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Chapter 1 Branches of Physics Measuring = units MASS [kg] LENGTH/DISTANCE [m] TIME [s] What do these have in common? Odd one out??? LBS vs. KG Weight is measured in pounds (USA) Mass is measured in kilograms 1 kg = 2.20462262 pounds 1 kg = 2.2 lbs 1 lb = 454 g MASS 50 – 75 kg MASS Bumblebee bat – 1.5g – 2.0 g MASS Blue whales: Newborn – 2.5 tons Avg. 100 – 120 tons Biggest – 190 tons CONVERT 1) your weight in lbs to mass in kg (1 kg = 2.2 lbs) 2) 190 tons to pounds 1 mile = 1.609344 kilometers 1 mile = 1.6 km 1 yard = 0.9144 m 1 foot = 0.3408 m 1m = 3.2808 ft Football field in meters? What is the length of a football field in meters? 120 yards 1 yard = 0.9144 m mph – km / h – m/s 65 mph = 104 km/h 104 km / h to m/s 104 km = 140,000 m; 1 h = 3600 s 65 mph = 29m/s km / h – m/s é km ù 1000 é m ù 10 é m ù êë h úû = 3600 êë s úû = 36 êë s úû [km / h] = [m / s] 3.6 75 km/h = 25 m/s = 120 km/h = 12 m/s = Scale of the Universe A super cool applet SN you need to remember: -9 nano n -6 micro m -3 milli m -2 centi c 10 3 kilo k 10 6 mega M 10 10 10 10 Convert, use Scientific Notation + BIG ® SMALL Þ BIG(10 ) - SMALL ® BIG Þ SMALL(10 ) Examples [cm] ® [m] - SMALL ® BIG Þ (10 ) 45cm ® ...[m] -2 -1 45cm = 45 ×10 m = 4.5 ×10 m Examples [m] ® [cm] + BIG ® SMALL Þ (10 ) 45m ® ...[cm] 45m = 45 ×10 cm = 4.5 ×10 cm 2 3 Examples [ mm] ® [m] - SMALL ® BIG Þ (10 ) 200 mm ® ...[m] 200 mm = 200 ×10 m = 2 ×10 m -6 -4 Examples [m] ® [ mm] + BIG ® SMALL Þ (10 ) 200m ® ...[ mm] 200m = 200 ×10 mm = 2 ×10 mm 6 8 Practice 1 2.5 days to seconds ________________________________________ 3.5 km to mm ______________________________________________ 43 cm to km _______________________________________________ 22 mg to kg _______________________________________________ 671 kg to µg _______________________________________________ 8.76 x 107 mW to GW _______________________________________ 1.753 x 10-13 s to ps _________________________________________ Practice The mass of the parasitic wasp Caraphractus cintus can be as small as 5x10-6 kg. What is the mass in a)g b)mg c) µg PRACTICE 2 dm - … mm 2h 10 min - … s 16 g - … micrograms 0.75 km - … cm 0.675 mg - …g 462 µm - … cm 35 km/h - … m/s Precision & Sig. Dig. LAB on Precision 1) Use the solid 1 m stick and measure the length of the lab table 2) Use the 1 m stick marked with dm 3) Use the 1 m stick marked with cm 4) Use the actual meter stick to measure the length of your desk. Write down the results to the maximum precision in each case. SIG FIGS MADE SIMPLE Sig. Fig. 100 000 100. 00 202 000 0.0050 340 505 0.00505 How many Sig.Figs? 300 000 000 m/s 3.00 ×108 m/s 25.030 °C 0.006 070°C 1.004 J 1.305 20 MHz Practice The value of the speed of light is now known to be 2.997 924 58 ×108m/s.Express the speed of light in the following ways: a) 3 SF b) 5 SF c) 7 SF Adding and Subtracting # of digits 0.______ (after the decimal point) = the least precise 3345.28 + 0.2 = 3345.48 = 3345.5 57.8 – 0.567 = 52.233 = 52.2 Multiplying and Dividing #SF (result) = the least #SF (A*B) 1.34 x 2300 = 3082 = 3.1103 #SF (result) = the least #SF (A/B) 23967 / 45 = 532.6 =5.3102 Practice Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in a) km/h and b) m/s - ? 1 mile = 1.61 km Practice a) find the sum of 756 g, 37.2 g, 0.83 g, and 2.5 g b) the quotient 3.2 m/ 3.563 s c) the product of 5.67 mm ×π d) 27.54 s - 3.8 s Density lab Trig Review c = a2 + b2 b = csin a a = ccosa a = csin b b = ccos b æ bö a = tan ç ÷ è aø æ aö b = tan ç ÷ è bø -1 a b c = = sin a sin b sin g -1 c2 = a2 + b2 - 2ab cos l Physics Quantities SCALARS – magnitude only VECTORS – magnitude and direction Vector vs. Scalar Velocity vs. Displacement v – scalar; vs. Speed Distance v - vector v – vector; (typed text) a) b) c) d) Comparing vectors Which vectors have the same magnitude? Which vectors have the same direction? Which arrows, if any, represent the same vector? Adding vectors a b a+b a+b b+a b+a Subtracting vectors (+ negative) a a-b a-b b b-a b-a Subtracting vectors (“fork”) a a-b b a-b b-a b-a Check your understanding Construct and label a diagram that shows the vector sum 2A + B. Construct and label a second diagram that shows B + 2A. Construct and label a diagram that shows the vector sum A – B/2. Construct and label a second diagram that shows B/2 - A. Adding ^ vectors R = 1600 + 400 = 44.7(km) -1 æ 40.0 ö q v = tan ç = 63.4 ÷ è 20.0 ø R qv qv 20.0km qh 40.0km æ 20.0 ö q h = tan ç = 26.6 ÷ è 40.0 ø -1 Practice (p. 24, #24) Vector A has a magnitude of 63 units and points due west, while vector B has the same magnitude and points due south. Find the magnitude and direction of (a) A+B and (b) A-B . Specify the directions relative to due west. Practice (p. 24, #25) (a) Two workers are trying to move a heavy crate. One pushes on the crate with a force A , which has a magnitude of 445 newtons and is directed due west. The other pushes with a force B, which has a magnitude of 325 newtons and is directed due north. What are the magnitude and direction of the resultant force A+B applied to the crate? (b) Suppose that the second worker applies a force - B instead of . What then are the magnitude and direction of the resultant force A-B applied to the crate? In both cases express the direction relative to due west. Adding vectors that are not To add vectors that are not perpendicular to each other, we will use components. Each vector has vertical and horizontal components, for example a has ax and ay ^ Components 3.0km 30 WN bx y 2.5km 30 NE b by a ay bx = -3.0sin 30 = -1.5(km) by = 3.0 cos 30 = 2.6(km) ax x ax = 2.5 cos 30 = 2.2(km) ay = 2.5sin 30 = 1.25(km) Adding vectors y b R a x To find the resultant… Rx Ry R We need the components Finding Rx and Ry y Rx - ? Rx = ax + bx b Ry - ? Ry = ay + by R R = Rx2 + Ry2 a x To find the resultant… Rx Rx = ax + bx = 2.2 - 1.5 = 0.7(km) Ry = ay + by = 1.25 + 2.6 = 3.85(km) Ry qv R R = Rx2 + Ry2 = 0.49 + 14.8 = 3.9(km) Direction? qh æ Ry ö q h = tan ç ÷ èR ø -1 x Answer : 3.9km 80 NE æ Rx ö q v = tan ç ÷ è Ry ø -1 or 3.9km 20 EN