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MATH SKILLS FOR PHYSICS

MATH SKILLS FOR PHYSICS. Units / Unit systems Scientific notation/ Significant figures Algebraic manipulation Geometry / Trig identities Graphing Dimensional analysis. MATHEMATICS.

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MATH SKILLS FOR PHYSICS

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  1. MATH SKILLSFOR PHYSICS Units / Unit systems Scientific notation/ Significant figures Algebraic manipulation Geometry / Trig identities Graphing Dimensional analysis

  2. MATHEMATICS • This unit is a review of most of the skills that are necessary for understanding and applying physics. A thorough review is critical. • Basic geometry, algebra, formula rearrangement, graphing, trigonometry, scientific notation, and such are normally assumed for beginning physics. • Please use this for review and preparation for classwork.

  3. Dimensions / Units • The raw material of science is measurement. Every measurement is a comparison to some standard. • Every measurement contains error • “The length of the football field is 100 yds.” • Dimension – the physical characteristic being measured – “length” • Unit – we are using the “yard” which is a unit of length in the common or “British” system. • Measurement – How many of these units? 100 (yds)

  4. Fundamental or basic Dimensions • We recognize seven fundamental or basic physical dimensions – the SI dimensions. • Know the five SI units in the table on page 958 of your text. • 2 more not listed there: • Mole – amount of substance • Candela – luminous intensity • These seven basic dimensions can be combined to derive other physical characteristics.

  5. Derived Dimensions • Use of the basic dimensions (with correct units) to describe many different physical characteristics – • Example – • From Houston to Austin is a measurement of about 180 miles. • If I cover that distance in 3 hours, I can find my average speed as 180 miles / 3 hours = 60 mi/hr. • I have “derived” a new measurement called speed.

  6. See other commonly used units (derived) on p. 959 of your text. • Take note of the following derived units: know the quantity measured and the “conversion” (basic units) • Hertz • Joule • Newton • volt

  7. Unit Table Dimension SI unit(MKS) cgs Common (B/E) unit Mass (M) _______ _______ ________ ______ s _______ ________ ______ _______ _______ ft ______ _______ cm3 ________ Velocity (L/T) m/s ______ ________

  8. Dimension MapCan you use the correct units?

  9. Units • The SI system uses the metric system which is base 10. (Sometimes referred to as the MKS system - meter, kilogram, second) • The cgs (centimeter, gram, second) system is more convenient for smaller quantities. That is why it is frequently used in chemistry – you don’t use a kilogram of a compound very often! • We use the “common” or “British” system of units. You can’t just multiply or divide by ten to change the size. You have to memorize the silly things: • examples: 12 inches in 1 foot 3 feet in 1 yard 1760 yards in 1 mile 5280 feet in 1 mile

  10. Working with units Similar dimensions can be added or subtracted – nothing changes. 3 m + 3 m = 6 m 52 kg - 12 kg = 40 kg . BUT ----You cannot add or subtract different dimensions 3 m + 12 kg = no answer You can’t add a distance to a mass – just common sense.

  11. All dimensions can be multiplied or divided • Similar dimensions If multiplied then they become squared or cubed. 3 m x 3 m = 9 m2 If divided, then they cancel 6 m / 3 m = 2 (no unit – it cancels out) Note: 6m2 / 3 m = 2 m (only one “m” is cancelled) • Different dimensions Multiplied: 3 m x 2 s = 6 m·s Divided (a ratio): 88 km / 4 s = 22 km/s

  12. CAREFUL! CAREFUL! • Even if working in the same dimension (like mass) I cannot work in different SIZES (this is what prefixes mean – like kilo, milli, Mega, etc)! • THE PREFIXES MUST BE THE SAME !!!!! • 5 kg – 2 kg = 3 kg All is good. • 5 kg – 2 g = DISASTROUS CATASTROPHY! • Gotta be the same - so, 5 kg - .002 kg is OK. • OR - 5000 g - 2 g is OK.

  13. - 9 = 0 . 000000001 10 - 6 = 0 . 000001 10 - 3 = 0 . 001 10 0 = 1 10 3 = 1000 10 6 = 1 , 000 , 000 10 9 = 1 , 000 , 000 , 000 10 Scientific notation provides a short-hand method for expressing very small and very large numbers. Examples: 93 000 000 mi = 9.30 x 107 mi 0.000 042 kg = 4.20 x 10-4 kg V = 1.39 x 10 5 m/s

  14. SCIENTIFIC (EXPONENTIAL)NOTATION • Since the metric system is base 10, this makes multiplying and dividing easy. Exponential notation is a shorthand for writing exceptionally large or small values – but it is also very helpful for controlling significant figures. • Using exponents can make the work much easier. • Learn the metric prefixes from Table 1-3 on page 12. Study Sample Problem on p. 14

  15. Metric prefixes are used to express very small or very large numbers. • Learn the metric prefixes from Table 1-3 on page 12. Study Sample Problem on p. 14

  16. PREFIX SUBSTITUTION • You MUST learn the value of each prefix. • Substitute the value for the prefix. This converts to the base unit. 3.5 x 10-8 Tm = 3.5 x 10-8 (1012) m = 3.5 x 104 m • From there you can convert to the needed value. 3.5 x 104 m x km = 3.5 x 101 km or 35 km 103 m Remember your dimensional analysis techniques !!!!

  17. Solve the problem: Use the fact that the speed of light in a vacuum is about 3.00 x 108 m/s to determine how many kilometers a pulse from a laser beam travels in exactly one hour. (ans: 1.08 x 109 km) How many meters? Easy, substitute 103 for “k” 1.08 x 109 (103) m = 1.08 x 10 12 m or 1.08 Tm

  18. Solve the problem: The largest building in the world by volume is the Boeing 747 plant in Everett, Washington. It measures approximately 0.631 km long, 1433 m wide and 7400 cm high. What is its volume in cubic meters? (ans: 6.70 x 107 m3)

  19. SIGNIFICANT FIGURES (SF) • Why is this concept so important in science? • Every measurement is limited in terms of accuracy. This is due to both the instrument and human ability to read the instrument. • The number of sig figs in a measurement includes the figures that are certain and the first “doubtful” digit. • With a metric ruler a desk can be measured to 65.2 cm – but not 65.0002 cm. It just ain’t that good ! • The final answer must have the same number of sig figs as the least reliable instrument.

  20. The rules for sig figs and rounding can be found • on pages 17- 19 of the text. • Use Tables 1-4, 1-5 and 1-6 for SF rules • How many sig figs (SF) in each of the following measurements? • a. 3000 000 000 m/s • 25.030 oC • 0.006 070 K • 1.004 J • 1.305 20 MHz

  21. Solve the problems: Find the sum of: 756g, 37.2g, 0.83g, and 2.5g Divide: 3.2m / 3.563 s Multiply: 5.67 mm x p (Ooohhh, sneaky. There’s a pi in there.)

  22. H W L Working With Formulas: Many applications of physics require one to solve and evaluate mathematical expressions called formulas. Consider Volume V, for example: V = LWH Applying laws of algebra, we can solve for L, W, or H:

  23. Formula RearrangementSolve for A Consider the following formula: Multiply by B to solve for A: Notice that B has moved up to the right. Thus, the solution for A becomes:

  24. Geometry and Trig Review • See pages 946 through 948 to review the basic geometry and trig needed for this course.

  25. R y q x Trigonometry Review • You are expected to know the following: Trigonometry y = R sin q x = R cos q y = x tan q R2 = x2 + y2 Θ= tan-1(y/x)

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