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Homework 19

# Homework 19 - Gozick Brandon Homework 19 Due 7:00 pm Inst D...

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Gozick, Brandon – Homework 19 – Due: Nov 21 2006, 7:00 pm – Inst: D Weathers 1 This print-out should have 10 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 1) 10 points Assume: The buoyant force of the air is neg- ligible. Given: The density of the oil is 841 kg / m 3 . The density of the water salt mixture is 1150 kg / m 3 . A rectangular parallelepiped block of uni- form density floats in a container which con- tains oil and salt water as shown. The block sticks up above the oil by a dis- tance d 1 = 0 . 35 m. The oil thickness is d 2 = 0 . 14 m. The block’s depth in the salt water is d 3 = 0 . 33 m. The horizontal area of the block is 0 . 019 m 2 . M d 1 d 3 d 2 Calculate the mass of the block. Correct answer: 9 . 44756 kg. Explanation: The mass of the salt water displaced is m 3 = ρ w d 3 a = (1150 kg / m 3 ) (0 . 33 m) (0 . 019 m 2 ) = 7 . 2105 kg . The mass of the oil displaced is m 2 = ρ o d 2 a = (841 kg / m 3 ) (0 . 14 m) (0 . 019 m 2 ) = 2 . 23706 kg . Since the mass of the block m b is equal to the liquid displace, we have m b = m 2 + m 3 = (2 . 23706 kg) + (7 . 2105 kg) = 9 . 44756 kg . keywords: 002 (part 1 of 1) 10 points A rectangular air mattress is 1 . 85 m long, 0 . 616 m wide, and 0 . 0617 m thick. The acceleration of gravity is 9 . 8 m / s 2 . If it has a mass of 1 . 21 kg, what additional mass can it support in water? Correct answer: 69 . 1033 kg. Explanation: The buoyant force exerted by the water, F w , is F w = ρ w V g = (1000 kg / m 3 )(1 . 85 m)(0 . 616 m)(0 . 0617 m) × (9 . 8 m / s 2 ) = 689 . 071 N . Thus, the total weight that can be supported is: w = m g = 689 . 071 N . The total mass supported is the sum of the mass of the mattress and the mass of the load, or M = m mattress + m = 689 . 071 N 9 . 8 m / s 2 = 70 . 3133 kg . The load mass is therefore: m = M - m mattress = 70 . 3133 kg - 1 . 21 kg = 69 . 1033 k keywords: 003 (part 1 of 1) 10 points A block of mass 5 . 1 kg is completely immersed in a liquid of density 908 kg / m 3 . The block is suspended by a thin wire, which experiences a tension of 25 . 6 N.

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Homework 19 - Gozick Brandon Homework 19 Due 7:00 pm Inst D...

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