Physics and Engineering Sciences

Physics and Engineering Sciences

(Part 2)

Units of Measure

Chapter 2

United States Measurement

Systems • International System of Units (SI) – Metric

• U.S. Customary System

T 2-1

SI Base Units

T 2-3

Metric Values

T 2-6

U.S. Customary System

T 2-7

U.S. Customary System

Conversions

Light

Chapter 3

Electromagnetic Radiation

• Light is electromagnetic radiation

• Light is that portion that is visible to the

human eye

Light

F 3-1 Electromagnetic Spectrum

• The product of the wavelength and frequency of light is

equal to its speed:

• C = v

• Where c is the speed of light in a vacuum in m/s, is the

wavelength in m, and v is the frequency in cycles per

second or hz.

F 3-2 Sensitivity of the eye to light

Ray Theory

• A ray of light is a straight path that the

light travels in from one point to another

• Two basic types: 1. Reflection

2. Refraction

Reflection

F 3-3 Reflected light

Refraction

F 3-4 Light refracted

T 3-1

Material

Air 1.00

Water 1.33

Fused Quartz 1.46

Flint Glass 1.66

Diamond 2.42

Various indices of refraction

1 2

2 1

2

12

2

sin

sin

sin 45 1.33

sin 1.00

.707sin

1.33

32

F 3-5 Light refracted

Sound

Chapter 4

Sound

• Sound is the transmission of mechanical

waves in matter

• Sound can only be transmitted through

matter and cannot be transmitted in a

vacuum

Wave Nature of Sound

• Sound is comprised of longitudinal

mechanical waves traveling through matter

• Sound waves are generated by the

successive compression and rarefaction of

the media that is transmitting it

Sound

F 4-1 Generation of sound waves

Intensity of Sound

The intensity of sound P is a measure of the

energy that it transmits. Intensity is defined

as:

I INTENSITYSurface Area

Power

Area

Energy

Time

Relative Intensity

2

12 2

Relative Intensity (dB) = 10log

where,

actual intensity( / )

10 /

o

o

I

I

I w m

I w m

Frequency of Sound

• The frequency of sound is normally referred

to as its pitch. Pitch describes the audible

effect that a frequency of sound waves has

on the human ear. Pitch is normally

measured in hertz (Hz) or cycles/second.

Sound

pitchrev

s

holes cycles

rev

cycles

sHz

12001

60

48

960 960

min

min ( )

Ex 4.3.1

Typical Sound Intensities

Sound Type Intensity

W/m2 dB

Jet Aircraft (close range) 1 120

Jackhammer 10-2 100

Automobile on Highway 10-4 80

Normal Speech 10-6 60

Whisper 10-10 20

F 4-2 Response of average human ear to sound at different frequencies

Response of The Human Ear to Sound

Electricity/Electronics

Chapter 5

Electricity/Electronics

• Electricity and electronics are interrelated

phenomena. They are involved in the

generation, transmission, and storage of

power in numerous applications.

Electrical Circuits

• Electrical circuits contain a source of

electrical power, passive components which

dissipate or store energy, and active

components which change the form of

electrical power.

Electrical Currents

• Direct current (DC) - current and voltage

does not vary with time

• Alternating current (AC) - current and

voltage varies (usually sinusoidally) with

respect to time

Electrical Quantities

Charge (Q) Electrical charge is an energy carrying quantity

that is measured in units of coulombs.

Current (I) Electrical current is the time rate of flow of

charge past a point in a circuit and is measured

in Amperes.

Voltage (V) Voltage is the change in energy per unit charge.

The unit of measure is the volt.

Energy (W) Electrical energy is the capacity to do

work. Energy is measured in joules.

Power (P) Electric power is the time rate of energy

flow. Electrical power is measured in

watts.

Resistance () Resistors are energy absorbing com-

ponents. Resistance is measured in ohms.

Circuit Components

• Resistors are energy absorbing elements

• Inductors are energy storing components where energy is

stored in a magnetic field

• Capacitors are energy storing components where energy is

stored in an electrical field

F 5-2 Parallel and series connections

Circuit Connections

Circuit Rules

Ohm’s Law

E = IR

I = E/R

R = E/I

R R R R

R

1 2 3

21 5 4

75

. .

.

1 1 1

13

17

21

1 2R R R

R

.

30+

-

V

Calculate Equivalent Resistance

30+

-

V

IER

I

I A

3075

4

.

