TUTORIAL 1

Mechanics

Mechanics

Statics

Dynamics-Equilibrium

-Selected Topics

Kinematics Kinetics

-Particles

-Rigid Bodies

-Particles

- Rigid Bodies

A branch of physical science which deals with ( the states of rest or motion of ) bodies under action of forces

Dynamics: Motion of bodies

Statics:

Equilibrium of bodies

(no accelerated motion)

under action of Forces

Basic Concept - Definition

Particle: Body of negligible dimensions

Rigid body: Body with negligible deformations

Non-rigid body: Body which can deform

In Statics, bodies are considered rigid unless stated otherwise.

Before considering whether the body can be assumed rigid-body or not,

you need to estimate the relevant force first.

SCALARS AND VECTORS

Scalars: associated with “Magnitude” alone

Vectors: associated with “Magnitude” and “Direction”

- mass, density, volume, time, energy, …

- force, displacement, velocity, acceleration, …

: Direction

or V| |V

Magnitude:

V or V

Vector :

THE PARALLELOGRAM LAW

The two vectors V1 and V2 ,treated as free vectors, can be replaced by their equivalent V, which is the diagonal of the parallelogram formed by V1 and V2 as its two sides.

2V

1V1V

2V V

1 2V V V

1V2V

V

1 2(generally )V V V

Note: If there are not free vectors, you can sum them if and only if they have the same point of the application.

Summation of Force

1F

2F1 2F F

1F

2F

1F

2F 1 2F F

if there are sliding vectors

concurrent forces

non-concurrent

Trigonometry Functions Of A Right-Angle Triangle

sine = opposite side = o = cosine hypotenuse h

cosine = adjacent side = a = sine hypotenuse h

tangent = opposite side = oadjacent side a

tangent = sin cos

ho

a

Sine And Cosine Rules

For triangles that are not right-angle, the following two laws are important in vector algebra introduced in chapter two later:

Sine Rule a = b = csin sin sin

Cosine Rule a2 = b2 + c2 – 2bc cos

b2 = a2 + c2 – 2ac cos

c2 = a2 + b2 – 2ab cos

Example 3

Find the length of the unknown side a and the angle .

200

6m 4m

a

Cosine rule : a2 = b2+c2-2bccos

i.e. a2 = 62+42-2x6x4cos200

a = 2.63m

Sine rule : 2.63 = 6sin 200 sin

= 6.9

= 36 +16-6x4xcos200

= 51.30sine = 6 x sin 200

2.63

Geometry

Some of the basic rules are shown below:

Sum of supplementary angles = 180 0

+ = 180 0

A straight line intersecting two parallel lines

= , =

= , =

Similar triangles ABC and ADE, by proportion

B

C

AB = BC = ACAD DE AE

Hence if AB = 6, AD = 3 and BC = 4, Then,

6 = 43 DE

DE = (3 x 4)6 = 2

D

AE

NEWTON’S LAWS OF MOTION (1st Law)

The study of rigid body mechanics is formulated on the basis of Newton’s laws of motion.

0F

First Law:An object at rest tends to stay at rest and an object in motiontends to stay in motion with the same speed and in the same direction, unless acted upon by an unbalanced force.

Question 1

Answer

Question 2

Answer

Question 3

Answer

Question 4

Answer