sy04_sept17_07hc - Page 1 Physics 207 – Lecture 4 Physics...

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Unformatted text preview: Page 1 Physics 207 – Lecture 4 Physics 207: Lecture 4, Pg 1 Physics 207, Physics 207, Lecture 4, Sept. 17 Lecture 4, Sept. 17 Agenda Agenda Assignment: Read Chapter 5 Assignment: Read Chapter 5 c MP Problem Set 2 due Wednesday (should have started) MP Problem Set 2 due Wednesday (should have started) c MP Problem Set 3, Chapters 4 and 5 (available soon) MP Problem Set 3, Chapters 4 and 5 (available soon) c Chapter 3, Chapter 4 (forces) Chapter 3, Chapter 4 (forces) x Vector addition, subtraction and components Vector addition, subtraction and components x Inclined plane Inclined plane x Force Force x Mass Mass x Newton Newton ’s 1 s 1 st st and 2 and 2 nd nd Laws Laws x Free Body Diagrams Free Body Diagrams Physics 207: Lecture 4, Pg 2 Vector addition Vector addition c The sum of two vectors is another vector. A = B + C B C A B C Physics 207: Lecture 4, Pg 3 Vector subtraction Vector subtraction c Vector subtraction can be defined in terms of addition. B - C B C B- C B - C = B + (-1) C A Different direction and magnitude ! Physics 207: Lecture 4, Pg 4 Unit Vectors Unit Vectors c A Unit Vector Unit Vector is a vector having length 1 and no units c It is used to specify a direction. c Unit vector u points in the direction of U x Often denoted with a “hat”: u = û U = |U| U = |U| û û x y z i j k c Useful examples are the cartesian unit vectors [ i, j, k i, j, k ] x Point in the direction of the x , y and z axes. R = r x i + r y j + r z k Physics 207: Lecture 4, Pg 5 Vector addition using components: Vector addition using components: c Consider C = A + B . (a) C = (A x i + A y j ) + (B x i i + B y j ) = (A x + B x ) i + (A y + B y ) (b) C = (C x i + C y j ) c Comparing components of (a) and (b): x C x = A x + B x x C y = A y + B y C B x A B y B A x A y Physics 207: Lecture 4, Pg 6 Lecture 4, Lecture 4, Exercise 1 Exercise 1 Vector Addition Vector Addition c Vector A = {0,2,1} c Vector B = {3,0,2} c Vector C = {1,-4,2} What is the resultant vector, D , from adding A + B + C ? A) A) {3, {3,-4,2} 4,2} B) B) {4, {4,-2,5} 2,5} C) C) {5, {5,-2,4} 2,4} Page 2 Physics 207 – Lecture 4 Physics 207: Lecture 4, Pg 7 Lecture 4, Lecture 4, Exercise 1 Exercise 1 Vector Addition Vector Addition A. A. {3, {3,-4,2} 4,2} B. B. {4, {4,-2,5} 2,5} C. C. {5, {5,-2,4} 2,4} D. None of the above c Vector A = {0,2,1} c Vector B = {3,0,2} c Vector C = {1,-4,2} What is the resultant vector, D , from adding A + B + C ?...
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This note was uploaded on 10/30/2011 for the course PHYS 207 taught by Professor Winnokur during the Spring '06 term at University of Wisconsin.

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sy04_sept17_07hc - Page 1 Physics 207 – Lecture 4 Physics...

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