Shaokoon Cheng, PhDEmail: Shaokoon.cheng@mq.edu.au

Tel: 98509063Office: E6A, Rm 223

Consultation time: 2pm to 5pm (Tuesday)Text book (non-mandatory): Engineering Mechanics. Statics. J.L. Meriam and L.G. KraigePre-requisite: Trigonometry, Vectors.

What are you required to do?1. Asterisk on slides. 2. Fill in the blanks. 3. Bring along your scientific calculator. 4. Test date 30th August 2013 (1 hour). 10% of overall mark. 5. Assignment 18th October 2013. Questions to be released on 25th September 2013.6. Give answers in two decimal places.

Engineering mechanicsLecture 1

Engineering mechanics Forces Force vectors Moment of forces Forces in members of structures and machines

OverviewLecture 1

Mechanics the physical science which deals with the effects of forces on objects.

The principles of mechanics are central to research and development in the fields of stability and strength of structures and machines, robotics, fluid flow, molecular, atomic, and sub- atomic behavior.

MechanicsLecture 1

Mechanical design. Cranes Remote controls Aeroplanes

MechanicsLecture 1

Wright.nasa.gov

Analyze failure mechanisms. Minneapolis I-35W bridge (2007)

(Undersized gusset plates, increase concrete surfacing load).

MechanicsLecture 1

Force

Science.

Mechanics

ForceForce

Stretching of red blood cells using optical tweezers.

ForceForce

Elucidating disease mechanismsEg. Malaria mosquito borne infectious disease. Year 2010, 2000 deaths per day.

Lecture 1

Work, health and safety

Mechanics

Reference: www.redbubble.com

Lecture 1

MechanicsMechanics

____________________

__________

Fluid mechanics

StaticsDynamics

Rigid body: A body is considered rigid when the change in distance between any two of its points is negligible.

Statics deals primarily with the calculation of external forces which act on rigid bodies in equilibrium. Determination of the internal deformations belongs to the study of the mechanics of deformable bodies.

Statics: study that concerns the __________ of bodies under action of forces.

Lecture 1

Statics

Force: ________" or ________" exerted by one body on another. Characterized by its ____________, _________, and point of application.

Eg: Gravity (weight), Tension, Compression, Friction

Length: Describe the size of a physical system in space.

Mass: Mass is defined as the quantity of matter in a body. Mass is a measure of the inertia of a body, which is its resistance to a change of velocity. The mass of a body affects the gravitational attraction force between it and other bodies.

Time: Principles of statics are generally time independent. This quantity plays an important role in the study of _______________.

Fundamental concepts

Lecture 1

Statics *

Force: Newtons (N)Length: Metres (m)Mass: Kilograms (Kg)Friction: Newtons (N)

SI units

0.000 000 001=10-9 - n (nano)0.000 001=10-6 - (micro)0.001=10-3 - m (milli)1000=103 - k (kilo)1 000 000=106 - M (mega)1 000 000 000=109 - G (giga)

Lecture 1

Newton's Laws

F1

F2 F3

F4

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Force vectors

F = mutual force of attraction between 2 particlesG = universal constant known as the constant of gravitationM, m = masses of the 2 particlesr = distance between the 2 particles

Newtons law of gravitation

2r

MmGF =

r

M

m

F-F

Two particles of mass M and m are mutually with equal and opposite forces.

Lecture 1

StaticsNewtons law of gravitation

Reference: Engineering Mechanics. Statics. J.L. Meriam and L.G. Kraige

Lecture 1

StaticsNewtons law of gravitation

2r

GMg =

MgrG

2

= 2r

MmGF =

= 2

2

r

MmMgrF

F = mg

W = mgWeight is the gravitational force acting on a mass. Weight mass

Lecture 1

ExampleLecture 1

Force vectors

A scalar is any physical quantity that can be completely specified by its _________________.Eg: time, mass.

A vector is any physical quantity that requires both a magnitude anddirection for its ___________________ .

A vector is shown graphically by an arrow.

The head of the arrow indicates the sense of direction of the vector.

For handwritten work, it is often convenient to denote a vectorquantity by simply drawing an arrow on top it.

In print, vector quantities are represented by bold face letters such as A, and its magnitude of the vector is italicized, Eg: 4V

Scalar and Vectors

V

Lecture 1

Force vectors*Vectors operationOperations - Eg: +, -, x, /

5 kg 5 kg 10 kg

1) Multiplication and division of vector by a scalar. If a vector is multiplied by a positive scalar, its magnitude is increasedby that amount. When multiplied by a negative scalar it will alsochange the _______________sense of the vector.

A2A

A

- 0.5 A

Lecture 1

Force vectors*Vectors operation2) Vectors addition

Vectors must obey the _________________ law of combination.

A B R=+

A

B

RA

A B

R

R

B

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Force vectors*Vectors operation3) Vectors subtraction

Vectors must obey the parallelogram law of combination.

A B R=-

A

-B

B

R

AB

R

Lecture 1

Force (vectors)Importance of interpreting force as vectors1) Finding resultant force.

Picture frameR

F1 F2 R=+

Lecture 1

Force (vectors) *Importance of interpreting force as vectors2) Finding components of a force.

RA

B

A

B

A

B

R R R

F1

F2

Lecture 1

ExampleLecture 1

RevisionTrigonometry

COS = A/H A = H COS

SIN = O/H O = H SIN

Lecture 1

RevisionTrigonometry

Lecture 1

30 o 10

x

X =

20o

8

x

X =

25o8

x

X =

30 o 10

x

X =

20o

8

x

X =

25o8

x

X =

RevisionTrigonometry

Lecture 1

RevisionTrigonometry

Lecture 1

ExampleFind the resultant force

SolutionsLecture 1

ExampleFind the resultant force

250 N

150 N150 N

Solutions

120o

R

60O

250 N

150 N150 N

R

60O

Cosine rulea2 = b2 + c2 2bc COS AR2 = 1502 + 2502 2(250)(150) COS 60oR = 217.94 N

Sine ruleSIN A

a =

SIN Bb

SIN 60o=

SIN x150217.94

= 81.59 o

x

x = 36.59 o

Lecture 1

ExampleFind the angle if the resultant force is directed horizontally to the right.

Solutions

8 kN

6 kN

50o

6 kN

50o

Sine rule

SIN Aa =

SIN Bb

SIN 50o=

SIN x68

xo

X = 35o

= 55o

Lecture 1

Statics

When dealing with the mechanics of a __________ body, we ignore deformations in the body and concern ourselves with only the net external effects of external forces.

For example, the force P acting on the rigid body may be applied at A or at B or at any other point on its LINE OF ACTION.

Principle of transmissibility

Rigid body

Lecture 1

Example

Fa

Fb

950N20o

50o50o

110o

Lecture 1

RevisionTrigonometry

Lecture 1