Lecture Notes for Sections 1_1-1_6_2.pdf

Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6 1

Chapter 1 – General Principles

Objectives: •  An intro to basic quantities & idealizations •  Statement of Newton’s Law of Motion and Gravitation •  Review SI System of Units •  Examine procedures for Numerical Analysis •  A general guide for problem solving

1.1 Mechanics

•  Branch of physical sciences concerned with the state of rest or motion of bodies subjected to forces


Mechanics

R. B. Mechanics

Mechanics of Deformable Bodies

Fluid Mechanics

•  required for other types of mechanics •  Useful for design/analysis of:

– Structural members – Mechanical components – Electrical devices

R.B. Mechanics


R. B. Mechanics

Statics Dynamics

•  Equilibrium of bodies at rest of moving with constant velocity

a = 0

Statics

•  Accelerated motion of bodies

a ≠0

Dynamics


•  Long history •  Derived from measurements of:

– Geometry – Force

History

•  Archimedes (287-212 BC) – Levers, pulley, inclined plane, wrench – Building construction

•  Galileo Galilei (1564-1642) – Pendulums, falling bodies – Dynamics: accurate measurement of time

History


•  Issac Newton (1642-1727) – 3 fundamentals laws of motion – Universal gravitational attraction

•  Applications of Newton’s Laws: – Euler – D’Alembert – Lagrane – etc

History

•  Basic Quantities – Length

•  Locate position of point in space • Describe size of physical system • Define standard unit of length

– Time • A succession of events • Not important in Statics •  Important for Dynamics

1.2 Fundamental Concepts


•  Basic Quantities – Mass

• A measure of a quantity of matter • Effects gravitational attraction between 2

bodies • A measure of resistance to change (Δ) in

velocity

•  Basic Quantities – Force

• A “push” or “pull” exerted by one body on another

• Direct contact, or • Acting over a distance

–  e.g. gravitational, magnetic, electrical forces

• Characterized by: – Magnitude –  Directions –  Point of Application

VECTOR!


•  Idealizations – Particle

• Has mass, but we neglect size/shape • Problem becomes much simpler

– Rigid Body (R.B.) • A collection of many particles, fixed relative to

one anther • Do not need to consider material properties • Deformations from applied forces sufficiently

small to consider rigid

•  Idealizations – Concentrated Force

• Effect of loads assumed to act on a point • Good idealization if area of application is small

compared to body


•  Newton’s Three Laws of Motion – Apply to motion of a particle measured

from a nonaccelerating (Newtonian) reference frame

– 1st Law – a particle at rest or moving in a straight line with constant velocity tends to remain in this state if not subjected to an unbalanced force

F1

F3

F2 v ΣF=0

•  Newton’s Three Laws of Motion – 2nd Law – a particle acted upon by an

unbalanced force F experiences an acceleration a in the same direction as F and proportional to the magnitude of F - |F|

F

a

ΣF=ma Accelerated motion!


•  Newton’s Three Laws of Motion – 3rd Law – the mutual forces of action and

reaction between two particles are equal, opposite and collinear

F

Action-reaction A B

F

For every action, there is an equal and

opposite reaction

•  Newton’s Law of Gravitational Attraction – Gravitation attraction between any 2

particles

F m1 m2

r

F


•  Weight – consider m1 = m as a particle relative to the Earth m2 = Me

Set

•  g depends on elevation •  For most problems we assume sea level

g is the acceleration due to gravity

1.3 Units

•  Given length, time, mass and force we consider how they are related – Remember Newton’s 2nd Law F=ma – Three are selected as base units – The fourth is derived from F=ma


SI Units – International system (metric)

Length Time Mass Force meter second kilogram Newton m s kg N

1 N = force required to give 1 kg mass an acceleration of 1 m/s2

Weight in N, W=mg (g=9.81 m/s2)

SI Units – US Customary (FPS)

Length Time Mass Force foot second slug pound ft s slug lb

1 slug= amount of matter accelerated 1 ft/s2 when acted upon by a force of 1 lb

Mass m = W/g , (g=32.2 ft/s2)


Conversion of Units (SI FPS)

Force 1 lb = 4.448 N Mass 1 slug = 14.59 kg Length 1 ft = 0.3048 m

1.4 SI System - Prefixes

103 kilo k 106 Mega M 109 Giga G

10-3 milli m 10-6 micro μ 10-9 nano n


Rules for use

•  Use dot () for compound units

•  Exponential on unit w/ prefix refers to both

•  Avoid prefix in denominator (except for kg)

Rules for use

•  Represent numbers in base or derived units converting all prefixes to powers of 10

or


1.5 Numerical Calculations

•  Dimensional Homogeneity – an equation must be dimensionally

consistent

•  Significant Figures 4981 --- 4 significant digits What about 23400 ?

We use engineering notation (multiples of 103 and 10-3)

5 sig digits 23.400 X 103

3 sig digits 23.4 X 103

3, 4, or 5?


•  Rounding 3.5587 rounded to 3 digits 3.56

> 5 round up; < 5 round as is;

= 5 round up if odd / not rounded if even

•  Calculations •  Do not round off until final result •  In text generally round to 3 sig digits

1.6 General Procedure – Problem Solving

•  YOU LEARN BY SOLVING PROBLEMS!! •  Show your Work!

– Clear, logical, orderly

•  Read problem carefully; correlate to actual physical situation

•  Document problem date; draw necessary diagrams

•  Apply relevant principles (in mathematical form)


1.6 General Procedure – Problem Solving

•  Check dimensional consistency/homogeneity

•  Solve equations; answer with no more than 3 sig digits

•  Check answer – does it make sense???

READING QUIZ

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

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


CONCEPT QUIZ

1. Evaluate the situation, in which mass (kg), force (N), and length (m) are the base units and recommend a solution.

A) A new system of units will have to be formulated.

B) Only the unit of time have to be changed from second to

something else.

C) No changes are required.

D) The above situation is not feasible.

CONCEPT QUIZ

(continued)

2. Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations.

A) Historically slide rules could not handle more than three significant figures.

B) Three significant figures gives better than one-percent accuracy.

C) Telephone systems designed by engineers have area codes consisting of three figures.

D) Most of the original data used in engineering calculations do not have accuracy better than one percent.


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 / revise your work.

ATTENTION QUIZ

2. In three step IPE approach to problem solving, what does P stand for?

A) Position B) Plan C) Problem

D) Practical E) Possible

1. For a static’s problem your calculations show the final answer as 12345.6 N. What will you write as your final answer?

A) 12345.6 N B) 12.3456 kN C) 12 kN

D) 12.3 kN E) 123 kN

Documents

Lecture Notes for Sections 1_1-1_6_2.pdf