Question

section 2.2 review

1. define density, write the formula (from memory!), and give two different units used to measure density.
2. one cubic centimeter (cm³) is the same volume as one
3. a materials density is the same, no matter how large or small the sample is, or what its shape is, as long as it is a solid, uniform piece of the material. explain how this is possible and give an example.
4. the density of balsa wood is about 170 kg/m³. convert to g/cm³. why do you think balsa wood, rather than oak or ash, is commonly used for building models? (use evidence from figure 2.9 on page 37.)
5. a certain material has a density of 0.2 g/cm³. is this material better for building a bridge or for making sofa cushions? explain, using evidence from figure 2.9 on page 37.
6. the piece of wood shown above has a mass of 20 grams. calculate its volume and density. then, use figure 2.9 on page 37 to determine which type of wood it is. what are the two factors that determine a materials density?
7. the density of maple wood is about 755 kg/m³. what is the mass of a solid piece of maple that has a volume 640 cm³?

Explanation:

Step1: Recall density formula

Density ($
ho$) is defined as mass ($m$) per unit volume ($V$), $
ho=\frac{m}{V}$. Common units are $kg/m^{3}$ and $g/cm^{3}$.

Step2: Answer question 2

$1$ cubic - centimeter ($cm^{3}$) is the same volume as one milliliter ($mL$).

Step3: Answer question 3

A material's density is the same for a solid, uniform piece regardless of size or shape because density is an intensive property. For example, a large gold cube and a small gold cube have the same density.

Step4: Convert density for question 4

We know that $1\ kg = 1000\ g$ and $1\ m^{3}=10^{6}\ cm^{3}$. So, if $
ho = 170\ kg/m^{3}$, then $
ho=170\times\frac{1000\ g}{10^{6}\ cm^{3}} = 0.17\ g/cm^{3}$. Balsa wood is good for building models because it is lightweight (low - density) as seen from its low density value compared to other woods in Figure 2.9.

Step5: Answer question 5

If $
ho = 0.2\ g/cm^{3}$, this material may be good for sofa cushions as it is likely to be soft and lightweight. From Figure 2.9, low - density materials are often more suitable for such applications.

Step6: Calculate volume and density for question 6

The volume of the rectangular - shaped wood $V = l\times w\times h=5\ cm\times3\ cm\times2\ cm = 30\ cm^{3}$. The density $
ho=\frac{m}{V}=\frac{20\ g}{30\ cm^{3}}\approx0.67\ g/cm^{3}$. The two factors that determine a material's density are the mass of the atoms/molecules in the material and how closely packed they are.

Step7: Calculate mass for question 7

First, convert the density of maple wood to $g/cm^{3}$. Since $
ho = 755\ kg/m^{3}=755\times\frac{1000\ g}{10^{6}\ cm^{3}} = 0.755\ g/cm^{3}$. Using $
ho=\frac{m}{V}$, we can solve for $m$. So, $m=
ho V=0.755\ g/cm^{3}\times640\ cm^{3}=483.2\ g$.

Answer:

1. Density is mass per unit volume, $

ho = \frac{m}{V}$. Common units: $kg/m^{3}$ and $g/cm^{3}$.

1. $1\ cm^{3}$ is the same as $1\ mL$.
2. A material's density is the same for a solid, uniform piece regardless of size or shape because it is an intensive property. Example: large and small gold cubes have the same density.
3. $170\ kg/m^{3}=0.17\ g/cm^{3}$. Balsa wood is good for building models due to its low density.
4. A material with $

ho = 0.2\ g/cm^{3}$ may be good for sofa cushions as it is likely soft and lightweight.

1. Volume $V = 30\ cm^{3}$, density $

ho\approx0.67\ g/cm^{3}$. Factors: mass of atoms/molecules and packing density.

1. Mass of maple wood piece is $483.2\ g$.