Question

homework problem set:

1. a large piece of wood has a volume of 2.0m³ and a mass of 1200 kg. what is the density of this piece of wood?

1. a dry beaker has a mass of 55.0 g. when 50.0 ml of water is added to the beaker, the mass of the water and the beaker is 105.0 g. what is the density of the water?

1. a rectangular object is 15.0 cm long, 10.0 cm wide and 5.0 cm thick. the object has a mass of 450g.

a) what is the density of the object?
b) will the object float or sink in water? how do you know?

1. a bar of gold is 5.0 cm thick, 10.0 cm long and 2.0 cm wide. it has a mass of exactly 193.0 g. what is the density of gold?

Explanation:

Problem 1

Step1: Recall density formula

Density formula is $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Substitute values

Given $m = 1200\ kg$, $V = 2.0\ m^3$. Substitute into formula: $
ho=\frac{1200\ kg}{2.0\ m^3}$.

Step3: Calculate density

$\frac{1200}{2.0}=600\ kg/m^3$.

Step1: Find mass of water

Mass of water $m =$ mass of beaker and water $-$ mass of beaker $= 105.0\ g - 55.0\ g = 50.0\ g$.

Step2: Recall density formula

Density $
ho=\frac{m}{V}$, volume of water $V = 50.0\ mL$ (since $1\ mL = 1\ cm^3$, $V = 50.0\ cm^3$).

Step3: Substitute and calculate

$
ho=\frac{50.0\ g}{50.0\ cm^3}=1.0\ g/cm^3$.

Step1: Calculate volume of object

Volume of rectangular object $V = l\times w\times h$, where $l = 15.0\ cm$, $w = 10.0\ cm$, $h = 5.0\ cm$. So $V = 15.0\times10.0\times5.0 = 750\ cm^3$.

Step2: Recall density formula

$
ho=\frac{m}{V}$, mass $m = 450\ g$.

Step3: Substitute and calculate

$
ho=\frac{450\ g}{750\ cm^3}=0.6\ g/cm^3$.

Answer:

The density of the wood is $600\ kg/m^3$.

Problem 2