1) A person on a diet might lose 1.9 kg per week. Express the mass loss rate in
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Question
1)A person on a diet might lose 1.9 kg per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss. ___mg/s
In the United States, a doll house has the scale of 1:12 of a real house (that is, each length of the doll house is 1/12 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:144 of a real house. Suppose a real house has a front length of L = 21 m, a depth of 12 m, a height of 6.0 m, and a standard sloped roof (vertical triangular faces on the ends) of height h = 3.4 m.
A person on a diet might lose 1.9 kg per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss. ___mg/s In the United States, a doll house has the scale of 1:12 of a real house (that is, each length of the doll house is 1/12 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:144 of a real house. Suppose a real house has a front length of L = 21 m, a depth of 12 m, a height of 6.0 m, and a standard sloped roof (vertical triangular faces on the ends) of height h = 3.4 m. What is the volume of the corresponding doll house in cubic meters? What is the volume of the corresponding miniature house in cubic meters? The Earth has a mass of 5.98 times 1024 kg. The average mass of the atoms that make up the Earth is about 38 u. Based on this average mass, how many atoms are in the Earth? Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The units of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police could not easily interfere. (Presumably, the police were originally upset because a Smoot is not an SI base units, but these days they seem to have accepted the units.) The figure below shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 75.0 Smoots in Willies? What is the length of 75.0 Smoots in Zeldas? Pluto is approximately a sphere of radius 1.5 times 106 m. What is its circumference in kilometers? What is its surface area in square kilometers? What is its volume in cubic kilometers?Explanation / Answer
1) 1.9kg/week = 1900000mg/week = 1900000mg/7*24*60*60 secs = 3.14mg/sec
2)
volume of normal house = 12*21*6 + 0.5*12*3.4*21 m^3 = 1940.4 m^3
a) volume of doll house = 1940.4/12^3 = 1.123 m^3
b) volume of meniature house = 1940.4/144^3 = 6.49*10^-4 m^3
3)mass of earth = 5.98 * 10^24 kg
mass of each atom =38 u = 6.3100479*10^-26kg
so number of atoms = 5.98 * 10^24/6.3100479*10^-26 = 9.4769 * 10^49
4)a) 75 smoots = 75*258/212 = 91.27 willies
b)212-32 smoots = 216-60 Zeldas
so 75 smoots = 75*156/180 = 65 zeldas
5)a)circumference = 2*pi*r = 2pi*1.5*10^3 kms = 9.42 * 10^3 kms
b)surface area = = 4pir^2 = 4pi*(1.5*10^6)^2 = 2.83 * 10^13 m^2 = 2.83*10^7 km^2
c) volume = (4/3)pi*r^3 = (4/3)pi*(1.5*10^3)^3 = 1.413 * 10^10 km^3
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