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Science 10

Science 10. Motion. Numbers vs. Measurement. There is a difference in between numbers used in math and measurement used in science. In math, every number carries importance In science, not every number in a measurement carries the same importance.

rochelle-meunier
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Science 10

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  1. Science 10 Motion

  2. Numbers vs. Measurement • There is a difference in between numbers used in math and measurement used in science. • In math, every number carries importance • In science, not every number in a measurement carries the same importance. • More important numbers are called significant figures. • Less important numbers are called place holders.

  3. Measurement • Every measurement contains an exact amount of significant figures. • It includes all numbers that were measured from the scale used. • Plus 1 extra ‘guessed number’ that is not on the scale. • Always include one more number than your scale tells you!

  4. Scale does not tell us any certain numbers, so we can only write down 1 guessed number The scale now tells us the tens so we can be certain of those numbers. We add a guessed number after the ones we are certain of. Our scale tells us the tens and the ones so we can be certain of those numbers. We add a guessed number after the ones we are certain of. 0 is a place holder and is not significant. 8 is a guessed number and it is significant 0 is a guessed number and it is significant 47.0 50 48 100cm 0cm 4 is a certain number and it is significant 5 is a guessed number and it is significant 47 are certain numbers and are significant

  5. Rules for Significant Figures • There are 2 rules for determining the number of significant figures. • Decimal rule- (use this rule when the measurement contains a decimal) • Count the numbers from left to right beginning at the first non-zero number.

  6. 0.001234- 12340.0- 6 sig. figs. 4 sig. figs. 1.234- 4 sig. figs. 12340.- 5 sig. figs. 0.123400- 6 sig. figs. 1.2340 x 10-3- 5 sig. figs.

  7. Rules for Significant Figures • Non-decimal rule- (use this rule when the measurement does not contain a decimal) • Count the numbers from right to left beginning at the first non-zero number.

  8. 1234- 4 sig. figs. 12340- 4 sig. figs. 102340- 5 sig. figs. 12340.- 5 sig. figs. 0.123400- 6 sig. figs. 100002- 6 sig. figs.

  9. Scientific Notation • Scientific notation is a method of writing numbers that: • Can make large numbers more easy to read. • Indicate the proper number of significant figures.

  10. Rules for Writing in Scientific Notation • Write down all the significant numbers • Put a decimal after the first number. (the number will now be between 1-10) • Write “x 10” • Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive) • Count the number of digits between where the decimal was before and where it is now

  11. 25 000 000 000 000 • Write down all the significant numbers • Put a decimal after the first number. (the number will now be between 1-10) • Write “x 10” • Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive) 25 . x 10 13

  12. 0.000 000 000 030 0 • Write down all the significant numbers • Put a decimal after the first number. (the number will now be between 1-10) • Write “x 10” • Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive) 300 . x 10 -11

  13. How do you write the number 10 000 with 3 significant figures? 4 100 . x 10

  14. Change 0.00123 x 10-3 into proper scientific notation. 123 . x 10 -6 -3 -3= -6

  15. Calculating using Significant Figures • There are 2 rules for calculating with significant figures. • Precision rule- (used for addition and subtraction) • The answer will have the sameprecision as the least precise measurement from the question.

  16. 10 cm Least precise 10. cm 10.0 cm 10.00 cm Most precise

  17. This value is the least precise value. The answer will end at the same spot. 1.234 +0.05678 1.29078 =1.291 Round the value after the last sig. fig.

  18. This value is the least precise value. The answer will end at the same spot. 12340 +5678000 5690340 =5690000 Round the value after the last sig. fig. =5.690 x 106

  19. Calculating using Significant Figures • Certainty rule- (used for multiplication and division) • The answer will have the samenumber of significant figures as the least number of significant figures from the question.

  20. 3 significant figures 123 X 45 2 significant figures 5535 The answer will have 2 significant figures 1 2 5500 Round the value after the last significant figure Place holders

  21. 2 significant figures 450 X 0.0123 3 significant figures 5.535 The answer will have 2 significant figures 1 2 5.5 Round the value after the last significant figure

  22. Units • A unit is added to every measurement to describe the measurement. Ex. • 100 cm describes a measured length. • 65 L describes a measured volume. • 12.4 hours describes a measured time. • 0.011 kg describes a measured mass.

  23. Units • In Canada we use the metric (SI) system. • The metric (SI) is a system designed to keep numbers small by converting to similar units by factors of 10. • Prefixes are added in front of a base unit to describe how many factors of 10 the unit has changed.

  24. Units • Base units of measurement are generally described by one lettre. • m- metre (length) • s- second (time) • g- gram (mass) *The base unit for mass is actually the kg (kilogram) • L- litre (volume)

  25. Units • Prefixes • Prefixes are added to the front of any base unit. Ex. mm, cm, dm, m, dam, hm, km Kilo hecto deca base deci centi milli (k) (h) (da) (d) (c) (m)

  26. Converting units • There are 2 methods to convert units • Step Method- count the number of places to move the decimal. • Dimensional Analysis- multiplication by equivalent fractions of 1.

  27. Converting Units • Step method- • Move the decimal the samenumber of spaces and direction as the distance in between prefixes.

