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Chapter 1: Problem 93

The canoe gliding gracefully along the water in the photograph is made of concrete, which has a density of about \(2.4 \mathrm{g} / \mathrm{cm}^{3}\). Explain why the canoe does not sink.

Short Answer

Expert verified
The concrete canoe does not sink because the overall density of the canoe (concrete + air) is less than the water density. Therefore, it can displace a weight of water equal to its own weight, resulting in floating due to Archimedes' principle.

Step by step solution

01

Understanding the question

We must explain why the concrete canoe does not sink in water even though the density of concrete is greater than the density of water, which is \(1 \mathrm{g} / \mathrm{cm}^{3}\). The exercise is based on the principle of Archimedes or buoyancy.
02

Understanding Archimedes' Principle

Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. This is why a hollow canoe floats; the weight of the water it displaces is equal to its own weight.
03

Applying the principle to our canoe

Although the canoe is more dense than the water due to the concrete, there is also air inside the canoe. This contributes to the overall density of the canoe, making it to be less than the density of water. Hence, the canoe can displace a weight of water equal to its own weight, making it able to float.

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Most popular questions from this chapter

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.

A tabulation of data lists the following equation for calculating the densities \((d)\) of solutions of naphthalene in benzene at \(30^{\circ} \mathrm{C}\) as a function of the mass percent of naphthalene. $$d\left(\mathrm{g} / \mathrm{cm}^{3}\right)=\frac{1}{1.153-1.82 \times 10^{-3}(\% \mathrm{N})+1.08 \times 10^{-6}(\% \mathrm{N})^{2}}$$ Use the equation above to calculate (a) the density of pure benzene at \(30^{\circ} \mathrm{C} ;\) (b) the density of pure naphthalene at \(30^{\circ} \mathrm{C} ;\) (c) the density of solution at \(30^{\circ} \mathrm{C}\) that is 1.15\% naphthalene; (d) the mass percent of naphthalene in a solution that has a density of \(0.952 \mathrm{g} / \mathrm{cm}^{3}\) at \(30^{\circ} \mathrm{C} .[\text { Hint: For }(\mathrm{d}),\) you need to use the quadratic formula. See Section A-3 of Appendix A.]

Describe the necessary characteristics of a scientific theory.

Blood alcohol content (BAC) is sometimes reported in weight-volume percent and, when it is, a BAC of \(0.10 \%\) corresponds to \(0.10 \mathrm{g}\) ethyl alcohol per \(100 \mathrm{mL}\) of blood. In many jurisdictions, a person is considered legally intoxicated if his or her BAC is 0.10\%. Suppose that a 68 kg person has a total blood volume of 5.4 L and breaks down ethyl alcohol at a rate of 10.0 grams per hour. \(^{*}\) How many 145 mL glasses of wine, consumed over three hours, will produce a BAC of \(0.10 \%\) in this 68 kg person? Assume the wine has a density of \(1.01 \mathrm{g} / \mathrm{mL}\) and is \(11.5 \%\) ethyl alcohol by mass. (* The rate at which ethyl alcohol is broken down varies dramatically from person to person. The value given here for the rate is a realistic, but not necessarily accurate, value.)

In an attempt to determine any possible relationship between the year in which a U.S. penny was minted and its current mass (in grams), students weighed an assortment of pennies and obtained the following data. $$\begin{array}{lllllll}\hline 1968 & 1973 & 1977 & 1980 & 1982 & 1983 & 1985 \\\\\hline 3.11 & 3.14 & 3.13 & 3.12 & 3.12 & 2.51 & 2.54 \\\3.08 & 3.06 & 3.10 & 3.11 & 2.53 & 2.49 & 2.53 \\\3.09 & 3.07 & 3.06 & 3.08 & 2.54 & 2.47 & 2.53 \\\\\hline\end{array}$$ What valid conclusion(s) might they have drawn about the relationship between the masses of the pennies within a given year and from year to year?
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