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Chapter 1- 1

ME 100

Engineering Mechanics

Lecture 3

Monday 13 Feb 2012

School of Electrical Engineering

& Computer Sciences (SEECS)

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Chapter 1- 2

Revision

Statics.rest or constant velocity

Particle. Mass but insignificant size

Rigid body. No deformation under load

Concentrated force. .. acting at a pt

Mass & weight.

SI Sys. N is derived unit

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Chapter 1- 3

Revision

Prefixes. G, M, k, m, , n

Rules for use

Calc. Ans in 3 significant figures

Verification of dimensional homogeneity

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Chapter 1- 4

2FORCE

VECTORS

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Chapter 1- 5

2: Force Vectors

Addition of forces

Resolution of forces into components

Express forces in Cartesian vector form

Dot product

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Chapter 1- 6

2: Force Vectors

1. Which one of the following is a scalarquantity?

A) Force B) Position C) Mass

D) Velocity

2. For vector addition, you have to use______ law.

A) Newtons Second, B) the arithmetic

C) Pascals, D) the parallelogram

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Chapter 1- 7

2.1 Scalars and Vectors

Scalar. Magnitude only

Vector. Magnitude and direction

Graphically by arrow

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Chapter 1- 8

2.2 Vector Operations

Multiplication & Division.

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Chapter 1- 9

2.2 Vector Operations

Addition. Resultant vector; Parallelogramlaw

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Chapter 1- 10

2.2 Vector Operations

Addition. Resultant vector; Triangle-Rule

Collinear Vectors

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Chapter 1- 11

2.2 Vector Operations

Subtraction. Resultant vector

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Chapter 1- 12

2.2 Vector Operations

Resolution. Breaking up a vector intocomponents along references lines;

parallelogram law in reverse

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Chapter 1- 13

2.3 Vector Addition of Forces

Find Resultant force. Components given

Find Components. Resultant given

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Chapter 1- 14

2.3 Vector Addition of Forces

Find Resultant force. Components given

Find Components. Resultant given

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Chapter 1- 15

2.3 Vector Addition of Forces

Analysis for Resultant force.Parallelogram Law

Make sketch by placing the vectors

together at their tails Find resultant(parallelogram diagonal) Label all known and unknowns

Force magnitudes Angles

Identify the two unknowns

(Resultant magnitude & direction)

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Chapter 1- 16

2.3 Vector Addition of Forces

Analysis for Resultant force.Trigonometry

Redraw half portion of parallelogram

Find magnitude by law of cosines Find direction by law of sines

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Chapter 1- 17

2.3 Vector Addition of Forces

Analysis for Components.Parallelogram Law

Make sketch by placing the vectors

together at their tails Find components(parallelogram sides) Label all known and unknowns

Force magnitudes Angles

Identify the two unknowns(Component magnitudes)

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Chapter 1- 18

2.3 Vector Addition of Forces

Analysis for Components.Trigonometry

Redraw half portion of parallelogram

Find two magnitude by law of sines

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Chapter 1- 19

Example 1

Find resultant force

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Chapter 1- 20

Example 1

Find resultant force

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Chapter 1- 21

Example 2

Resolve into components

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Chapter 1- 22

Example 2

Resolve into components