Calculate Equivalent Resistance

R R R

R

1 2

5 19

24

1 1 1

124

18

6

1 2R R R

R

Calculate Equivalent Resistance

R R R

R

1 2

6 15

21

1 1 1

121

19

63

1 2R R R

R

.

Calculate Equivalent Resistance

Calculate Equivalent Resistance

R R R R

R

1 2 3

63 2 2

85

. .

.

IER

I A

1785

2

.

F 5-3 Parallel and series connections of various components

Circuit Analysis Using

Kirchoff’s Laws • Kirchoff’s Loop Rule (KLR) is a statement of

conservation of energy. It states that the sum of

voltage rises or drops around a closed path or loop

must be zero.

• Kirchoff’s Point Rule (KPR) is a statement of

conservation of charge. It states that the flow of

charges (current) into or out of a point (junction of

electrical connections) must add to zero.

Statics

Chapter 6

• Analysis of mechanical equilibrium of rigid bodies subjected to force systems

• Analysis is restricted to bodies at rest

Statics

Statics

F 6-1 Transmissibility of forces

F 6-2 Resultant of two forces

F 6-3 Reaction to an applied force

F 6-4 Rectangular components of a force

Given: Three Forces: F1, F2, F3

Find: Resultant and Force

F 6-5 Forces applied to an eyebolt

tan

R

R

y

x

150

73

64

R

R

73 150

167

2 2

• A moment is the tendency to rotate that a force imparts to a rigid body

• The magnitude of the moment is the product of the magnitude of force and the perpendicular distance between the line of action of the force and the point or axis of rotation

Moment of Force

F 6-6 Moment of a force about a point

Moment of Force

• A couple is formed when two forces of

equal magnitude and opposite sense

with parallel lines of action

Force Couples

F 6-7 A couple resulting from a system of forces

Force Couples

• Isolate the body from the ground of any bodies in contact with it

• Indicate all external forces acting on a body

• Identify the magnitude and direction of reactions from the ground or other bodies in contact by the application of Newton’s First Law

Free-Body Diagram

Procedure

F 6-8 Simple supported beam and corresponding free-body diagram

Free-Body Diagrams

• The force of friction acts opposite to the direction of any impending motion that would result from an applied force

• To overcome friction and cause a body to move, a force F must be applied that is greater than or equal to force of friction

• F = uN

• u = coefficient of friction and N = the normal force

Friction

F 6-11 Conditions for frictional forces

Friction

Dynamics

Chapter 7

• Kinematics: the study of the motion of particles

and bodies.

• Kinetics: the study of the forces and moments

required to induce motion.

Dynamics (Bodies in Motion)

An automobile skids to a stop in 200 ft. after its brakes are

applied when it was moving at 60 miles per hour. Find the

acceleration in units of ft/s2, assuming the deceleration is

constant.

Solution: The initial velocity must be put in appropriate units.

vmiles

hour

hour

s

ft

mile0

60 1

3600

5280

Rectilinear Motion

The following equation of rectilinear motion will be applied:

v v as2

0

2 2

If the final velocity is taken as zero, this equation can be

algebraically rearranged to yield:

av

s

ft

s 0

2 2

2

88

2 20019 4 2

( )( ).

The negative sign indicates that the vehicle is decelerating.

F 7-1 Angular Motion

Angular Motion

Work is defined as the product of an applied force,

F, and the distance over which the force is applied,

s. For a constant force, this relation is given by:

W = F · s

Energy Methods

Energy

For a body in linear motion, this is given by:

KE mv1

2

2

For a body in angular motion, this is given by:

KE I1

2

2

Kinetic Energy

Strength of Materials

Chapter 8

Strength of Materials

• Strength of materials is the study of

deformable bodies subject to applied

forces and moments.

Issues: Strength of Materials

• How much load can be safely applied to a

structure or component?

• What material should be chosen to fabricate a

component to safely withstand a particular load?

• How much will a component deflect under load?

Stress/Strain Loading

• Axial Loading: If an object is subjected to a

positive strain in one direction, it is normal for the

object to contract or experience a negative strain

in another direction.

• Torsional Loading: Shafts and other machine

elements that are subjected to equilibrating

couples at each end (torque) are in torsion.

Stress/Strain Loading

• Beam Loading: Beams are machine elements

that are typically much longer than they are wide

and are loaded in a direction that is perpendicular

to their long dimension.

• Column Loading: A column is a long slender

member that is loaded axially in compression.

