hw10 - irshad(si2865 – HW10 – distler –(57205 1 This...

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Unformatted text preview: irshad (si2865) – HW10 – distler – (57205) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. A somewhat shorter homework for this week... 001 10.0 points A copper telephone wire has essentially no sag between poles 39 m apart on a winter day when the temperature is − 17 ◦ C. How much longer is the wire on a summer day when the temperature is 33 ◦ C? As- sume that the thermal coefficient of copper is constant throughout this range at its room temperature value of 1 . 7 × 10 − 5 ( ◦ C) − 1 . Correct answer: 3 . 315 cm. Explanation: Let : T = − 17 ◦ C , L = 39 m , T 1 = 33 ◦ C , and α = 1 . 7 × 10 − 5 ( ◦ C) − 1 . The relation between length and tempera- ture is Δ L = L 1 − L = L α ( T 1 − T ) , = (39 m) bracketleftbig 1 . 7 × 10 − 5 ( ◦ C) − 1 bracketrightbig × [33 ◦ C − ( − 17 ◦ C)] parenleftbigg 100 cm 1 m parenrightbigg = 3 . 315 cm . 002 (part 1 of 2) 10.0 points An air bubble originating from an under water diver has a radius of 9 . 8 mm at some depth h . When the bubble reaches the surface of the water, it has a radius of 7 mm. Assuming the temperature of the air in the bubble remains constant, determine the abso- lute pressure at this depth h . The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 2 . 77144 × 10 5 Pa. Explanation: Let : ρ = 1000 kg / m 3 , g = 9 . 8 m / s 2 , P atm = 1 . 01 × 10 5 Pa , R 1 = 7 mm = 0 . 007 m , and R 2 = 9 . 8 mm = 0 . 0098 m . From the ideal gas law P V = nRT = constant , so P 1 V 1 = P atm V atm P 1 P atm = V atm V 1 P 1 P atm = 4 3 π R 3 2 4 3 π R 3 1 P 1 = P atm R 3 2 R 3 1 = (1 . 01 × 10 5 Pa) (0 . 0098 m) 3 (0 . 007 m) 3 = 2 . 77144 × 10 5 Pa . 003 (part 2 of 2) 10.0 points Determine the depth of the diver. Correct answer: 17 . 9739 m. Explanation: The absolute pressure is P 1 = P atm + ρg h h = P 1 − P atm ρg = 2 . 77144 × 10 5 Pa − 1 . 01 × 10 5 Pa (1000 kg / m 3 ) (9 . 8 m / s 2 ) = 17 . 9739 m ....
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hw10 - irshad(si2865 – HW10 – distler –(57205 1 This...

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