Physics 10 Homework Solutions

Chapter 12

(1) In a crystalline substance such as ordinary table salt, atoms are located in an orderedfashion throughout the material. For instance, in table salt, the sodium (Na) ions and Chlorineions (Cl) are located at the corners of cubes that repeat throughout. In an amorphous solid,such as ordinary glass, the atoms have no ordered arrangement; instead, they are randomlydistributed throughout the material.

(2) When a loaf of bread is squeezed, the amount of space it occupies is decreased. The volumeof a body is defined to be the amount of space it occupies, so the volume of a loaf of bread de-creases as it is squeezed. However, a squeezed loaf of bread contains the same number (andtype, of course) of atoms as it did before it was squeezed. Thus, its mass remains the same.Since the density of a body is its mass divided by its volume, the density of the loaf of breadincreases as it is squeezed.

(3) Tension results from a stretching. For instance, two teams in a tug-o-war are pulling on therope, which stretches the rope and puts tension in the rope. Compression results from a squash-ing. For instance, when a statue is placed on a pedestal, the weight of the statue down on thepedestal squashes it slightly and places it in compression.

(4) Water expands when it freezes. Its mass, however, remains the same. If its volume is largerwith the same mass, its density, which is its mass divided by its volume, must decrease as itfreezes.

(5) A 100 kg of small apples contains a larger number of small apples than 100 kg of largeapples. To make things simple, suppose we have one apple that weighs 100 kg and eight applesthat weigh 12.5 kg each. A 12.5-kg apple has one eighth the volume of the 100-kg apple, whichmeans that its radius is of the radius of the 100-kg apple because a linear dimen-sion cubed is a volume. The surface area goes like the square of the radius, so the surface areaof a 12.5-kg apple is the surface area of the 100-kg apple. However, we have eight 12.5-kgapples, so the surface area of all the apples is times the surface area of the 100-kgapple. Thus, the larger the number of apples for a given total mass of apples, the greater thesurface area. In case you are interested, the general formula (treating the apples as spheres) is

1 2where n and n are the numbers of apples in the two batches, each of which has the same

1 2mass, and A and A are the respective total surface areas. Thus, the candy maker needs lesstaffy to cover the larger apples.

(6) In a dry desert climate, the human body keeps cool by perspiring. We will learn why in alater chapter. The body stores water in its volume, but loses water through its surface. Theratio of the surface area of a child to its volume is larger than the same ratio for an adult.Everything else being equal (which is not the case), a child will need to drink more water thanan adult.