Equality: Force and Resultant Force Essay

Submitted By khushi454
Words: 794
Pages: 4
Open Document
The Equilibrium of Forces: The First Law©98
Experiment 4

Objective: To study the methods of vector addition as applied to the first law of the equilibrium of forces.

Discussion:

The first law of the equilibrium of forces states that the vector sum of the forces acting on an unaccelerated object is zero. One way to measure the validity of this law is to add vectorially all the forces acting on a stationary object except one, and then to note by what amount the resultant force differs from the expected force. An example is shown in Fig.1. Here, there are three forces acting on the object. Two of these forces, F1 and F2, are added by geometric construction to produce the resultant force, F. This force should be equal and opposite to F3 and can be compared with it by finding the percent deviation in their magnitudes and the percent error between their angular separation and 180º.

The mathematical formulation of these ideas is as follows: we let F1 and F2 be the measured values of the magnitudes of two of the forces. Then constructing a diagram like that shown in Fig. 1 (using the parallelogram rule for adding vectors), we measure the magnitude, F, of the resultant. We compare this value with the magnitude F3 using the equation for percent error:

(1)

Letting  be the angle between F and F3, we compare the direction of F relative to F3 by comparing  with the theoretical value of 180 degrees. That is, we find the percent error using:

(2)

Another way in which the law can be verified is to determine the algebraic sum of the components of the forces in a given direction. As an example, the rectangular components of the vector are shown in Fig. 2. Regardless of the direction chosen, the sum should be zero. However, in general the sum is not zero because unavoidable errors invariably appear. This sum is actually the difference between the components in the positive sense of the direction chosen and the components in the negative sense. Hence, dividing this sum by either the sum of the components in the positive sense or the sum in the negative sense is a measure of the error in that direction. A complete measure of the error is obtained when the error is calculated once for the x-direction (chosen arbitrarily) and again for the corresponding y-direction.

The mathematical formulation of these comparisons for the x-direction is as follows: Defining 1 to be the angle between F1 and the x-axis in Fig. 2, we have
(3)

Similar equations can be written for the other two forces. The percent error for the x-direction is

(4)

A similar expression can be written for the y-components of the forces, except that the cosine appearing in Eq. (3) is replaced with the sine.

Exercises:

1. Determine the resultant force of two vectors a number of times.
a. On the equilibrium-of-forces apparatus,
i) Choose arbitrary directions for the three forces, but do not make any of the angles between the forces right angles. ii) Adjust the weights and/or angles so as to produce equilibrium (the ring should be centered on
Show More

Related Documents: Equality: Force and Resultant Force Essay

The Crucible: Arthur Miller's View on Conflicts Essay

true fears, desires and jealousies for one another's powers, pride riches and social status have undoubtedly risen in times of conflict where underlying real truths have emerged from long hatreds for each other. Such fears and disputes of social equality and differences become the fuel and more so, the catalys,t for the social issues introduced and presented in the play, the Crucible. Arthur Miller's subtle illustration of the then current social parallels of McCarthyism with Puritanism largely drew…

Words 1633 - Pages 7

Unit 5011V1 Essay

staff recruitment and selection 1.2 Identify organisational procedures and processes that affect staff recruitment and selection 1.3 Discuss fairness, objectivity and equality of opportunity as elements of recruitment and selections The major piece of legislation in the UK that impacts on staff recruitment and selection is The Equality Act of 2010. This statute consolidated nine separate pieces of anti-discrimination legislation into a single Act these were The Equal Pay Act 1970 The Sex Discrimination…

Words 6927 - Pages 28

Concept Of Abortion

1. Important concepts: * Positive and negative duties (in an abortion case) * Negative duties – avoid actions that inflict harm or injury on other * Positive duties – certain actions that aid or benefit others * Negative duties take precedent over positive duties when in conflict * Obligation (in an abortion case) * Rachels: * Does the third party (doctor) have the right to abort the fetus? * Nobody is morally required to make large sacrifices…

Words 5114 - Pages 21

The Detachment Of Particles From Coalescing Bubble Pairs

detach either in the collection zone [4,5] where the bubble-particle interaction takes place or in the froth layer [6–9]. A particle that has become attached to the surface of a bubble can become detached when the forces that hold it at the surface are exceeded by the detachment forces [10,11]. In the collection zone, the main cause for particle detachment is the presence of turbulence [4,12,13]. Turbulence is necessary to bring bubbles and particles together for collision * Fax: +61 2 4960 1445…

Words 6860 - Pages 28

Task 1. Education & Teaching Guide Essay

Teaching Role and Responsibilities for New Teachers – A Guide What we want is to see the child in pursuit of knowledge, and not knowledge in pursuit of the child. – George Bernard Shaw Introduction: Welcome to your new career choice in the challenging yet fulfilling employment as a new teacher. This guide has been produced as a reference point for your personal use, however, it does not cover all aspects of teaching. As a teacher you will be expected to abide by the Code Education and Training…

Words 8188 - Pages 33

The Philosophy of Farciophilia in American-type Societies Essay

The Philosophy of Farciophilia in American-type Societies As a society, America is now fundamentally about consumption. For an average American, nothing is more important than things. We surround ourselves with mementos from every moment—pivotal or not—of our lives. Nearly all of our national problems are due to this addiction (environmental destruction for more shopping centers, want of bigger houses, and for the materials we think we require; “over qualification” for jobs because people are earning…

Words 4030 - Pages 17

CRM 1301 Midterm uOttawa Carolyn Gordon Essays

The Demonic Perspective Trephining Individual who were having illusions or were delusional had a hole drilled in their skull in order to get rid of the spirits. If that person was still alive, the procedure was successful Witchcraft Correlated with ‘The Crucible’ where Tituba, Sarah Good & Sarah Osborne are accused of witchcraft in Salem, 1692 What to do with the witches?! Exodus 22:18- Thou shalt not suffer a witch to live Leviticus 20:27- A man also or woman that hath a familiar spirit…

Words 10213 - Pages 41

Global Business Cultural Analysis

GBCA 1 Global Business Cultural Analysis: India BUSI 604: International Business April Joyner Liberty University Abstract The nation that I have chosen for this Global Business Cultural Analysis research is India. India has one of the fastest growing and largest economies despite being one of the poorest countries. The academic…

Words 7075 - Pages 29

Essay about The Future of Marriage in America

http://marriage.rutgers.edu/Publications/SOOU/TEXTSOOU2007.htm The State of Our Unions The Social Health of Marriage in America 2007 Essay: The Future of Marriage in America David Popenoe © Copyright 2007 Introduction In this year’s essay, David Popenoe argues that long-term trends point to the gradual weakening of marriage as the primary social institution of family life. More Americans today are living together, marrying at older ages or not at all, and rearing children in cohabiting…

Words 9365 - Pages 38