Density

Derived Units Not all quantities can be measured with

base units.

25 mph 25 miles

hour

A derived unit is one that is derived by

a combination of units.

Volume

The volume of a solid is a derived unit.

1 cm x 1 cm x 1 cm = 1 cm3

Length x Width x Height = Volume

Volume

Volume Volume of irregular shaped objects can

be measured using Archimedes

Principle and the water displacement

method

Water Displacement

200 mL

Add the object

Note the initial volume

Subtract the initial volume

from the final volume

260 mL – 200 mL = 60 mL

Why does one object sink

while another, of similar

volume, float?

Is it really weight?

Mass per Volume There is more mass per unit of

volume in the bowling ball

Mass 1 Bowling Ball = Mass of 18 Basketballs

Density Density refers to the amount of matter

(mass) there is in a given amount of

space (volume)

Derived Units

Solids - g/cm3 Liquids – g/mL

Calculating Density

Density Problem What is the density of gold, if one liter

has a mass of 19,280 g?

d = m/v

m = 19,280 g v = 1,000 mL

d = m/v = 19,280 g/1,000 mL

d = m/v = 19.3 g/mL

When people used to pan for gold, they often found

pyrite, otherwise known as fool’s gold. The only way

they could be sure if they had found real gold was to

determine the density of the material.

Most substances have

a unique density.

Pyrite has a

density of

5.01 g/mL

Gold has a

density of

19.3 g/mL

Real Life Application

Solving for Mass

Density = Volume

Mass

d = m

v

(v)(d) = m(v)

v

Mass= (Volume)(Density)

1

2

3 (v)(d) = m

m = (d)(v) 4

Mass Problem What is the mass of 20 cm3 of gold

that has a density of 19.3 g/cm3?

m = dv

d = 19.3 g/cm3 v = 20 cm3

m = dv = (19.3 g/cm3)(20 cm3)

m = 386 g

Solving for Volume

Density = Volume

Mass

d = m

v

(v)(d)= m (v)

v

Volume = Mass / Density

1

2

3 (v)(d) = m

d

v = m

d

4

Volume Problem Gold has a density of 19.3 g/cm3.

What is the volume of 60 g of gold?

m = 60 g d = 19.3 g/cm3

v = m/d

V = m/d = 60 g/19.3 g/cm3

V = 3.1 cm3

Density of Water 1 g of water is equal to 1 cm3 or 1 mL

1 cm

Density = Mass

Volume

Density = 1 g = 1 g/cm3

1 cm

Sink or Float?

Objects with a

density less than

1 g/cm3 will float

Density of water is 1g/mL or 1 g/cm3

Objects with a

density greater than

1 g/cm3 will sink

Coke vs. Diet Coke

39 g of

sugar 125 mg of

aspartame