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PHYSICAL CONCEPTS

PHYSICAL CONCEPTS. 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 10 3

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PHYSICAL CONCEPTS

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

  2. 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

  3. 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

  4. Dividing in Sci. Not. • Divide Coefficients • Subtract Powers of 10 • Read More About Exponents in Appendix A

  5. Quantities Come in 2 Flavors: • Scalar Quantities • magnitude only • Vectorial or Vector Quantities • magnitude AND direction

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

  7. Vector Quantities • Have BOTH magnitude and direction • Example: Velocity • Combining Vectors is more complicated

  8. Basic Units • Length • Time • Mass • (Charge)

  9. Other Units may be derived: • Area = Length x Length (or L2) • Volume = L3 • Speed = Length/Time • Acceleration = L/T2

  10. 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

  11. 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

  12. 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)

  13. 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”

  14. 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

  15. Energy & Related Concepts • WORK • POTENTIAL AND KINETIC ENERGY • POWER

  16. 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

  17. 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)

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

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

  20. 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?

  21. SHM 3 • Why does displacement decrease over time? • RESISTANCE • -- Energy is lost to HEAT through FRICTION

  22. SHM 4 • Amplitude --Displacement • Period-- Time taken to complete one cycle • Frequency--Number of Cycles per Second • Phase--Describing points in the Cycle

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

  24. 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

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

  26. 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

  27. Phase Values Through a Cycle 90 180 270 360

  28. FREE VIBRATION • Pendulum illustration represents FREE VIBRATION • Force applied and object allowed to respond • Frequency of Free Vibration =Resonant or NaturalFreq. • --determined by the object’s Mass and Stiffness

  29. 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

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

  31. 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

  32. Impedance and Frequency: • Resistance is generally the same across frequency • Reactance Components change with frequency

  33. 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

  34. Mass and Stiffness Reactance Resonant Freq.

  35. 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

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