Answers: 1. C 2. D READING QUIZ 1. Which one of the following is a scalar quantity? A) Force B) Position C) Mass D) Velocity 2. For vector addition you have to use ______ law. A) Newton’s Second B) the arithmetic C) Pascal’s D) the parallelogram Answers: 1. C 2. D Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

SCALARS AND VECTORS (Section 2.1) Scalars Vectors Examples: mass, volume force, velocity Characteristics: It has a magnitude It has a magnitude (positive or negative) and direction Addition rule: Simple arithmetic Parallelogram law Special Notation: None Bold font, a line, an arrow or a “carrot” In the PowerPoint presentation vector quantity is represented Like this (in bold, italics, and yellow). Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Triangle method (always ‘tip to tail’): How do you subtract a vector? How can you add more than two concurrent vectors graphically ? Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

TOOLS FOR COMPUTATION: THE SINE LAW AND THE COSINE LAW

RESOLUTION OF A VECTOR “Resolution” of a vector is breaking up a vector into components. It is kind of like using the parallelogram law in reverse. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

Answers: 1. C 2. A CONCEPT QUIZ 1. Can you resolve a 2-D vector along two directions, which are not at 90° to each other? A) Yes, but not uniquely. B) No. C) Yes, uniquely. 2. Can you resolve a 2-D vector along three directions (say at 0, 60, and 120°)? A) Yes, but not uniquely. B) No. C) Yes, uniquely. Answers: 1. C 2. A Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

EXAMPLE 1 Find the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. Plan: Sketch the system and show vector addition using the parallelogram law. Sketch a triangle showing head-to-tail addition. Apply trig to find the missing information. Apply the results to the original diagram to solve the problem. Perform a check calculation. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

Resolve the force F2 into components acting along the u and v axes. EXAMPLE 2 Resolve the force F2 into components acting along the u and v axes. Plan: Sketch the system and show the components using the parallelogram law. Sketch a triangle showing head-to-tail addition. Apply trig to find the missing information. Apply the results to the original diagram to solve the problem. Perform a check calculation. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

EXERCISE 1 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured clockwise from the positive u axis. Plan: Sketch the system and show vector addition using the parallelogram law. Sketch a triangle showing head-to-tail addition. Apply trig to find the missing information. Apply the results to the original diagram to solve the problem. Perform a check calculation. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

EXERCISE 2 2-15: Resolve the force F1 into components acting along the u and v axes. 2-16: Resolve the force F2 into components acting along the u and v axes. Plan: Sketch the system and show the components using the parallelogram law. Sketch a triangle showing head-to-tail addition. Apply trig to find the missing information. Apply the results to the original diagram to solve the problem. Perform a check calculation. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

Example 1: FR = 72.1 lb, θ = 73.9° (measured CCW from +x axis) ANSWERS Example 1:  FR = 72.1 lb, θ = 73.9° (measured CCW from +x axis) Example 2:  F2u = 86.6 lb, F2v = -50.0 lb Exercise 1:  FR = 605 N, θ = 85.4° (measured CW from +u axis) Exercise 2:  F1u = 183 N, F1v = 129 N, F2u = 150 N, F2v = 77.6 N Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4