UT hw 1 Measurement - Solution

UT hw 1 Measurement - Solution - xu (px228) Homework 1...

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Unformatted text preview: xu (px228) Homework 1 nevils (77401) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Welcome to UT Homework! This assign- ment has 21 questions. I will use this forum to assign you some AP multiple choice and free response questions. You may always col- laborate, but you must do all of the work yourself. You will have plenty of time to com- plete this assignment, which is Due Saturday at 11:59. Please always pay attention to your due dates! They will not always be the same day. Your first exam will be September 4th. Good luck! 001 10.0 points It is known that the total volume of water in the oceans is approximately 1 . 26 10 10 km 3 . The density of sea water is 1040 kg / m 3 , and the heat capacity of the water is 4270 J / kg C. Estimate the increase in mass of sea water corresponding to an increase in temperature of 72 . 7 C. Correct answer: 4 . 51985 10 10 kg. Explanation: Let : V = 1 . 26 10 10 km 3 = 1 . 26 10 19 m 3 , = 1040 kg / m 3 , c h = 4270 J / kg C , and T = 72 . 7 C . The energy increase corresponding to a tem- perature change is E = c h V T = (4270 J / kg C) (1040 kg / m 3 ) (1 . 26 10 19 m 3 ) (72 . 7 C) = 4 . 06786 10 27 J , so the corresponding mass increase is m = E c 2 = 4 . 06786 10 27 J (3 10 8 m / s) 2 = 4 . 51985 10 10 kg . keywords: 002 (part 1 of 2) 10.0 points The radius of a certain planet is 5 . 63 10 7 m, and its mass is 6 . 98 10 26 kg. Find the density of this planet. Hint: The volume of a sphere is given by 4 3 r 3 . Correct answer: 0 . 933774 g / cm 3 . Explanation: Let : r = 5 . 63 10 7 m and m = 6 . 98 10 26 kg . Convert the mass of the planet to grams (1 kg = 1000 g). Convert the radius to cm (1 m = 100 cm). Use the given formula to find the volume of the planet in cm 3 . 003 (part 2 of 2) 10.0 points Find its surface area s in square feet. Hint: The surface area of a sphere is given by 4 r 2 . Correct answer: 4 . 28784 10 17 ft 2 . Explanation: For the second part convert the radius to ft (1 m = 3 . 28 ft). 004 10.0 points A cylinder, 19 cm long and 8 cm in radius, is made of two different metals bonded end-to- end to make a single bar. The densities are 4 . 5 g / cm 3 and 6 . 3 g / cm 3 . 1 9 c m 8 cm , radius What length of the lighter-density part of the bar is needed if the total mass is 19941 g? Correct answer: 11 . 4009 cm. xu (px228) Homework 1 nevils (77401) 2 Explanation: Let : = 19 cm , r = 8 cm , 1 = 4 . 5 g / cm 3 , 2 = 6 . 3 g / cm 3 , and m = 19941 g . Volume of a bar of radius r and length is V = r 2 and its density is = m V = m r 2 so that m = r 2 x x r Let x be the length of the lighter metal; then x is the length of the heavier metal....
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UT hw 1 Measurement - Solution - xu (px228) Homework 1...

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