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Chapter 1: Problem 59
The density of aluminum is \(2.70 \mathrm{g} / \mathrm{cm}^{3} .\) A square piece of aluminum foil, \(22.86 \mathrm{cm}\) on a side is found to weigh 2.568 g. What is the thickness of the foil, in millimeters?
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A non-SI unit of mass used in pharmaceutical work is the grain (gr) $(15 \mathrm{gr}=1.0 \mathrm{g}) .$ An aspirin tablet contains 5.0 gr of aspirin. A 155 lb arthritic individual takes two aspirin tablets per day. (a) What is the quantity of aspirin in two tablets, expressed in milligrams? (b) What is the dosage rate of aspirin, expressed in milligrams of aspirin per kilogram of body mass? (c) At the given rate of consumption of aspirin tablets, how many days would it take to consume 1.0 kg of aspirin?
In the third century \(\mathrm{BC}\), the Greek mathematician Archimedes is said to have discovered an important principle that is useful in density determinations. The story told is that King Hiero of Syracuse (in Sicily) asked Archimedes to verify that an ornate crown made for him by a goldsmith consisted of pure gold and not a gold-silver alloy. Archimedes had to do this, of course, without damaging the crown in any way. Describe how Archimedes did this, or if you don't know the rest of the story, rediscover Archimedes's principle and explain how it can be used to settle the question.
Calculate the mass of a block of iron \(\left(d=7.86 \mathrm{g} / \mathrm{cm}^{3}\right)\) with dimensions of \(52.8 \mathrm{cm} \times 6.74 \mathrm{cm} \times 3.73 \mathrm{cm}\).
The volume of seawater on Earth is about \(330,000,000 \mathrm{mi}^{3} .\) If seawater is \(3.5 \%\) sodium chloride by mass and has a density of \(1.03 \mathrm{g} / \mathrm{mL}\), what is the approximate mass of sodium chloride, in tons, dissolved in the seawater on Earth ( 1 ton \(=\) 2000 lb)?
A typical rate of deposit of dust ("dustfall") from unpolluted air was reported as 10 tons per square mile per month. (a) Express this dustfall in milligrams per square meter per hour. (b) If the dust has an average density of \(2 \mathrm{g} / \mathrm{cm}^{3}\), how long would it take to accumulate a layer of dust \(1 \mathrm{mm}\) thick?
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