Transcript
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
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