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hw 13 - shah(rps587 HW 13 Kleinman(58225 This print-out...

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shah (rps587) – HW 13 – Kleinman – (58225) 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. This HW covers Chs. 18, 19. 001 10.0 points A water hose 2 . 23 cm in diameter is used to fill a 26 L bucket. One liter is equal to 1000 cm 3 . If it takes 1 . 85 min to fill the bucket, what is the speed at which the water leaves the hose? Correct answer: 59 . 9724 cm / s. Explanation: Let : r = 1 . 115 cm , V = 26 L , and t = 1 . 85 min . The cross-sectional area of the hose is A = π r 2 = π (1 . 115 cm) 2 = 3 . 90571 cm 2 . According to the data given, the flow rate is equal to q = V t = 26 L 1 . 85 min min 60 s 10 3 cm 3 L = 234 . 235 cm 3 / s . Equating this to the product of the velocity of the water v and the cross-sectional area of the hose A gives v A = q . Solving for v yields v = q A = 234 . 235 cm 3 / s 3 . 90571 cm 2 = 59 . 9724 cm / s . 002 10.0 points A 1 . 3 m wide by 2 . 1 m long water bed weighs 1084 N. Find the pressure that the water bed exerts on the floor. Assume that the entire lower surface of the bed makes contact with the floor. Correct answer: 397 . 07 Pa. Explanation: Let : W = 1084 N , w = 1 . 3 m , and = 2 . 1 m . P = W A = W w ℓ = 1084 N (1 . 3 m) (2 . 1 m) = 397 . 07 Pa . 003 10.0 points Blood of density 604 kg / m 3 that is to be ad- ministered to a patient is raised about 1 . 03 m higher than the level of the patient’s arm. How much greater is the pressure of the blood than it would be if the container were at the same level as the arm? The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 6096 . 78 Pa. Explanation: Let : ρ = 604 kg / m 3 , h = 1 . 03 m , and g = 9 . 8 m / s 2 . Δ P = ρ g h = (604 kg / m 3 ) (9 . 8 m / s 2 ) (1 . 03 m) = 6096 . 78 Pa . keywords: 004 (part 1 of 2) 10.0 points In a machine shop, a hydraulic lift is used to raise heavy equipment for repairs. The sys- tem has a small piston with a cross-sectional area of 0 . 045 m 2 and a large piston with a cross-sectional area of 0 . 234 m 2 . An engine weighing 3500 N rests on the large piston.
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shah (rps587) – HW 13 – Kleinman – (58225) 2 What force must be applied to the small piston in order to lift the engine? Correct answer: 673 . 077 N. Explanation: Let : A 1 = 0 . 045 m 2 , A 2 = 0 . 234 m 2 , and F 2 = 3500 N . The pressure is the same, so F 1 A 1 = F 2 A 2 F 1 = A 1 F 2 A 2 = (0 . 045 m 2 ) (3500 N) 0 . 234 m 2 = 673 . 077 N . 005 (part 2 of 2) 10.0 points If the engine rises 0 . 266 m, how far does the smaller piston move? Correct answer: 1 . 3832 m. Explanation: Let : d 2 = 0 . 266 m . A hydraulic lift is effectively 100% efficient, so W in = W out F 1 d 1 = F 2 d 2 d 1 = F 2 d 2 F 1 = (3500 N) (0 . 266 m) 673 . 077 N = 1 . 3832 m . 006 10.0 points A simple U-tube that is open at both ends is partially filled with a heavy liquid of density 1000 kg / m 3 . A liquid of density 410 kg / m 3 is then poured into one arm of the tube, forming a column 5 . 7 cm in height, as shown. h 5 . 7 cm light liquid 410 kg / m 3 heavy liquid 1000 kg / m 3 What is the difference in the heights of the two liquid surfaces? Correct answer: 3 . 363 cm. Explanation: Let : = 5 . 7 cm , ρ = 410 kg / m 3 , and ρ h = 1000 kg / m 3 .
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