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Physics

Physics. A Mathematical Science. Science. An organized way of studying our surroundings. Technology. Applied science Using discoveries to create useful products. Physics. Study of matter and energy and their relationships Experimental Research using equipment Theoretical

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Physics

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  1. Physics A Mathematical Science

  2. Science • An organized way of studying our surroundings

  3. Technology • Applied science • Using discoveries to create useful products

  4. Physics • Study of matter and energy and their relationships • Experimental • Research using equipment • Theoretical • Construction of theory using mathematics to explain experimental data • Basic to all other sciences • Chemistry, engineering, architecture, medicine • A few laws describe most physical relationships

  5. Traits Helpful to a Physicist: • Knowledge • Insight • Creativity • Imagination • Patience

  6. Scientific Method Use observations Recognize the Problem Make predictions Revise/ repeat experiment Draw Conclusions Form a Hypothesis Test the Hypothesis Collect data Design an experiment Conduct the experiment

  7. Data Analysis Chapter 2

  8. Measurement • quantitative description • Requirements: • Know property attempting to measure • Must have a standard for comparison • Must have a method of comparison

  9. International System of Measurement • SI • Created by the French in 1795 • Used by most countries • Units are related to powers of 10 • No fractions are used

  10. Peta - 1015 Tera - 1012 Giga - 109 Mega - 106 Kilo - 103 Hecto - 102 Deka - 101 Deci – 10-1 Centi – 10-2 Milli – 10-3 Micro – 10-6 Nano – 10-9 Pico – 10-12 Femto - 10-15 Powers of ten

  11. SI base units

  12. SI base units

  13. Derived units • made from basic units • Volume: amount of space occupied • Volume may determined by: • Calculating from dimensions • Graduated cylinder – if liquid • Water displacement – if irregular in shape • Acceptable units: L, mL, m3, cm3, dm3

  14. Determining Volume from Dimensions V = l x w x h = 1 dm3 = 1 L 1000 cm3 = 1000 mL 1 cm3 = 1 mL 1 dm 1 dm 1 dm

  15. Other Derived Units • Density – mass per unit volume • D = m/V • units: g/cm3 • can be used to identify an unknown sample of matter • Weight – measure of force of gravity between 2 objects • W = mg • Newton (kg·m/s2) • Measured with a spring scale

  16. Scientific Notation • way to express extremely large or small numbers as powers of ten M x 10n M = # between 1 and 10 n = any whole number +n – # is larger than 1 -n – # is smaller than 1

  17. Examples: 123456778 = 1.23456778x 108 0.0000456 = 4.56 x 10-5

  18. To add or subtract, exponents must be the same. Adjust exponents and decimal place Add or subtract M’s Keep n the same Adjust exponent and decimal on final answer if needed Example: 2 x 102 + 3 x 103 2 x 102 30 x 102 = 32 x 102 = 3.2 x 103 Operations:

  19. To multiply: multiply M’s Add n’s To divide: Divide M’s Subtract n’s Example: (2.0 x 102)(3.0 x 103) = 6.0 x 10(2 + 3) = 6.0 x 105 Operations

  20. Using a Calculator for Scientific Notation • Locate or • This stands for “x 10” • Example: (2.0 x 102)(3.0 x 103) • Enter “2.0 EE 2 times 3.0 EE 3 = ” • 6.0 x 105 should appear on the display • Use the +/- key to enter negative exponents • If the answer does not appear in sci. not., check the mode or punch SCI. EE EXP

  21. Solving Problems Using Dimensional Analysis • AKA: factor-label method, conversion factors, bridge method • Units are treated as factors • Multiply by a series of factors to cancel the unwanted units • No need to memorize lists of formulas • You do have to know the conversion factors

  22. Factors are equivalent. 1 m or 1 min 100 cm 60 s Ex: ? m = 500 cm ? m = 500 cm 1 m 100 cm = 5 m

  23. Arrange factors to cancel unwanted units • Multiply by numbers on the top of the bar • Divide by numbers on the bottom • If the units match on each side of the =, the problem should be correct.

  24. Uncertainties of Measurement: • All instruments are subject to external forces and interpretation by people

  25. Accuracy and Precision: • Describe the reliability of a measurement • Accuracy: how close a measurement is to the correct value • May be expressed as percent error % error = accepted value – experimental value x 100 accepted value

  26. Accuracy and Precision: • Precision: how close repeated measurements are to each other • Depends on the exactness of the instrument scale • Measurements are recorded using the correct number of significant digits

  27. Parallax • Apparent shift in position of an object when viewed from various angles • Meter reading • Graduated cylinder reading

  28. Significant digits • All definitely known digits plus one estimated digit. • The number of sig. digs. should be observed in all calculations using measurements. • Rules for determining number of sig digs in a recorded measurement are on page 39. • Nonzero digits • Captured zeroes • Zeros after a decimal and after a number

  29. Examples • 300 m 1 sig dig • 303 m 3 sig digs • 3030 m 3 sig digs • 30.0 m 3 sig digs • 0.3 m 1 sig dig • 0.0003 m 1 sig dig • 0.00300 m 3 sig digs • 0.03030 m 4 sig digs

  30. Reading Instrument Scales

  31. Reading Instrument Scales

  32. Reading Instrument Scales

  33. Reading Instrument Scales

  34. Rounding Off Numbers • If adding or subtracting measurements, round your answer to the least number of decimal places. • If multiplying or dividing measurements, round your answer to the least number of significant digits. Problems – pages 27-28

  35. Solving Equations Using Algebra • Isolate unknown on the left side of the equation before plugging in known values when possible • Remember the order of operations. • Perform same operations to both sides of equation • Example: Solve the following expression for b. 3y = 6x + 2ab2

  36. Units in Equations: • Operations performed on numbers are also performed on units • Proper units = correct answer • Good check method • Measurements of the same type must have the same units • Make conversions using dimensional analysis • Example: 6 cm + 5 m + 2 mm

  37. Representing Data observations →charts → graphs →equations • Graph – visual display • Circle – parts of a whole (percents) • Bar – how one quantity varies with another • Line – (same as bar) • Determine relationship (verbal or equation) • Determine slope (rate of change of y to x) • Interpolate – read between data points • Extrapolate – read beyond data points (predict)

  38. Variables • Independent – one manipulated in an experiment • Plotted on the x-axis • Dependent – changes as a result of manipulating independent variable • Plotted on the y-axis

  39. Linear Relationships • Data points form a straight line • Equation: y = mx + b • Slope (m) = rise/run • y-intercept (b) = value of y when x = 0 • Direct relationship: • As x increases, y increases x

  40. Parabolic Relationship • Data forms an upward curve (parabola) • Equation: y = kx2 • K = constant = y/x2 • Power curve: as x increases, y increases more each time x

  41.  y is greater for each increment of x

  42. Root Curve • Data points form a an upward curve which levels off • Equation: y = kx

  43. Inverse Relationship • Data points slope downward (hyperbola) • Equation: y = k/x • As x increases, y decreases x

  44. Identify these relationships:

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