Resolution of vector Introduction: The main objective of this lab is to add and resolve vectors using three distinct methods. 1) Graphical: When two forces act upon an object‚ their combined effect can be determined by adding the vectors‚ which represent forces. One method of performing this addition is known as graphical method of vector addition. In this method‚ arrows are drawn in the direction of forces. The lengths of arrows are proportional to the magnitude of vectors. The resultant
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12e 2 Force Vectors Part 2 Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Objectives • Cartesian vector form • Dot product and angle between 2 vectors Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Outline 1. 2. 3. 4. 5. Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product Copyright © 2010 Pearson Education South Asia Pte Ltd 2.5 Cartesian Vectors • Right-Handed
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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 vector addition
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"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
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each of the following vectors in terms of and (a) (b) (c) (Total 4 marks) 2. The vectors ‚ are unit vectors along the x-axis and y-axis respectively. The vectors = – + and = 3 + 5 are given. (a) Find + 2 in terms of and . A vector has the same direction as + 2 ‚ and has a magnitude of 26. (b) Find in terms of and . (Total 4 marks) 3. The circle shown has centre O and radius 6. is the vector ‚ is the vector and is the vector . (a) Verify
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Acceleration Velocity Displacement Distance Time Definition 1. Acceleration is the rate of change of velocity with time. Velocity is a vector physical quantity; both magnitude and direction are required to define it. the length of an imaginary straight path‚ typically distinct from the path actually travelled by P. Distance is a numerical description of how far apart objects are. In physics or everyday usage‚ distance may refer to a physical length‚ or an estimation Time in physics is
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1.1.1 Show how to find A and B‚ given A+B and A −B. 1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax‚Ay ‚ and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B‚ vrel‚ is defined by the equation vrel = vA − vB‚ where vA is the velocity of A and vB is the velocity of B. Determine the velocity
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be seen depicted throughout history in sci-fi movies. In the particular movie entitled‚ The Matrix‚ directed and written by brothers Laurence and Andrew Wachowski in 1999. This film shows a new form of technology‚ not only in through the plot but also its special affects and symbols. The upcoming millennium also marked a perfect time to release such a complex film for the public viewing pleasures. The Matrix takes place nearly century ahead in the future. The human race is nothing‚ but virtual slaves
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quantity which depends on direction a vector quantity‚ and a quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics‚ a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type‚ you have to compare both the magnitude and the direction. For scalars‚ you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding‚ subtracting‚ multiplying
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Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary‚ a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A‚ in handwriting A . The magnitude of the vector is denoted by A A
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