Hold a block of wood and a steel ball of the same size and the steel ball is far heavier, because each material packs a different mass into the same volume.
Density is mass divided by volume, so for one material it stays the same whether you chip off a little or gather a lot, which makes it a property you can use to tell materials apart.
Density also decides whether an object floats or sinks in water: less than water (1 g/cm³) and it floats, more and it sinks.
Change the mass and volume until the density drops below 1 and the object rises, and you can also see that the fraction under the water equals the density.
Same Size, Different Mass
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An object in water: less dense than water floats, denser sinks
10 g
8 cm³
💡 What Decides Floating and Sinking
①An object less dense than water floats and a denser one sinks. What matters is not heavy or light but the mass of equal volumes.
②The lower the density of a floating object, the more of it shows above the water. At 0.5 g/cm³ half of it is under water; at 0.9 g/cm³, 90 % is.
③Ice has a density of about 0.92 g/cm³, so it floats with most of it below the surface; an iceberg is far bigger under the water than above it.
④An object with the same density as water neither rises nor sinks and stays put at whatever depth it is placed.
Each Material Has Its Own Density
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Density of several materials (g/cm³): dashed line is water, 1.0
🔍 Density Is a Property of the Material
①One material has one density whatever the amount: a gold ring and a gold bar both have a density of 19.3 g/cm³.
②So measuring mass and volume is enough to guess what a material is. A fake gold crown mixed with silver comes out less dense than the real thing.
③Wood ranges from about 0.4 to 0.8 g/cm³ depending on the kind, but most of it is less dense than water and floats.
④For most materials a rise in temperature makes the volume grow, so the density drops slightly.
Calculating with the Density Formula
Density
ρ = mV
Density (g/cm³) = mass (g) ÷ volume (cm³): how many grams are packed into each cubic centimeter.
Finding mass
m = ρ × V
Mass = density × volume
Finding volume
V = mρ
Volume = mass ÷ density
📐 Measuring Mass and Volume
①Mass is measured with an electronic balance, in grams.
②The volume of a liquid or of a regular object is read with a graduated cylinder, and 1 cm³ = 1 mL.
③For an irregular stone, drop it into a graduated cylinder with water; how far the level rises is the stone's volume.
④Match units before dividing: change kg to g and L to mL (cm³).
Exam Key Points
Summary
ρ = mV
Density is fixed for each material, and comparing it with water (1 g/cm³) tells you whether an object floats or sinks.
🎯 Exam Points
①Density = mass ÷ volume, in g/cm³.
②The same material has the same density whatever the amount, so density helps identify materials.
③Less dense than water (below 1 g/cm³) floats; denser sinks.
④Ice (about 0.92) < water (1.0), so ice floats with most of it submerged.
⑤The volume of an irregular object is measured by the rise of the water level in a graduated cylinder.
Examples and Unit Test
Example 1
What is the density of an object with a mass of 60 g and a volume of 20 cm³?
1
Density is found by dividing mass by volume.
2
60 g ÷ 20 cm³ = 3 g/cm³, so each cubic centimeter of this object holds 3 g.
▸ 3 g/cm³
With mass in grams and volume in cm³ before dividing, the answer comes out in g/cm³ directly.
Example 2
If the object above, with a density of 3 g/cm³, is put into water (density 1.0 g/cm³), will it float or sink? Why?
1
Compare the object's density with water's: denser than water sinks, less dense floats.
2
3 g/cm³ > 1.0 g/cm³, so the object sinks.
▸ It sinks (the object's density > water's density)
It sinks not because its mass is large but because it is heavier than the same volume of water; a massive log still floats because its density is small.
Unit-test style
Which statement about density is correct?
①Density is found by mass × volume
②For the same material, density is the same even if the amount differs
③An object denser than water floats
④The unit of density is g
⑤Ice is denser than water, so it sinks
▸ ② For the same material, density is the same even if the amount differs
1
Density is a property of the material, so the same material has the same density whatever the amount; ② is correct.
2
Density is mass ÷ volume (①), an object denser than water sinks (③), the unit is g/cm³ (④), and ice (0.92) is less dense than water (1.0), so it floats (⑤).