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# TEST3 - Version 011/AAACD – TEST3 – Tsoi –(58020 1...

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Unformatted text preview: Version 011/AAACD – TEST3 – Tsoi – (58020) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 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 409 kg / m 3 is then poured into one arm of the tube, forming a column 6 . 2 cm in height, as shown. h 6 . 2 cm light liquid 409 kg / m 3 heavy liquid 1000 kg / m 3 What is the difference in the heights of the two liquid surfaces? 1. 10.98 2. 2.5298 3. 1.3528 4. 6.216 5. 3.6642 6. 1.728 7. 2.5 8. 1.4824 9. 3.48 10. 4.1635 Correct answer: 3 . 6642 cm. Explanation: Let : ℓ = 6 . 2 cm , ρ ℓ = 409 kg / m 3 , and ρ h = 1000 kg / m 3 . Because the liquid in the U-tube is static, the pressure exerted by the heavy liquid col- umn of height ℓ − h in the left branch of the tube must balance the pressure exerted by the liquid of height h poured into the right branch, so P + ( ℓ − h ) ρ h g = P + ℓ ρ ℓ g . h = ℓ parenleftbigg 1 − ρ ℓ ρ h parenrightbigg = (6 . 2 cm) parenleftbigg 1 − 409 kg / m 3 1000 kg / m 3 parenrightbigg = 3 . 6642 cm . 002 10.0 points A glass of ice water is sitting on the counter at room temperature. The water reaches the rim of the glass. Ice cubes stick out above the rim of the glass. What happens once the ice melts? 1. The water overflows. 2. There is not enough information given. 3. The level of the water remains the same. correct 4. The level of the water drops to below the rim. Explanation: Water has a greater density than ice. The ice cube and the water that the ice melts into are same. Therefore, they have the same mass. Because the ice cube is buoyant, no water is spilled. 003 10.0 points A light balloon is filled with helium at stan- dard temperature and pressure, and is then released from the ground. Use helium density 0 . 175 kg m 3 . The acceleration of gravity is 9 . 8 m / s 2 . Determine its initial acceleration in terms of the densities of helium and air. 1. 61.6237 2. 74.48 Version 011/AAACD – TEST3 – Tsoi – (58020) 2 3. 69.7094 4. 55.3649 5. 65.9006 6. 67.7583 7. 59.282 8. 54.7 9. 62.44 10. 60.8257 Correct answer: 62 . 44 m / s 2 . Explanation: Let : a = 9 . 8 m / s 2 , ρ He = 0 . 175 kg m 3 , and ρ air = 1 . 29 kg m 3 . summationdisplay F y = ma gives a = B − W m where B is the buoyant force and W is the weight of helium in the balloon. But B = ρ air V g, and W = mg = ρ He V g, so a = ( ρ air − ρ He ) V m g = parenleftbigg ρ air ρ He − 1 parenrightbigg ρ He V m g = parenleftbigg ρ air ρ He − 1 parenrightbigg g = parenleftbigg 1 . 29 kg m 3 . 175 kg m 3 − 1 parenrightbigg (9 . 8 m / s 2 ) = 62 . 44 m / s 2 ....
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TEST3 - Version 011/AAACD – TEST3 – Tsoi –(58020 1...

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