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Ditmire - baltazar(kmb2869 HW1 ditmire(58216 This print-out...

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baltazar (kmb2869) – HW1 – ditmire – (58216) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (3 . 2 m , 2 . 4 m), what is the distance of the fly from the corner of the room? Correct answer: 4 m. Explanation: Let : Δ x = 3 . 2 m and Δ y = 2 . 4 m . Using the Pythagorean Theorem, d = radicalBig x ) 2 + (Δ y ) 2 = radicalBig (3 . 2 m) 2 + (2 . 4 m) 2 = 4 m . 002 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 · L 2 2. [ C ] = T · L M 3. [ C ] = T M 4. [ C ] = M L 3 correct 5. [ C ] = M T 2 · L 2 6. [ C ] = M T 7. [ C ] = T 2 · L M 8. [ C ] = T 2 · L 2 M 9. [ C ] = M L 2 10. [ C ] = T · L 2 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 . 003 10.0 points Consider a cube of soft, spongy material. Which piece below has the larger density? 1. cutting out a piece of the cube that has one-eighth the volume 2. Unable to determine 3. compressing the cube until it has one- eighth the volume correct 4. Densities are the same. Explanation:
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baltazar (kmb2869) – HW1 – ditmire – (58216) 2 ρ 1 = m V Compressing the cube results in a denser ma- terial. Compared to the piece cut out, the compressed piece has density ρ 2 = m 1 8 V = 8 m V = 8 ρ 1 . 004 (part 1 of 3) 10.0 points There are roughly 10 59 neutrons and protons in an average star and about 10 11 stars in a typical galaxy. Galaxies tend to form in clus- ters of (on the average) about 10 3 galaxies, and there are about 10 9 clusters in the known part of the Universe. Approximately how many neutrons and protons “#” are there in the known Universe? 1. # 10 43 2. # 10 87 3. None of these 4. # 10 52 5. # 10 47 6. # 10 82 correct Explanation: Let : N n = 10 59 , N s = 10 11 , N g = 10 3 and N c = 10 9 . The number of particles in the observable Universe equals the product of the numbers of particles in each astrophysical unit N nU = N n N s N g N c = ( 10 59 ) ( 10 11 ) ( 10 3 ) ( 10 9 ) = 10 82 neutrons and protons . 005 (part 2 of 3) 10.0 points Suppose all this matter were compressed into a sphere of nuclear matter such that each nuclear particle occupied a volume of 1 . 401 × 10 45 m 3 (which is approximately the “volume” of a neutron or proton). What would be the radius of this sphere of nuclear matter? 1. R 10 12 m correct 2. R 10 14 m 3. R 10 23 m 4. R 10 35 m 5. R 10 25 m 6. None of these Explanation: Let : V p = 1 . 401 × 10 45 m 3 The volume of the sphere would equal the product of the number of protons and neu- trons in the observable Universe and the vol- ume of such particles; i.e. , N nU V p = 4 3 π r 3 r = parenleftbigg 3 N nU V p 4 π parenrightbigg 1 3 = bracketleftBigg 3 ( 10 82 ) ( 1 . 401 × 10 45 ) 4 π bracketrightBigg 1 3
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