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# oldhw1_s - oldhomewk 01 YOO HEE Due 4:00 am Explanation...

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oldhomewk 01 – YOO, HEE – Due: Jan 17 2008, 4:00 am 1 Question 1, chap 1, sect 5. part 1 of 1 10 points A newly discovered giant planet has an av- erage radius 17 times that of the Earth and a mass 181 times that of the Earth. Calculate the ratio of the new planet’s den- sity to the Earth’s density. Correct answer: 0 . 036841 (tolerance ± 1 %). Explanation: Let : R n = 17 R E and m n = 181 m E . Density is the ratio of mass to volume, ρ = m V . A spherical planet of average radius R has volume 4 3 π R 3 and hence density ρ = m 4 3 π R 3 . For two planets of respective radii R 1 and R 2 and masses m 1 and m 2 we have ρ 1 ρ 2 = m 1 4 3 π R 3 1 m 2 4 3 π R 3 2 = parenleftbigg m 1 m 2 parenrightbigg parenleftbigg R 1 R 2 parenrightbigg 3 = 181 (17) 3 = 0 . 036841 . Question 2, chap 1, sect 5. part 1 of 1 10 points A sphere of metal has a radius of 5 . 7 cm and a density of 6 . 81 g / cm 3 . What is the mass of the sphere? Correct answer: 5282 . 75 g (tolerance ± 1 %). Explanation: Let : r = 5 . 7 cm and ρ = 6 . 81 g / cm 3 . Density is mass per unit volume, so ρ = m V m = ρ V = ρ 4 3 π r 3 = ( 6 . 81 g / cm 3 ) 4 3 π (5 . 7 cm) 3 = 5282 . 75 g . Question 3, chap 1, sect 99. part 1 of 1 10 points A cylinder, 20 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 5 g / cm 3 and 6 . 1 g / cm 3 . 20 cm 8 cm What length of the lighter metal is needed if the total mass is 21565 g? Correct answer: 13 . 4041 cm (tolerance ± 1 %). Explanation: Let : = 20 cm , r = 8 cm , ρ 1 = 5 g / cm 3 , ρ 2 = 6 . 1 g / cm 3 , and m = 21565 g .

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oldhomewk 01 – YOO, HEE – Due: Jan 17 2008, 4:00 am 2 Volume of a bar of radius r and length is V = π r 2 and its density is ρ = m V = m π r 2 so that m = ρ π r 2 x x r Let x be the length of the lighter metal; then x is the length of the heavier metal. Thus, m = m 1 + m 2 = ρ 1 π r 2 x + ρ 2 π r 2 ( x ) = ρ 1 π r 2 x + ρ 2 π r 2 ρ 2 π r 2 x .
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oldhw1_s - oldhomewk 01 YOO HEE Due 4:00 am Explanation...

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