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Chapter 1: Problem 5

(a) Three spheres of equal size are composed of aluminum \(\left(\right.\) density \(\left.=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right),\) silver \(\left(\right.\) density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the spheres from lightest to (b) Three cubes of equal mass are composed of gold \(\left(\right.\) density \(\left.=19.32 \mathrm{~g} / \mathrm{cm}^{3}\right)\), platinum (density \(\left.=21.45 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and lead (density \(\left.=11.35 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the cubes from smallest to largest. [Section 1.4]

Short Answer

Expert verified
(a) The order of spheres from lightest to heaviest based on density is: aluminum, nickel, and silver. (b) The order of cubes from smallest to largest volume based on equal mass and reciprocal densities is: platinum, gold, and lead.

Step by step solution

01

Since the spheres have the same volume, we can use the mass and density relationship: mass = density × volume. To compare their masses, we can ignore the volume factor and simply compare their densities because volume is the same for all spheres. 2. Compare the densities

We are given the densities: aluminum (2.70 g/cm³), silver (10.49 g/cm³), and nickel (8.90 g/cm³). Comparing the densities, we find the order is aluminum < nickel < silver. 3. List the spheres from lightest to heaviest
02

Based on density comparison, the order from lightest to heaviest is: aluminum, nickel, and silver. #Part (b)#: 1. Determine the relationship between mass, density, and volume for equal mass cubes

Since the cubes have the same mass, we can use the mass and density relationship: mass = density × volume. To compare their volumes, we can rearrange the formula to: volume = mass / density. In this case, we can ignore the mass factor and just compare the reciprocal of their densities because mass is the same for all cubes. 2. Compare the reciprocal of the densities
03

We are given the densities: gold (19.32 g/cm³), platinum (21.45 g/cm³), and lead (11.35 g/cm³). Taking the reciprocal of the densities, we have: gold (1/19.32), platinum (1/21.45), and lead (1/11.35). Comparing these values, we find the order is platinum > gold > lead. 3. List the cubes from smallest to largest

Based on the reciprocal density comparison, the order from smallest to largest volume is: platinum, gold, and lead.

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Most popular questions from this chapter

A \(40-\mathrm{lb}\) container of peat moss measures \(14 \times 20 \times 30 \mathrm{in}\). A \(40-\mathrm{lb}\) container of topsoil has a volume of 1.9 gal. (a) Calculate the average densities of peat moss and topsoil in units of \(\mathrm{g} / \mathrm{cm}^{3}\). Would it be correct to say that peat moss is "lighter" than topsoil? Explain. (b) How many bags of peat moss are needed to cover an area measuring \(15.0 \mathrm{ft} \times 20.0 \mathrm{ft}\) to a depth of 3.0 in.?

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (c) \(77 \mathrm{~K},(\mathbf{d}) 100,000 \mathrm{~km}^{2},\) (b) \(374.2 \mathrm{mg}\) (e) \(1.06 \mu \mathrm{m},(\mathrm{f}) 16 \mathrm{nm}^{2}\) \((g)-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\), (i) \(28 \mathrm{~cm}^{3}\). [Section 1.4].

A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains \(1.50 \mathrm{~g}\) of carbon and \(2.00 \mathrm{~g}\) of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains \(6.35 \mathrm{~g}\) of carbon. How many grams of oxygen does it contain? Which law are you assuming in answering this question?

A thief plans to steal a gold sphere with a radius of \(28.9 \mathrm{~cm}\) from a museum. If the gold has a density of \(19.3 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the sphere in pounds? [The volume of a sphere is \(\left.V=(4 / 3) \pi r^{3} .\right]\) Is the thief likely to be able to walk off with the gold sphere unassisted?

Show the steps to convert the speed of sound, 344 meters per second, into miles per hour. [Section 1.6]
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