Transcript PHYSICAL CONCEPTS

PHYSICAL CONCEPTS
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Number issues
Physical Quantities
Force/Friction/Energy/Work, etc.
Simple harmonic motion
Vibration: Free and Forced
Impedance
Scientific Notation
• number between 1.00 and 9.99 times
10 raised to some power
• E.G.,
1492 becomes
1.492 x 103
• 1.492 is called the COEFFICIENT
Multiplying numbers in Sci. Not.
• Multiply coefficients
• sum powers of 10
• E.G.
2.3 x 102 x 4x103
= (2.3 x 4) x 10(2+3)
= 9.2 x 105
Dividing in Sci. Not.
• Divide Coefficients
• Subtract Powers of 10
• Read More About Exponents in
Appendix A
Quantities Come in 2 Flavors:
• Scalar Quantities
– magnitude only
• Vectorial or Vector Quantities
– magnitude AND direction
Scalar Quantities
• Have magnitude only
• Examples include Mass, Length,
Volume
• Can be added or subtracted directly
Vector Quantities
• Have BOTH magnitude and
direction
• Example: Velocity
• Combining Vectors is more
complicated
Basic Units
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Length
Time
Mass
(Charge)
Other Units may be
derived:
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Area = Length x Length (or L2)
Volume = L3
Speed = Length/Time
Acceleration = L/T2
Force: A push or a pull
• Force = Acceleration x mass
• Therefore Force = ML/T2
• MKS force unit is Newton = 1 kg
m/s2
• cgs unit is dyne = 1 g cm/s2
Force and Elasticity
• Hooke’s Law:
• Force = (-)spring constant times displacement
• Stress = force per unit area (aka pressure)
• Strain = change in length
• Stress = Elasticity x Strain
Final Comment on Elasticity
• Compliance is the inverse of Stiffness
• Greater compliance yields more
displacement per unit force
• Units: L/ML/T2
• (meters/newton, or cm/dyne)
Friction
• Energy converted into heat when molecules
rub against each other.
• To move an object, the applied force must
overcome friction.
• Effect of Friction is “Resistance”
Friction produces Resistance
• Resistance = ratio of Force to resulting velocity
(R = f/v)
• measured in Ohms
• Acoustically, we talk about the influence of
friction as DAMPING
Energy & Related Concepts
• WORK
• POTENTIAL AND KINETIC ENERGY
• POWER
WORK
• Force applied through a distance
• No motion--no work
• Work = force x distance = ML/T2 x L
• Units JOULE = 1 Newton Meter
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erg = 1 dyne cm
ENERGY COMES IN 2 FLAVORS
• Kinetic-- Energy of motion
• (Inertia can be thought of as the ability to
store kinetic energy)
• Potential--Energy of position
• (Elasticity --ability to store potential
energy)
POWER
• Rate at which work is done
• Work/Time
• Unit Watt = joule/second or 107 erg/sec
SIMPLE HARMONIC MOTION
• Vibration involves interplay of force,
inertia, elasticity, and friction
• Applying a force displaces object
• Overcoming inertia
• Traveling away from rest until ?
Simple Harmonic Motion 2
• Why does object stop and then move back
toward rest?
• Why doesn’t the object then stop at rest?
• Where is potential energy the greatest?
• Where is kinetic energy the greatest?
SHM 3
• Why does displacement decrease over time?
• RESISTANCE
• -- Energy is lost to HEAT through
FRICTION
SHM 4
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Amplitude --Displacement
Period-- Time taken to complete one cycle
Frequency--Number of Cycles per Second
Phase--Describing points in the Cycle
DISPLACEMENT
A Waveform Shows Amplitude as
a Function of Time
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
PEAK
1/1/00
2/1/00
PEAK-TO-PEAK
3/1/00
TIME
4/1/00
AMPLITUDE MEASURES
• Instantaneous- amplitude at any given
instant
• Peak
• Peak to Peak
• Root Mean Square--A way of getting
average amplitude
• =Square root of Averaged Squared
Amplitudes
Period and Frequency
• Frequency = 1/Period (in seconds)
• Units of Frequency = cycles per second or
HERTZ
PHASE--Each cycle broken up
into 360 degrees
• 0 degrees = 0 displacement and about to
head positively
• 90 degrees = positive maximum
• 180 degrees=0 disp. About to head
negatively
• 270 degrees= negative maximum
Phase Values Through a Cycle
Displacement
90
1.5
1
0.5
0
-0.5
-1
-1.5
1/1/00
180
2/1/00
270
360
3/1/00
Time
4/1/00
FREE VIBRATION
• Pendulum illustration represents FREE
VIBRATION
• Force applied and object allowed to respond
• Frequency of Free Vibration =Resonant or
Natural Freq.
• --determined by the object’s Mass and
Stiffness
FORCED VIBRATION
• Force is applied back and forth
• Vibration occurs at the frequency of the
applied force
• Object’s mass and stiffness determine
amplitude of vibration
IMPEDANCE
• The opposition to vibration, or
• What, other than motion, happens to your
applied force?
• That is what do you have to overcome?
Impedance has 3 components:
• Resistance: Energy lost to heat through
friction
• Mass Reactance: Energy taken to overcome
inertia
• Stiffness Reactance: Energy taken to
overcome restoring force
Impedance and Frequency:
• Resistance is generally the same across
frequency
• Reactance Components change with
frequency
Reactance and Frequency:
• Mass reactance is greater at high
frequencies
• --it’s harder to get massive objects to vibrate
quickly
• Stiffness reactance is greater at low
frequencies
• --it’s harder to get stiff objects to vibrate
slowly
Resonant Freq.
Mass and Stiffness Reactance
1.2
Reactance
1
0.8
0.6
Xm
Xs
0.4
0.2
0
100
500
1000
Frequency
4000
At Resonant Frequency
• Mass and Stiffness Reactance Cancel
• Only opposition to vibration is Resistance
• In Forced Vibration, you get the most
vibratory amplitude for amount of force
applied