How to calculate a dot product

Slides:



Advertisements
Similar presentations
Work Work is done only when a force moves an object.
Advertisements

 Learn what “work” is!  Learn how to calculate work  See who can do the most work!  Learn about power.  Learn Hooke’s Law.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Section 6.7 Dot Product.
Lesson 6-3 The Scalar Product AP Physics C. 6 – 3 The scalar product, or dot product, is a mathematical operation used to determine the component of a.
Physics 218, Lecture X1 Physics 218 Lecture 10 Dr. David Toback.
Calculating Work. The Joule  Work is force acting over a distance, and has units equal to units of force times units of distance. With 1-dimensional.
Review of Work Work Done on a Point Charge by a Point Charge
10.5 The Dot Product. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property.
Phy 212: General Physics II Chapter : Topic Lecture Notes.
Section 6.7 The Dot Product. Overview From last section, adding two vectors results in another vector. So also does multiplying a scalar (real number)
Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 7 Work and Kinetic Energy.
Lecture 1eee3401 Chapter 2. Vector Analysis 2-2, 2-3, Vector Algebra (pp ) Scalar: has only magnitude (time, mass, distance) A,B Vector: has both.
Chapter 7 Kinetic energy and work Key contents Work and kinetic energy Work done by gravity, springs and a variable force Power.
WORK AND EFFICIENCY. WHAT IS WORK? Definition:  The use of force to move an object Not all force used to move an object does work The force must be applied.
Kinetic energy Vector dot product (scalar product) Definition of work done by a force on an object Work-kinetic-energy theorem Lecture 10: Work and kinetic.
6.4 Vectors and Dot Products
12.9 Parallel & Perpendicular Vectors in Two Dimensions
6.4 Vectors and Dot Products The Definition of the Dot Product of Two Vectors The dot product of u = and v = is Ex.’s Find each dot product.
Section 13.3 The Dot Product. We have added and subtracted vectors, what about multiplying vectors? There are two ways we can multiply vectors 1.One results.
The concept of energy (and the conservation of energy) is one of the most important topics in physics. Work Kinetic energy Energy approach is simpler than.
Five-Minute Check (over Lesson 8-2) Then/Now New Vocabulary
Section 13.4 The Cross Product. Torque Torque is a measure of how much a force acting on an object causes that object to rotate –The object rotates around.
Electric Potential and Electric Potential Energy
Section 18.1 The Idea of a Line Integral. If you can imagine having a boat in our gulf stream example from last chapter, depending on which direction.
Advanced Higher Physics Electric Potential. Electric Potential 1 V = work done / q(measured in J C -1 ) Defined as ‘the work done per unit positive charge.
1. Determine vectors and scalars from these following quantities: weight, specific heat, density, volume, speed, calories, momentum, energy, distance.
Work AP style. Energy Energy: the currency of the universe. Everything has to be “paid for” with energy. Energy can’t be created or destroyed, but it.
Assigned work: pg.398 #1,3,7,8,11-14 pg. 419 #3 (work) Recall: Dot Product.
Electric Potential and Energy. Objectives Define work and relate it to energy Define electric potential difference, and relate it to the work done on.
Chapter 7 Work and Energy HW5 due on Monday 12 instead of Friday 9. Study Guide will be posted on Friday 9.
8.1 and 8.2 answers. 8.3: Vectors February 9, 2009.
Work. Definition Work is done on an object by a constant force moving the object through a distance It is the product of the displacement and the component.
Work and Energy. Scalar (Dot) Product When two vectors are multiplied together a scalar is the result:
Electric Field magnitude of the electric force on a small, positive test charge divided by the magnitude of that test charge direction of the electric.
5.4 Electric energy, Electric Potential, and Electric Potential Difference p Electric Potential Energy In Uniform Fields The Work-Energy theorem.
8.5 The Dot Product Precalculus. Definition of the Dot Product If u= and v= are vectors, then their dot product (u v) is defined by: u v = a 1 a 2 + b.
6.4 Vector and Dot Products. Dot Product  This vector product results in a scalar  Example 1: Find the dot product.
Dr. Shildneck. Dot Product Again, there are two types of Vector Multiplication. The inner product,called the Dot Product, and the outer product called.
Vectors and Dot Products OBJECTIVES: Find the dot product of two vectors and use the properties of the dot product. Find the angle between two vectors.
Vectors and Dot Products 8.4 Part 2. 2  Write a vector as the sum of two vector components.  Use vectors to find the work done by a force. Objectives.
Dot Product of Vectors.
Additional Topics in Trigonometry
Work, Power Problems Answers
Parallel & Perpendicular Vectors in Two Dimensions
Vectors.
WORK And Energy and Power.
Work – review from gr 11 Units - Joules (J) = Nm = kgm2s-2
4.4 The Dot Product.
Section 3.5 – Curvilinear Motion
Chapter 25 Electric Potential.
Vectors, Linear Combinations and Linear Independence
Find {image} , if {image} and {image} .
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
IV . Electric ______________
The Work Energy Principle
Storing Electrical Energy Electrical Potential (Voltage)
Chapter 7 Work and Energy
Mechanical Energy Kinetic Energy, energy of motion,
Find {image} , if {image} and {image} .
What is Motion? Motion: A change in position of an object compared to a reference point Motion can be measured in the following ways:
12.9 Parallel & Perpendicular Vectors in Two Dimensions
Physics 133 Electromagnetism
Work.
Kinetic energy and work
Vectors and Dot Products
Last time… - +.
Concept of Work.
Work Work is done when a force is exerted on an object and the object moves a distance x. Work = force ·distance W = F · d units: N·m = Joule Work is.
PHYS 172: Modern Mechanics Summer 2012
Torque Rotational analogue of Force Must contain Use door example
Presentation transcript:

How to calculate a dot product A dot product is the multiplication of two vectors to form a scalar. There are two ways to calculate the dot product. where θ is the angle between A and B Component of A along B A θ B

Examples of Dot Products

Definition of Work Work is defined as the amount of force acting over a distance. The unit of work is either Joules (J) or electron-volts (eV) Dr F

Example of Work y Δw Δh1 x m Δh2 The following is an example of the work done by gravity on a mass. y Δw Δh1 x m Δh2

Example of Work F (N) 1 -1 A1 X (m) 1 2 A2 This is an example using the the fact that integrals are areas under a curve. F (N) 1 -1 A1 X (m) 1 2 A2