parallelogram method, we got:
R = 10.4
θ = 92°
Scale = 208 grams
Discussion:
In this lab, we were asked to set up a force table as instructed on the lab manual before starting the actual experiment. We began the experiment by mounting a pulley on the 20C angle mark on the force table and hanging a total of 100 grams over it. We continued by doing the same on the 120° angle mark and hanging a total of 200 grams over it. Then, we were asked to draw a vector diagram to scale and determine graphically the direction and magnitude of the resultant by using the parallelogram...

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