Unit 1: Introduction Measurement and Scientific Notation. Measurements in physics are carried out in SI units, aka the.

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1 Measurement and Scientific Notation Measurements in physics are carried out in SI units, aka the. Measurement Unit Symbol Length Mass Time Speed Acceleration Force Energy Prefixes Prefix Symbol Factor mega- kilo- hecto- deca deci- centi- milli- micro- nano- Units of Time Unit Symbol Value minute hour day year Metric / Imperial Conversion Factors 1 inch = 2.54 cm 1 foot = 12 inches 1 m = 3.28 feet 1 yard = 3 feet 1 km = 0.62 miles 1 mile = 5280 feet 1 kg = 2.2 lbs Method 1: Converting Units 1. Determine the conversion factor of the units 2. Write the conversion factor as a fraction with the units you want to change as Method 2: Converting Units 1: Find the 2: Find the of each prefix. 3: Use the! 3. Multiply the numbers and cancel the Ex. 1) Convert 165 mm to m 2) Convert 280 g to mg Ex. 1) Convert 165 mm to m 2) Convert 380 cg to mg 3) Convert 56 ML to L 3) Convert 24 ML to ml

2 Multiple Conversions When converting multiple units, change one unit at a time using its conversion factor 1) Convert 90 km/h to m/s 2) Convert 24 m/s to km/h When converting between m/s and km/h remember the magic number: Scientific Notation - Move the decimal point until only... Ex: à à - The # of spaces moved is the... - Move left and the exponent is - Move right and the exponent is Measurement & Scientific Notation Practice 1. Convert the following metric measurements: 1000 mg = g 198g = kg 8 mm = cm 160 dm = mm 75 ml = L 6.3 cm = mm 109 Mg = kg 50 cm = dam 5.6 m = cm 250 m = km 5 ML = ml 26,000 cm = km 14 km = m 16 cm = nm 1 L = ml 65 g = mg 355 ml = L m = µm 2. Convert the following quantities. a) 565,900 seconds into days b) 17 years into minutes c) 43 miles into feet d) 165 pounds into kilograms e) 100 yards into metres f) 2678 cm into feet g) 60 miles per hour into metres per second h) 130 meters per second into miles per hour i) 1100 feet per second into miles per hour j) 53 yards per hour into inches per second k) 721 lbs per week into kg per second l) 88 inches per second into miles per day 3. Write the following numbers in scientific notation: a) 5,500,000,000 b) 780 c) d) Write the following numbers in regular notation: a) 5.5 x 10-4 b) 7.1 x 10 6 c) 1.0 x Compute the following: a) 10 3 x 10 5 b) 4 x 10-3 x 5 x 10-5 c) 10-3 x 10 5 d) (8.0 x 10 5 )(1.2 x 10 8 ) e) f) (2.3 x 10-3 ) (1.0 x 10-5 ) g) h) (3 x 10 8 ) 2

3 Math Review is the basic language of physics. When working with equations for the unknown variable first, then substitute your known variables Ex: 1. Solve for d given that v = d/t v = 36 m/s and t = 8.0 s Ex: 1. Solve for a à F = ma 2. Solve for t à v = d/t 2. Solve for m given that F = ma F = 150 N and a = 2.50 m/s 2 3. Solve for c à E = mc 2 4. Solve for u à v 2 = u 2 +2ad Algebra Review 1. Solve each formula for the variable indicated. a) A = lw, w b) A = 1 / 2 bh, h c) g = a + w, a d) P = s e, s e) v = u + at, u f) W = R + Ht, t 2. Solve for the variable indicated. a) d = vt + ½at 2, solve for a b)c = ne, solve for E nr +R mn c) F = solve for n 2 d 3. The formula for the circumference of a circle is C = πd, where π = a) Solve the formula for d. b) Canada s largest tree is a Douglas fir on Vancouver Island. Its circumference is m. Use the formula for find the diameter of Canada s largest tree to the nearest thousandth. 4. Density can be calculated by the formula D = m / V, where D = density, m = mass and V = volume. Find the mass of: a) 55.2 cm 3 of aluminum (D Al = 2.70 g/cm 3 ) b) 82.3 cm 3 of mercury (D Hg = 11.4 g/cm 3 ) 5. The temperature below the Earth s surface, T, in degrees Celsius, is given by the formula: T = 10d + 20, where d is the depth in kilometers. a) The deepest hole in the Earth is a test- drilling hole in Russia. At the bottom of the hole the temperature is expected to reach 170 C. Estimate the depth of the drilling. b) Estimate the depth of a mine in which the temperature is 420 C. 1a) w =! b ) h =!! c) a = g w d) s= P + e e) u = v at f) t =!!!!!! 4a) 149 g b) 938 g 5. a) 15 km b) 40 km 2. a) a =!(!!!") b) E =!(!"!!) c) n =!!! 3. a) d =! b) 3.99 m!!!!!