Tension

Compression

Shear

Rivet Under Shear Stress

LOAD FORCE ON A STEEL BEAM

LOAD

FORCE

STRAIN

PERMANENT DEFORMATION

ELASTICITY

Combination of Forces on a

Structural Member

Torsional Load

F 8-4 Shaft loaded in torsion

Torsional Loading

F 8-5 Steel rod in torsion

Torsional Loading

Thermodynamics and

Heat Transfer Chapter 9

Thermodynamics

and

Heat Transfer

•The thermal properties of matter are

controlled by temperature

•Temperature is a measure of the

tendency of an object to absorb or

dissipate energy in the form of heat

Kº = Cº + 273º

Cº = 5/9 (Fº - 32º)

Fº = 9/5 Cº + 32º

Temperature Conversions

Thermal Expansion

• The dimensions of most solid materials will

expand and contract with increasing and

decreasing temperatures. The change in a linear

dimension, such as length or diameter, is

proportional to the change in temperature of the of

the object T, its length L and a constant , the

coefficient of expansion.

F 9-2 Expansion by increase of temperature

Expansion of an Object

FD a D TxF

in F

in

FHGG

IKJJ

6106 10

2 000 230

005

..

.

b ge j

A brass sheet has a 2.000 inch diameter hole at 70F. The sheet is

heated to 300F. Find the new diameter of the hole.

The change in diameter can be found as:

**Therefore, the new diameter is 2.005 in.**

Material (m/m/C = 1 / C)

Glass 9 x 10 -6

Concrete 10 x 10 -6

Iron 12 x 10 -6

Brass 19 x 10 -6

Aluminum 25 x 10 -6

Coefficients of Expansion

T 9-1

Heat Capacity

• The heat capacity of a material defines the amount

of energy that is needed to change its temperature.

The temperature change that will occur with a

given amount of energy.

Heat Units

• Calorie (cal)

– The amount of heat required to raise the temperature of one gram of water by one degree Celsius.

• British Thermal Unit (BTU)

– The amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.

Heat Units

Laws of Thermodynamics

1. Energy can neither be created or destroyed; the sum total of all

energy remains constant.

Q = U + W

Q - quantity of heat

U - change in internal energy

W - the work performed.

F 9-3 The first law of thermodynamics

Thermodynamics

2. Conversion of heat to work is limited by the temperature at

which conversion occurs.

Wout = QH - QL

QL - Quantity of heat from cold object.

QH - Quantity of heat from hot object.

F 9-4 Thermodynamic cycles

Thermodynamics

Heat Transfer

• Conduction: Energy transfer from a high temperature

region to a low temperature region through a solid object.

• Convection: Energy transfer from a surface by the flow

of a fluid over an object.

• Radiation: Electromagnetic radiation carries energy

from one body to another.

F 9-5 Heat transfer by conduction

Heat Transfer

F 9-6 Heat transfer by convection

Heat Transfer

Fluid Power

Chapter 10

Fluid Dynamics

• Study of the flow of fluids:

– Velocity

– Pressure

– Force

That cause fluids to move

Density, , is the ratio of mass, m, to volume, V, of a

substance.

m

V

Specific Volume, , is the volume occupied by a unit mass of

substance.

1

Fluid Properties

Specific Weight, , is the force of gravity on a mass per unit

volume.

g

Specific Gravity, S, is the ratio of the density of substance to

the density of water.

SH O

2

H O

g

cm231

F 10-1 Pressure definitions

Pressure

Atmospheric Pressure at

Sea Level

14.7 lb/in2

29.92 in. of Hg

76 cm of Hg

1.013 x 105 N/m2

Pa = N/m2

F 10-2 Pascal’s law

Pressurized Fluid in a

Sealed System

Principles of

Fluid Dynamics

Conservation of mass is described by the continuity

equation:

A1v1 = A2v2

where A is the area that the fluid flows through, v is the

velocity of the fluid and the subscripts refer to the point

here the fluid enters and exits the system.

Conservation of energy is described by the energy

equation, also known as the Bernoulli equation:

where p is the pressure of the fluid and z is the elevation of

the system relative to a datum. It will be assumed that

flow is steady state and incompressible with a uniform

velocity profile.

v

g

pz

v

g

pz1

2

11

2

2

22

2 2

Water flows through a 100 mm diameter pipe at 8 m/s.

Downstream, the pipe is reduced in diameter to 40mm. Find

the velocity of the water in the smaller diameter.

A v A v

dv

dv

v vd

dms

1 1 2 2

1

2

12

2

2

2 11

2

2

2

2

2

4 4

8100

4050