Resnick & Halliday Solutions for Chapter: Measurement, Exercise 1: Problems

Grains of fine California beach sand is approximately spheres with an average radius of $60\mathrm{ }\mathrm{\mu m}$ and are made of silicon dioxide, which has a density of $2600 \mathrm{kg}\mathrm{ }{\mathrm{m}}^{-3}$. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube $1.00 \mathrm{m}$ on an edge?

$\left(a\right)$ Using the known values of Avogadro’s number and the atomic mass of sodium, find the average mass density of sodium atom assuming its radius to be about $1.90 \stackrel{\circ }{\mathrm{A}}$.

$\left(b\right)$ The density of sodium in its crystalline phase is $970 \mathrm{kg}\mathrm{ }{\mathrm{m}}^{-3}$. Why do the two densities differ? (Avogadro’s number, that is the number of atoms or molecules in one mole of a substance, is $6.023\times {10}^{23}$)

The mass and volume of a body are $5.324 \mathrm{g}$ and $2.5 {\mathrm{cm}}^3,$ respectively. What is the density of the material of the body?

A grocer’s balance shows the mass of an object as $2.500\mathrm{kg}$. Two gold pieces of masses $21.15 \mathrm{g}$ and $21.17 \mathrm{g}$ are added to the box. What is

(a) the total mass in the box and

(b) the difference in the masses of the gold pieces to the correct number of significant figure?

Einstein’s mass-energy equation relates mass $m$ to energy $E$ as $E={\mathrm{mc}}^2$ where $c$ is speed of light in vacuum. The energy at nuclear level is usually measured in $\mathrm{MeV}$, where $1\mathrm{ }\mathrm{MeV}=1.60218\times {10}^{-13} \mathrm{J}$. The masses are measured in unified atomic mass unit $\left(\mathrm{u}\right)$ where $1 \mathrm{u}=1.66054\times {10}^{-27} \mathrm{kg}$. Prove that the energy equivalent of $1 \mathrm{u}$ is $931.5 \mathrm{MeV}$.

On a spending spree in Malaysia, you buy an ox with a weight of $28.9$ piculs in the local unit of weights.$1 \mathrm{picul}=100 \mathrm{gins}, 1 \mathrm{gin}=16 \mathrm{tahils}, 1 \mathrm{tahil}=10 \mathrm{chees}$ and $1 \mathrm{chee}=10 \mathrm{hoons}$. The weight of $1 \mathrm{hoon}$ corresponds to a mass of $0.3779 \mathrm{g}$. When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions)

Water is poured into a container that has a small leak. The mass of the water is given as a function of time $t$ by $m=5.00t^{0.8}-3.00t+20.00$ with $t\ge 0, m$ in grams and $t$ in seconds.

(a) At what time is the water mass greatest?

(b) What is the greatest mass?

In kilograms per minute, determine the rate of mass change at

(c) $t=3.00 \mathrm{s}$ 

(d) $t=5.00 \mathrm{s}$

A vertical container with a base area measuring $14.0 \mathrm{cm}$ by $17.0 \mathrm{cm}$ is being filled with identical pieces of candy, each with a volume of $50.0 {\mathrm{mm}}^3$ and a mass of $0.0200\mathrm{g}$. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at the rate of $0.250\mathrm{cm}\mathrm{ }{\mathrm{s}}^{-1}$, at what rate (kilograms per minute) does the mass of the candies in the container increase?