HW1-phy2048-Spring-2014-solution

1km 1m in these units the thickness becomes 1 phy2048

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Unformatted text preview: area and the thickness. The area of the semicircle is A = πr2/2, where r is the radius. Therefore, the volume is π V = r2 z 2 where z is the ice thickness. Since there are 103 m in 1 km and 102 cm in 1 m, we have ⎛ 103 m ⎞ ⎛ 102 cm ⎞ 5 r = ( 2000 km ) ⎜ ⎟⎜ ⎟ = 2000 × 10 cm. ⎝ 1km ⎠ ⎝ 1m ⎠ In these units, the thickness becomes 1 PHY2048 Spring 2014 HW1 ⎛ 102 cm ⎞ 2 z = 3000 m = ( 3000 m ) ⎜ ⎟ = 3000 × 10 cm ⎝ 1m ⎠ which yields V = π 2000 × 105 cm 2 ( ) (3000 × 10 2 2 ) cm = 1.9 × 1022 cm3 . 1P23. We introduce the notion of density: ρ= m V and convert to SI units: 1 g = 1 × 10−3 kg. (a) For volume conversion, we find 1 cm3 = (1 × 10−2m)3 = 1 × 10−6m3. Thus, the density in kg/m3 is −3 3 ⎛ 1 g ⎞ ⎛ 10 kg ⎞ ⎛ cm ⎞ 3 3 1 g cm3 = ⎜ 3...
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