Basic Concepts in Physics

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The Formula for Density

The Formula for Density

You calculate a substance's density by dividing mass by volume.

The density of water VS. the density of lead

There is the same volume of water and lead in this image?

Does the lead and the water in this image have the same mass?

So the water and the lead have the same volume (1 litre), but different mass. Do you think water and lead have the same density?

Which substance is more dense?

The formula for density

First of all, 1 litre is the same as $1,000 \space cm^3$

So 1 litre of water or lead is the same as $1,000 \space cm^3$ of water or lead.

Have a look at the image. What is the mass of $1,000 \space cm^3$ of lead?

Now, the density of lead is $11.34 \space g/cm^3$ . So how do you calculate the density of lead?

So you calculate the density of lead like this $\frac{11,340 \space g}{1,000 \space cm^3}$ . So what is the generalised formula for calculating density?

What is the density of water in $g/cm^3$ ?

Recap!

The density of an object is dependent on its volume and mass

For example, if you have two objects of the same volume, but one has more mass than the other, then the heavier object will be the denser one.

The formula for density is $density = \frac{mass}{volume}$

The density of water is $1 \space g/cm^3$ The density of lead is $11.34 \space g/cm^3$

So one litre of lead is more than 11 kilos heavy

That is more than 11 times heavier than the same amount of water!

Units for density

$g/cm^3$ is probably most common unit used for the density of substances on Earth. Which one of these options could we also use?

The unit $kg/cm^3$ also contains a unit for mass and a unit for volume, so it is a density unit. However, we don't use it much, because it implies that an object is extremely _____________.

So the more common units for density are $g/cm^3$ or $kg/m^3$

We don't really use for example $kg/cm^3$ about objects on Earth, because materials here just aren't so dense that they weigh several kilos per cubic centimetre!

A substance has mass $16 \space g$ and volume $8 \space cm^3$ . What is the substance's density in $g/cm^3$ ?

A substance has mass $240 \space kg$ and volume $6 \space m^3$ . What is the substance's density in $kg/m^3$ ?

Which one of these objects is the most dense? Answer A, B or C.

Summary!

The formula for density is $density = \frac{mass}{volume}$

This gives you units like $g/cm^3$ or $kg/m^3$

For example, here object C is denser than objects A and B

Object A has a density of $3 \space g/cm^3$

Object B has a density of $5 \space g/cm^3$

Object C has a density of $6\space g/cm^3$