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hw2 - Overton Mays Homework 2 Due 4:00 am Inst Turner This...

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Overton, Mays – Homework 2 – Due: Jan 26 2005, 4:00 am – Inst: Turner 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points Grains of fine beach sand are assumed to be spheres of radius 54 . 1 μ m. These grains are made of silicon dioxide which has a density of 2600 kg / m 3 . a) What is the mass of each grain of sand? Correct answer: 1 . 72446 × 10 - 9 kg. Explanation: Since ρ = m V , then each grain has a mass of m = ρ V = ρ 4 3 π r 3 = ( 2600 kg / m 3 ) 4 3 π (54 . 1 μ m) 3 × 1 m 10 6 μ m 3 = 1 . 72446 × 10 - 9 kg . 002 (part 2 of 2) 10 points Consider a cube whose sides are 0 . 546 m long. b) How many kg of sand would it take for the total surface area of all the grains of sand to equal the surface area of the cube? Correct answer: 0 . 083866 kg. Explanation: Each grain of sand has a surface area of A g = 4 π r 2 , and the cube has a surface area of A c = 6 a 2 , so the required number of grains of sand is n = A c A g = 6 a 2 4 π r 2 . Thus the total mass of the sand will be M tot = n m = 3 m a 2 2 π r 2 = 3 (1 . 72446 × 10 - 9 kg) (0 . 546 m) 2 2 π (54 . 1 μ m) 2 × 10 6 μ m 1 m 2 = 0 . 083866 kg . 003 (part 1 of 1) 10 points Water flows into a swimming pool at the rate of 8 . 37 gal / min. If the pool dimensions are 34 . 3 ft wide, 49 ft long and 17 . 4 ft deep, how long does it take to fill the pool? (1 gallon = 231 cubic inches) Correct answer: 26136 . 4 min. Explanation: Basic Concepts The volume of the pool is given by V = lwh Solution The flow rate is v = V t Thus t = V v = 218762 gal 8 . 37 gal / min = 26136 . 4 min Dimensional analysis of V : ft 3 · 12 in ft 3 · 1 gal 231 in 3 = gal 004 (part 1 of 1) 10 points The position-versus-time graph below de- scribes the motion of three different bodies (labelled 1, 2, 3).
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Overton, Mays – Homework 2 – Due: Jan 26 2005, 4:00 am – Inst: Turner 2 1 2 3 x B x A t A t B x t A B Consider the average velocities of the three bodies. Which of the following statements is correct? 1. ¯ v 1 > ¯ v 2 > ¯ v 3 2. ¯ v 1 < ¯ v 2 < ¯ v 3 3. ¯ v 1 = ¯ v 2 = ¯ v 3 correct 4. ¯ v 1 > ¯ v 2 and ¯ v 3 > ¯ v 2 Explanation: The definition of average velocity is ¯ v = displacement time = x B - x A t B - t A . All three bodies have exactly same displace- ment in exactly same time, hence all three av- erage velocities are exactly equal, ¯ v 1 = ¯ v 2 = ¯ v 3 . 005 (part 1 of 1) 10 points A 22-car train standing on the siding is started in motion by the train’s engine. There are 9 cm of slack between the engine and each of the cars. The engine moves at a constant speed of 42 cm / s.
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