MECHANICS, UNITS, NUMERICAL CALCULATIONS & GENERAL PROCEDURE FOR ANALYSIS

In-Class activities:

• Reading Quiz

• What is Mechanics

• System of Units

• Numerical Calculations

• Concept Quiz

• Problem-Solving Strategy

• Attention Quiz

Today’s Objectives:

Students will be able to:

a) Explain mechanics / statics.

b) Work with two types of units.

c) Round the final answer appropriately.

d) Apply problem-solving strategies.

Some Important Points

• Studio course (combined lesson & problem session)

• Sessions do not require laptops• Important tools: syllabus, textbook (listed in

syllabus), pencil and paper, Web site of course• Website: http://lms.rpi.edu/• http://www.rpi.edu/dept/core-eng/

WWW/IEA for back exams

Course format• Mini lectures• In class activities• 3 mid term exams: 3x15% = 50% *

*Highest exam will be worth 20%• 1 final exam: 25%• Assigned problems:

HW: 20%CA: 5%

WHAT IS MECHANICS?

Study of what happens to a “thing” (the technical name is “BODY”) when FORCES are applied to it.

Either the body or the forces can be large or small.

BRANCHES OF MECHANICS

S t a t i c s D y n a m i c s

R i g i d B o d i e s( T h i n g s t h a t d o n o t c h a n g e s h a p e )

D e f o r m a b l e B o d i e s( T h i n g s t h a t d o c h a n g e s h a p e )

I n c o m p r e s s i b l e C o m p r e s s i b l e

F l u i d s

M e c h a n i c s

UNITS OF MEASUREMENT (Section 1.3)

Four fundamental physical quantities (or dimensions).

• Length

• Mass

• Time

• Force

Newton’s 2nd Law relates them: F = m * a

We use this equation to develop systems of units.

Units are arbitrary names we give to the physical quantities.

UNIT SYSTEMS

Force, mass, time and acceleration are related by Newton’s2nd law. Three of these are assigned units (called base units)and the fourth unit is derived. Which one is derived varies bythe system of units.

We will work with two unit systems in statics:

• International System (SI)

• U.S. Customary (USCS)

Table 1-1 in the textbook summarizes these unit systems.

COMMON CONVERSION FACTORS

Work problems in the units given unless otherwise instructed!

THE INTERNATIONAL SYSTEM OF UNITS (Section 1.4)

• No plurals (e.g., m = 5 kg, not kgs )

• Separate units with a • (e.g., meter second = m • s )

• Most symbols are in lowercase.

• Some exceptions are N, Pa, M and G.

• Exponential powers apply to units, e.g., cm • cm = cm2

• Compound prefixes should not be used.

• Table 1-3 in the textbook shows prefixes used in the SI system

NUMERICAL CALCULATIONS (Section 1.5)

Must have dimensional “homogeneity.” Dimensions have to be the same on both sides of the equal sign, (e.g. distance = speed time.)

Be consistent when rounding off.

- greater than 5, round up (3528 3530)

- smaller than 5, round down (0.03521 0.0352)

- equal to 5, see your textbook for an explanation.

Use an appropriate number of significant figures (3 for answer, at least 4 for intermediate calculations). Why?

PROBLEM SOLVING STRATEGY IPE: A 3 Step Approach

1. Interpret: Read carefully and determine what is given and what is to be found/ delivered. Ask, if not clear. If necessary, make assumptions and indicate them.

2. Plan: Think about major steps (or a road map) that you will take to solve a given problem. Think of alternative/creative solutions and choose the best one.

3. Execute: Carry out your steps. Use appropriate diagrams and equations. Estimate your answers. Avoid simple calculation mistakes. Reflect on and then revise your work, if necessary.

Scalar and vectors

• A scalar quantity is completely described by a magnitude (number).

-Examples: mass, density, length, speed, time, temperature.

• A vector quantity has a magnitude and direction and obeys the parallelogram law of addition.

-Examples: force, moment, velocity, acceleration.

Vector

Direction of arrow direction of vector

Length of arrow magnitude of vector

Initial point

Terminal point

The sum of two vectors – geometrical representation

• Two vectors can be added vectorially using the parallelogram law.

R

F1

F2

•Position vector F1 so that its initial point coincides with the initial point of F2. The vector F1+F2 is represented by the vector R.

Vectors in rectangular coordinate systems- two dimensional

(v1,v2)

x

y

(v1,v2) are the terminal points of vector

V = v1 i + v2 j

V

V

The sum of two vectors – analytic representation (two dimensional )

x

y

v (v1,v2)

(w1,w2)

w

w1v1

w2

v2

(v1+w1,v2+w2)

v + w = (v1 + w1, v2 + w2)

v + w = (v1 + w1 )i + (v2 + w2 ) j

The sum of two vectors – rectangular components (Three dimensional )

z

x

y

(a1,a2,a3)

(b1,b2,b3)

a

b

a + b = (a1 + b1, a2 + b2, a3 + b3)

a + b = (a1 + b1 )i + (a2 + b2 ) j + (a3 + b3 ) k

Vectors with initial point not at the origin

P1(x1 ,y1 ,z1)

vw

y

z

x

P2(x2 ,y2 ,z2)

w + P1P2 = vP1P2 = v – w = (x2i + y2j + z2k) – (x1i + y1j+ z1k) = (x2-x1) i + (y2-y1) j + (z2-z1) k

ExampleFind the components of the vector having initial point P1 and terminal point P2

P1(-1,0,2), P2(0,-1,0)

Solution:

V = (0 + 1, -1 - 0, 0 - 2) = (1,-1,-2)

READING QUIZ

1. The subject of mechanics deals with what happens to a body when ______ is / are applied to it.

A) a magnetic field B) heat C) forces

D) neutrons E) lasers

2. ________________ still remains the basis of most of today’s engineering sciences.

A) Newtonian Mechanics B) Relativistic Mechanics

C) Greek Mechanics C) Euclidean Mechanics

Class Assignment

Find the components of the vector having initial point P1 and terminal point P2

P1(3, -2, 5), P2(-1, -3, 8)

 ENGR-110 (IEA)

Fall-2015

CA 1 Solution

Find the components of the vector having initial point P1 and

terminal point P2:

P1 (3, -2, 5), P2 (-1, -3, 8)

P1P2 = (-1, -3, 8) - (3, -2, 5)

= (-4, -1, 3)