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Forces and Energy in Physics

Learn about physical quantities, force, friction, energy, work, simple harmonic motion, vibration, impedance, scientific notation, and more in the realm of physics. Understand units and concepts behind force, elasticity, friction, energy conversion, and simple harmonic motion. Explore the interplay of force, inertia, elasticity, and friction in vibrating systems.

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Forces and Energy in Physics

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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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