  28. Convert 34.56 cm into m Kilo hecto deca base deci centi milli (k) (h) (da) (d) (c) (m) It starts at centi (for centimetre) We move 2 spaces to the left to get from centimetre to metre So we move the decimal 2 places to the left in our number 0 3456 . cm m

  29. Convert 21.0 kg into g Kilo hecto deca base deci centi milli (k) (h) (da) (d) (c) (m) It starts at kilo (for kilogram) We move 3 spaces to the right to get from kilogram to gram So we move the decimal 3 places to the right in our number 210 . 00 kg g =2.10 x 104g

  30. Converting Units • Dimensional Analysis- • Multiply the measurement by a fraction that equals 1 • The fraction will contain the old unit and the new unit. • The fraction must cancel out the old unit. (follow the rule that tops and bottoms cancel out)

  31. Convert 34.56 cm into m Kilo hecto deca base deci centi milli 1 m 34.56 cm Move 2 places so we need 2 0’s (k) (h) (da) (d) (c) (m) = 0.3456 m 100 cm We need to make the fraction equal 1. Put the larger measurement as 1 and add 0’s to the smaller measurement. (# of zeroes equals the number of places the prefixes are moved. Counted and exact values do not count for significant figures Multiply the tops and divide the bottoms The fraction must contain the new and old unit. Tops and bottoms cancel out Multiply by a fraction

  32. Convert 21.0 kg into g 1000 g 21.0 kg = 21000g = 2.10 x104g 1 kg

  33. Convert 15.0 m/s into km/h 1 km 60 s 60 min 15.0 m s 1000 m 1 min 1 h = 54.0 km/h We multiply the tops, and divide the bottoms. We follow the same rules, but we convert 1 unit at a time.

  34. Convert 80.0 km/h into m/s 1 h 80.0 km h 1000 m 1 km 3600 s = 22.2 m/s We multiply the tops, and divide the bottoms. We follow the same rules, but we convert 1 unit at a time.

  35. Defined Equations • Relationships between variables can be expressed using words, pictures, graphs or mathematical equations. • A defined equations is a mathematical expression of the relationship between variables Ex. Mass and Energy are related by the speed of light E = mc2

  36. Defined Equations • Defined equations can be manipulated to solve for any of the variables. • We use the same principles from math. • There are 2 rules that must be followed to isolate a variable. • It must be alone • It must be on top (numerator)

  37. Solve E = mc2 for m m must be isolated Divide both sides by c2 E = mc2 E = m c2 c2 m is already on top so we will not touch m. We have to isolate m by moving c2 to the other side.

  38. Solve d = m/v for v Multiply by v on both sides Divide by d on both sides v d = m v d v d v is on the bottom so we need to move v first and then isolate.

  39. Speed • The distance travelled by the amount of time. • How fast something is moving. v = Δd Δt • Speed is measured in m s

  40. Speed • You can look at speed in 3 different ways • Average- the speed over the whole trip. • Total distance divided by total time. • Instantaneous- the speed at one point in the trip. • Looking at the speedometer. • Constant- the speed remains the same over a period of time.(uniform motion) • Cruise control.

  41. Calculations for speed • Using the formula, v = d/t, we can make some mathematical calculations about speed. • Follow the same 3 steps to solve every problem. • Identify your givens and unknowns. • Identify the defined equation and isolate for the unknown variable. • Solve the equation using proper significant figures and units.

  42. A trip to Calgary is 758 km. If you were to complete the trip in 7.25 h, what was you speed? Givens Formula Solve d= 758 km t= 7.25 h v= ? v = d t v = 758km 7.25 h v = 105km h

  43. What type of speed did we calculate in the previous problem? Average speed

  44. If someone is travelling at a constant speed of 40.0 km/h, how far would they travel in 32.4 min. Givens Formula Solve d= ? t= 32.4 min v= 40.0 km h v = d t d = 40.0km (0.54 h) h d = v t d = 21.6 km 1 h 32.4 min = 0.540 h 60 min

  45. Representing Speed Graphically • We can represent speed with words (fast, slow), numbers (32 km/h) and we can also represent it visually with a graph. • Speed is represented on a distance vs. time graph. • The slope of the graph is the speed.

  46. Travelled the greatest distance in the same time. (fastest speed) Distance (m) The slope of the line is equal to the speed The steeper the slope, the greater the speed. A straight line indicates a constant speed. Travelled the least distance in the same time. (slowest speed) A curved line indicates non-constant speed. (speeding up or slowing down.) Time (s)

  47. Describe the motion in the following graph? 1.Moving slowly at a constant speed 2.Moving faster at a constant speed Where is the person going in this graph? 3.Not moving 4.Moving back to the start at a constant speed 5.Speeding up Back to the original starting position. Distance (m) What is the speed of this graph? 0 m/s Time (s)

  48. Identify the 3 types of speed on the graph? Average Instantaneous Constant Distance (m) the speed remains the same over a period of time the speed over the whole trip the speed at one point in the trip Time (s)

  49. Acceleration • The change in speed by the amount of time. • How quickly something is speeding up (or slowing down) a = Δv Δt • Acceleration is measured in m s2

  50. Acceleration • You can look at 2 types of acceleration. • Average- the acceleration over the whole time period. • The change in speed over time. • Constant- the acceleration remains the same over a long period of time.

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