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solution1_pdf - arellano(aa39398 Practice Homework 1...

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arellano (aa39398) – Practice Homework 1 Solutions – Weathers – (17101) 1 This print-out should have 73 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A sphere of metal has a radius of 6 . 7 cm and a density of 9 . 27 g / cm 3 . What is the mass of the sphere? Correct answer: 11678 . 7 g. Explanation: Let : r = 6 . 7 cm and ρ = 9 . 27 g / cm 3 . Density is mass per unit volume, so ρ = m V m = ρ V = ρ 4 3 π r 3 = ( 9 . 27 g / cm 3 ) 4 3 π (6 . 7 cm) 3 = 11678 . 7 g . 002 10.0 points To protect her new two-wheeler, Iroda Bike buys a length of chain. She finds that its linear density is 0 . 77 lb / ft. If she wants to keep its weight below 1 . 5 lb, what length of chain is she allowed? Correct answer: 1 . 94805 ft. Explanation: Let : ρ = 0 . 77 lb / ft and W = 1 . 5 lb . applying dimensional analysis, the length is defined by = W ρ = 1 . 5 lb 0 . 77 lb / ft = 1 . 94805 ft . 003 10.0 points A plastic tube allows a flow of 12 . 6 cm 3 / s of water through it. How long will it take to fill a 213 cm 3 bottle with water? Correct answer: 16 . 9048 s. Explanation: Let : r = 12 . 6 cm 3 / s and V = 213 cm 3 . cm 3 ÷ cm 3 s = cm 3 · s cm 3 = s , so the time is t = V r = 213 cm 3 12 . 6 cm 3 / s = 16 . 9048 s . 004 10.0 points Evaluate [ r ]; i.e. , the units of r , in the expres- sion r = radicalbigg ( s - a ) ( s - b ) ( s - c ) s , where s = 1 2 ( a + b + c ) , and a , b , and c have units of meters. 1. [ r ] = m 1 / 3 2. [ r ] = 1 m 2 3. [ r ] = 1 m 1 / 3 4. [ r ] = 1 m 5. [ r ] = m 3 6. [ r ] = m 2 7. [ r ] = m 1 / 2 8. [ r ] = 1 m 1 / 2 9. [ r ] = m correct Explanation:
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arellano (aa39398) – Practice Homework 1 Solutions – Weathers – (17101) 2 The unit of measure for s = a + b + c 2 is also meters (we are averaging them), and the unit of measure for radicalbigg ( s - a ) ( s - b ) ( s - c ) s is radicalbigg m × m × m m = m 2 = m . 005 10.0 points When an object falls through air, there is a drag force ( with dimension M · L / T 2 ) that depends on the product of the surface area of the object and the square of its velocity; i.e. , F air = C A v 2 , where C is a constant. What is the dimension for constant C ? 1. [ C ] = M T 2 · L 2 2. [ C ] = M T · L 2 3. [ C ] = T M 4. [ C ] = T · L 2 M 5. [ C ] = T 2 · L 2 M 6. [ C ] = M L 3 correct 7. [ C ] = T · L M 8. [ C ] = M L 2 9. [ C ] = M T 10. [ C ] = T 2 · L M Explanation: [ F ] = M · L / T 2 , [ A ] = L 2 , and [ v ] = L / T , so [ C ] = [ F ] [ A ] [ v ] 2 = M · L / T 2 L 2 · (L / T) 2 = M · L T 2 · T 2 L 4 = M L 3 . 006 (part 1 of 3) 10.0 points The world’s longest river is the Nile river in Egypt. Its length is 4,145 miles. Find its length in kilometers. Correct answer: 6669 . 31 km. Explanation: Let : = 348 mi . = (348 mi) parenleftbigg 1 . 609 km 1 mi parenrightbigg = 6669 . 31 km . 007 (part 2 of 3) 10.0 points Find its length in meters. Correct answer: 6 . 6693 × 10 6 m. Explanation: l = (6669 . 31 km) parenleftbigg 1000 m 1 km parenrightbigg = 6 . 6693 × 10 6 m . 008 (part 3 of 3) 10.0 points Find its length in centimeters. Correct answer: 6 . 6693 × 10 8 cm. Explanation: l = (6 . 6693 × 10 6 m) parenleftbigg 100 cm 1 m parenrightbigg = 6 . 6693 × 10 8 cm . 009 (part 1 of 3) 10.0 points
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arellano (aa39398) – Practice Homework 1 Solutions – Weathers – (17101) 3 A right circular cylinder has a diameter of 5 . 1 in and a height of 5 ft.
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