PHYSICAL%20CONCEPTS

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PHYSICAL CONCEPTS

• Number issues
• Physical Quantities
• Force/Friction/Energy/Work, etc.
• Simple harmonic motion
• Vibration Free and Forced
• Impedance

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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

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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(23)
• 9.2 x 105

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Dividing in Sci. Not.

• Divide Coefficients
• Subtract Powers of 10
• Read More About Exponents in Appendix A

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Quantities Come in 2 Flavors

• Scalar Quantities
• magnitude only
• Vectorial or Vector Quantities
• magnitude AND direction

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Scalar Quantities

• Have magnitude only
• Examples include Mass, Length, Volume
• Can be added or subtracted directly

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Vector Quantities

• Have BOTH magnitude and direction
• Example Velocity
• Combining Vectors is more complicated

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Basic Units

• Length
• Time
• Mass
• (Charge)

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Other Units may be derived

• Area Length x Length (or L2)
• Volume L3
• Speed Length/Time
• Acceleration L/T2

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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

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Force and Elasticity

• Hookes Law
• Force (-)spring constant times displacement
• Stress force per unit area (aka pressure)
• Strain change in length
• Stress Elasticity x Strain

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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)

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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

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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

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Energy Related Concepts

• WORK
• POTENTIAL AND KINETIC ENERGY
• POWER

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WORK

• Force applied through a distance
• No motion--no work
• Work force x distance ML/T2 x L
• Units JOULE 1 Newton Meter
• erg 1 dyne cm

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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)

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POWER

• Rate at which work is done
• Work/Time
• Unit Watt joule/second or 107 erg/sec

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SIMPLE HARMONIC MOTION

• Vibration involves interplay of force, inertia,
  elasticity, and friction
• Applying a force displaces object
• Overcoming inertia
• Traveling away from rest until ?

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Simple Harmonic Motion 2

• Why does object stop and then move back toward
  rest?
• Why doesnt the object then stop at rest?
• Where is potential energy the greatest?
• Where is kinetic energy the greatest?

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SHM 3

• Why does displacement decrease over time?
• RESISTANCE
• -- Energy is lost to HEAT through FRICTION

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SHM 4

• Amplitude --Displacement
• Period-- Time taken to complete one cycle
• Frequency--Number of Cycles per Second
• Phase--Describing points in the Cycle

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A Waveform Shows Amplitude as a Function of Time
PEAK
PEAK-TO-PEAK
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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

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Period and Frequency

• Frequency 1/Period (in seconds)
• Units of Frequency cycles per second or HERTZ

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PHASE--Each cycle broken up into 360 degrees

• 0 degrees 0 displacement and about to head
  positively
• 90 degrees positive maximum
• 180 degrees0 disp. About to head negatively
• 270 degrees negative maximum

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Phase Values Through a Cycle
90
180
270
360
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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 objects Mass and Stiffness

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FORCED VIBRATION

• Force is applied back and forth
• Vibration occurs at the frequency of the applied
  force
• Objects mass and stiffness determine amplitude
  of vibration

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IMPEDANCE

• The opposition to vibration, or
• What, other than motion, happens to your applied
  force?
• That is what do you have to overcome?

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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

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Impedance and Frequency

• Resistance is generally the same across frequency
• Reactance Components change with frequency

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Reactance and Frequency

• Mass reactance is greater at high frequencies
• --its harder to get massive objects to vibrate
  quickly
• Stiffness reactance is greater at low frequencies
• --its harder to get stiff objects to vibrate
  slowly

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Mass and Stiffness Reactance
Resonant Freq.
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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