Density Dive

How much is packed in

A small pebble can be heavier than a large balloon. That surprises people because they judge by SIZE, but the real measure is DENSITY: how much mass is packed into a given amount of space. You work it out by dividing the mass by the volume, so density is mass divided by volume. ⭐⭐ This is why size can fool you. A large object made of a light, spread-out material can weigh less than a small object made of a heavy, tightly packed one. What matters is the mass for the space it takes up, not the space alone. ⭐ The particle picture fits neatly. In a solid the particles are packed closely together, so a solid is usually the densest state. In a gas the particles are spread far apart, so a gas is the least dense. A liquid sits in between. ⭐⭐ Density also decides floating and sinking. An object floats if it is LESS dense than the liquid it sits in, and sinks if it is MORE dense. A steel ship floats not because steel is light, but because its overall shape packs in a lot of air, making the whole ship less dense than water. This module is about density itself. The states of matter and how they change from one to another belong to a different module. ⚠️ Carry one question the whole way through: how much mass is in how much space, and does that float or sink?

Mass per space, and what it decides

The first column is how you find density, the second is the particle picture, and the third is what density decides.

Tap the two true of density

Tap the TWO statements about density that are TRUE.

• Density is the mass divided by the volume.
• A small dense object can weigh more than a large light one.
• The bigger an object is, the denser it must be.
• An object floats because it is more dense than the liquid.

Float or sink

A block is placed in water and it sinks. What does this tell you about the block?

• It is more dense than the water
• It is less dense than the water
• It is simply heavy, whatever its size
• It must be a large object

The language of density

Six terms this topic turns on. The first three are the calculation, the rest the states and floating.

Match each to what is true of it

Two true of the particle picture

Select the TWO statements that are TRUE about density and the arrangement of particles.

• A solid is usually densest because its particles are packed closely
• A gas is least dense because its particles are far apart
• A gas is the densest state
• A bigger object is always denser

Answering a density question

Density questions reward using the calculation cleanly and reasoning about floating. ⭐⭐ USE THE CALCULATION BOTH WAYS. Density is the mass divided by the volume. To find a mass, multiply the density by the volume; to find a volume, divide the mass by the density. Keep the units matched, grams with cubic centimetres or kilograms with cubic metres. ⭐ MEASURE VOLUME THE RIGHT WAY. For a regular block, multiply its lengths. For an odd shape, lower it into water and measure the water it pushes out of the way; that displaced water has the same volume as the object. ⭐⭐ DECIDE FLOATING BY COMPARING DENSITIES. An object floats if it is less dense than the liquid, and sinks if it is more dense. Never say it floats because it is light or small; say it floats because it is less dense than the liquid. EXPLAIN A SHIP CORRECTLY. Steel is denser than water, yet a steel ship floats because its shape encloses a lot of air, so the whole ship, air included, is less dense than water. It is the overall density that counts. ⚠️ A units habit. Put the mass on top and the volume underneath, keep the units consistent, and if a shape is irregular use displacement rather than guessing the volume. Keep the one question to hand: how much mass is in how much space, and does that float or sink?

Order how to find a density

Put the steps of finding the density of an irregular object into a sensible order.

• Measure the mass of the object on a balance
• Part-fill a measuring cylinder with water and read the level
• Lower the object in and read the new water level
• Subtract to find the volume of water pushed aside
• Divide the mass by that volume to get the density

Work out the density

A metal block has a mass of 240 grams and a volume of 30 cubic centimetres. Density is the mass divided by the volume. What is its density, in grams per cubic centimetre?

The density run

Five quick decisions about density. Three lives.

Two removal boxes, one size

Leave physics aside for a screen. Picture two moving boxes of exactly the same size sitting side by side on the floor. ⭐ One is crammed to the brim with heavy books; the other holds just a few soft cushions with plenty of empty space around them. They look identical from the outside, yet lifting them tells a very different story: the crammed box is a struggle, the loose one floats up in your hands. ⭐⭐ What made the difference was not the size of the box, which is the same for both. It was how much was packed into that same space. The more you cram into a fixed space, the heavier it is for its size; the more empty room you leave, the lighter it is for its size. So if someone asks which box is heavier without lifting it, the only useful question is how tightly each one is packed, not how big it is. ⭐ And drop both into a swimming pool: the book-crammed box goes straight down, while the barely filled one bobs on the surface, because it is so lightly packed for its size. ⚠️ Hold that picture. The box is a fixed space, the amount crammed in is the mass, how tightly it is packed for its size is the density, a tightly packed box behaves like a solid and a nearly empty one like a gas, and the lightly packed box bobbing up is exactly why a less packed object floats.

Finish each density line

The amount of mass packed into a given volume is the _____. Density is worked out as the mass divided by the _____. An object floats if it is less _____ than the liquid it sits in. In this state the particles are packed closely and it is usually the densest: a _____. In this state the particles are far apart and it is the least dense: a _____.

Three density puzzles

Three situations arise. For each, choose the response the density rules support.

• A large block of foam and a small ball bearing are dropped into water; the foam floats and the ball bearing sinks.
• You need the volume of an irregular pebble to find its density.
• A student is puzzled that a heavy steel ship floats when a small steel nail sinks.

Explain density and floating

Explain what density is and how you would measure it for an irregular object, and explain why some things float and others sink. Use the particle picture to say why a solid is usually denser than a gas.

• Define density as mass divided by volume
• Explain how to measure the volume of an irregular object by displacement
• Explain why an object floats or sinks by comparing its density with the liquid
• Use particles to explain why a solid is usually denser than a gas
• Explain why a steel ship can float even though steel is denser than water