Physics Demystified, 2nd edition

Stan Gibilisco

Explanations for Quiz Answers in Chapter 5

1. A solid material that we can stretch into a long, thin strand exhibits excellent ductility. The correct choice is B. Hardness (choice A) has little or nothing to do with how easily we can stretch a material. A material with a high degree of brittleness (choice C) can't stretch very much, if at all, without breaking. Viscosity (choice D) generally applies to liquids, not to solids.

2. The mass of any particular material sample does not depend on the gravitational acceleration to which we subject it. If we move an object from one planet to another, its mass won't change. Therefore, if its volume remains the same, its mass density will also remain the same. The correct choice is A.

3. The weight of any particular material sample, unlike the mass, varies depending on the gravitational acceleration in the environment. If we move an object from one planet to another, then its weight will increase or decrease in direct proportion to the change in the gravitational acceleration. If its volume remains the same, therefore, its weight density will increase or decrease right along with its weight. If an object has a weight density of 1.5 x 104 N/m3 on our planet and we take it to Mars where the gravitational acceleration is 37% (0.37 times) the earth's gravitational acceleration, then its weight density will decrease to 0.37 x 1.5 x 104 = 5600 N/m3, which we can also express as 5.6 x 103 N/m3. The answer is B.

4. According to Pascal's law for incompressible liquids, the forces that we impose on the pistons (or the forces that the pistons themselves exert) vary in direct proportion to the surface areas that the pistons expose to the liquid medium. In the situation shown by Fig. 5-6 on page 156 (and described in the text for this question on page 155), the left-hand piston exposes 0.040 m2 of surface area to the liquid, while the right-hand piston exposes 0.010 m2 to the liquid. The area of the left-hand piston therefore equals 4.0 times the area of the right-hand piston. The right-hand piston exerts an upward force of 12 N. We must impose 4.0 times as much force, or 48 N, downward on the left-hand piston in order to produce the described effect on the right-hand side. The correct choice is A.

5. We have a rubber cord with a spring constant of 0.20 meters per newton (m/N) for stretching forces of up to 10 N. Our cord measures exactly 1.0 m long when we don't impose any stretching force on it. If we pull outward on the ends of the cord with a net force of 3.0 N (well within the maximum force limit of 10 N), the cord's length will increase by 0.20 x 3.0 = 0.60 m. With the applied stretching force, the cord will measure 1.0 + 0.60 = 1.6 m long. The correct choice is C.

6. A volume of exactly one milliliter (1 ml) equals exactly one cubic centimeter (1 cm3), which in turn equals exactly 0.000001 cubic meter (10-6 m3). Our liquid has a mass density of 1500 kg/m3. To get the mass density in kilograms per milliliter (or kilograms per centimeter cubed), we multiply this figure by 10-6, getting 0.001500 kg/ml. Because one kilogram (1 kg) equals precisely 1000 grams, we can convert the mass density value to 0.001500 x 1000 = 1.500 g/ml. If we take 80.00 ml of this stuff and pour it into a container, we'll end up with 80.00 x 1.500 g, or 120.0 g, of liquid in the container. The correct choice is C.

7. Our cubical container measures 10.0 cm, or 0.100 m, along each edge, so the chamber's volume equals (0.100)3 = 0.00100 m3. We recall that one mole (1 mol) equals 6.02 x 1023. If we gather up 3.01 x 1022 atoms, we have (3.01 x 1022) / (6.02 x 1023) = 0.0500 mol of atoms. If we put them all into our cubical container and let them float around so that they attain a uniform density throughout the interior, we'll have 0.0500 mol of atoms in a volume of 0.00100 m3. The particle density therefore equals 0.0500 / 0.00100 = 50.0 mol/m3. The correct choice is C.

8. If we place samples of two different gases into a confined space, and if those gases have nearly identical mass densities, they'll readily diffuse. The question poses a false premise! The answer is A.

9. If we place a solid object having a specific gravity of 1.2 into a container of pure liquid water, and if the object doesn't dissolve in the liquid, the object will sink to the bottom of the container. (We assume, of course, that this experiment takes place in an environment with gravitational acceleration such as the earth's surface, and not in a "weightless" situation such as we'd have in an orbiting spacecraft!) The correct choice is C.

10. The Mohs scale was invented so that people can conveniently estimate the hardness of a solid sample. The answer is D.