4 Pythagorean Theorem Trigonometry Ex. Solve the following triangle Angle of Elevation: The Trig Relationships Angle of Depression: Trigonometry Draw Diagrams. Show work. Round off all answers to one decimal place. 1. The angle of elevation of the summit from the bottom of the lift at Snow Bowl is 33. If a skier rides 1000 m on this lift to the summit, what is the vertical distance between the bottom of the lift and the summit? 2. The angle of depression (below the horizontal) of an aircraft carrier from an approaching airplane is If the plane is 700 m above level of the deck of the carrier, how far away is the plane from the carrier? 3. The navigator on a bomber finds that the angle of depression of a target 4.00 km away is At what altitude is the plane flying? 4. Billy's kite has a string 40 m long and is flying 27 m above his eye level. Find the angle of elevation of the kite. 5. At an airport, cars drive down a ramp 96 m long to reach the lower level baggage- claim area 13 m below the main level. What angle does the ramp make with the ground at the lower level? 6. A pendulum 40 cm long is moved 30 from the vertical. How high is the lower end of the pendulum lifted? 7. The angle of depression of the top of Billings Building from the roof of the Wolcott Building (in the same vertical plane) is 33.10, and from the 15 th floor it is If the distance between the roof and the 15 th floor is 101 m, how far apart are the buildings? m m km cm m

5 Significant Figures In physics we will be taking measurements and using a lot of numbers for calculations. However, we have to be aware of significant figures (sig figs) because every measurement has a certain degree of uncertainty. Accuracy: Precision: When making a measurement, the last digit is always All recorded data is considered, however the last digit is deemed. A measuring instrument generally has a precision of 1) All non- zero numbers The Sig Fig Rules Examples: How many sig figs are in each number? 1) ) ) ) Ex: 321 has sig figs 2) Zeroes that occur Ex: 1001 has sig figs 3) In a non- decimal number 5) ) ) ) Multiplying and Dividing When multiplying or dividing numbers, our final answer is always Ex: 350 x 1.15 = Ex: 5200 has sig figs 4) Zeroes to the left x 150 = x 100 = Ex: has sig figs 5) In a decimal number Adding and Subtracting When adding or subtracting numbers, the final answer is always Ex: has sig figs Ex: = = =

6 Significant Figures Activity 1) Counting sig figs: write down the number of sig figs each piece of data has: a) m d) 410 kg b) 200,000 m 3 e) s c) s f) m 2 2) Multiplication with sig figs: a) m 1.01 m = e) m cm = b) N 4.24 s = f) 2001 kg 12.6 m/s = c) 4000 kg m/s g) 610 N 4002 s = 3) Division with sig figs: a) 12 m 31.2 s = d) 1800 kg 410 s = b) 69.4 kg s = e) m 100 ms = c) m s = f) 1001 m 3 40 ks = 4) Addition and subtraction with sig figs: a) 14 m m = d) s s = b) kg kg kg = e) m m = c) kg kg kg = 5) Chain calculations with sig figs: round off to the appropriate number of sig figs at the end! a) (0.045 m 9.92 kg) s = b) (9000 m 4.01 m) m = c) (0.21 m 6.23 s) m = d) (18.01 m 0.41 m) (14.62 kg 12 s) =

7 Graphing Graphing Rules Label the axis Ø variable on the x- axis Ø variable on the y- axis Direct Relationship Give the graph an. Scale each axis Ø Use Ø Choose a scale that is Ø Plot the points and draw a. Finding Slope To find the slope of a straight line: Remember the equation of a line is: Choose Choose them as Use only Determine the slope and y- intercept of the graph shown and write the equation describing this line

8 Graphs of Wrath Mr. House was interested in seeing the relationship between the variables velocity and time. He took three souped-up Hot Wheels cars and ran them through an extensive timing circuit. Here are three sets of data recorded in Mr. House s secret laboratory lair: Car 1 Car 2 Car 3 Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Your challenge as Mr. House s assistant/lackey is to provide a beautiful graph of all three sets of data on only ONE piece of graph paper (Mr. House s lab is a bit budget). Follow the steps like we did in our notes and you will be fine. You MUST have all data fit on your graphs, so you will have to make some tough decisions about your variable range on the axes. Also, use as much space as possible. Make sure your graph is readable and all your labeling and calculations are on the graph as well.

9 The Quadratic Formula Any quadratic equation can be solved using something called If the quadratic equation is in the form ax! ± bx ± c = 0, the quadratic formula is: Solve using the quadratic formula. Determine solution(s) to 2 decimals where necessary. a) 3x! + 5x 2 = 0 b) x! = 2x + 1 c) 3x! = 9 d)! =!!!!!" Quadratic Formula Activity Solve each of the equations below using the quadratic formula. Determine solution(s) to 2 decimals where necessary. a. x 2 8x + 16 = 0 b. 2x 2 + x 5 = 0 c. x 2 5x 1= 0 d. 3x 2 + 7x = 4 e. x 2 64 = 0 f. 27 r 2 = 0 g. 3t 2 2t 3 = 0 h. 4m 2 = 6m +3 i. 2 (x + 1) 2 = 2 j. 0.1a a 23 = 0 k x + = x 1 x 1 Solutions a. 4 b or 1.85 c or 0.19 d. 1 or 1.33 e. ± 8 f. ± 5.20 g or 0.72 h or 0.40 i. 0 or 2 j or k. 2 or 1