Density

DensityWe know that matter is

anythingthat occupies a space and hasmass.

Density is the amount of matter there is in a given space.

Mass = the amount of matter in an object

Volume = the space an object occupies

ExamplesMetal vs. Wood

Metal

Wood

Water vs. Oil

Water

Oil

The amount of particles there are in the metal and water that occupies the space provided is a lot more than the amount of particles present in the oil and wood in the same amount of space.

Water and metal are more dense.

What do we use density for?

Density is one of the basic ways to measure and compare the physical properties of different matter

Which one is more dense?

People in a square (popular place vs. not popular place)

How about this: Which square is more dense?

A B

•Do they occupy the same volume?

•Do the have the same amount of particles?

Which one is more dense?

Now which one is more dense?

•Do they occupy the same volume?

•Do the have the same amount of particles?

B

A

A is more dense because for the small volume it holds, it has more matter.

Even though they have the same amount of particles, if A was the same size as B, A would have 4 times as much particles.

B

A A A

A A

What is density?

To find density, the amount of mass (a measurement if the particles present) is divided by the volume of the substance.

Density = mass OR mass ÷ volume.

volume

Mass is measured in grams and kilograms.Volume is measured in cubic centimeters

or cubic milliliters.Mass

Grams is represented as a g Kilograms is represented as a kg

VolumeCubic centimeters = cm, solidCubic milliliters = mL, liquid1mL3 = 1cm3

So if Density = mass , Density = g or g

3

3

volume cm3 mL3

ALWAYS REMEMBER

UNITS!

SI Units: International System of UnitsModern metric system, measurements

Mass Grams = g Kilograms = kg Length Meter = m Millimeter = mmLiquid Liters = L Milliliter = mL

Time Seconds = s Milliseconds = ms

Conversions Milli = m __ centi= c __ Kilo =k __

ALWAYS REMEMBER

UNITS!

Let’s try a density problem together

Frank has a paper clip. It has a mass of 9g and a volume of 3cm3. What is its density?

Given:

D =

m =

V =

Formula:

Solve:

Answer:

V

mD

?

9 g

3cm3

D= m/V =9g/3cm3

= 3g/cm3

3g/cm3

ALWAYS REMEMBER

UNITS!

Frank also has an eraser. It has a mass of 4g, and a volume of 2cm3. What is its density?

Given:

Formula

Solve:

Answer:

V

mD

D = ?

m =4 g

V =2cm3

D= m/v =4g/2cm3

= 2g/cm3

2g/cm3

ALWAYS REMEMBER

UNITS!

Work on these problems with your neighbor.

Jack has a rock. The rock has a mass of 6g and a volume of 3cm3. What is the density of the rock?

Jill has a gel pen. The gel pen has a mass of 8g with a volume of 4cm3. What is the density of the rock?

Now, try these on your own.

Alicia has a watch. It has a mass of 4g and a volume of 2cm3. What is the density of the watch?

Mia has a wallet. It has a mass of 15g and a volume of 5cm3. What is the density of the wallet?

•To actually calculate density we need measuring instruments.•To measure the mass, we need to use a balance.

•If we use a scale, we measure the weight of the object. The weight is the force due to gravity pulling down.

•You weigh less on the moon because gravity is less. But the amount of particles you are made of doesn’t change.

•Only mass is measured by the balance because the object’s mass counteract with the weights on the balance.

Measuring the volume of an object can be very tricky as well. Most objects are not regular shapes that we have formulas for to calculate the volume.

Cube orCubic

rectangle

lw

hCylinder

r

h

hwlV hrV 2

Frank measured another eraser. He used a balance to measure the mass at 4g. However Frank is having trouble finding the volume. Can you help him?

l = 5cmw = 1cm

h = 2 cm hwlV

Given:

Formula

Solve:

Answer:L = 5 cmw = 1 cmh = 2 cm

hwlV

V = 5cm x 1cm x 2cm

= 10 cm3

10 cm3

ALWAYS REMEMBER

UNITS!

Frank has a cup for soda. He wants to know how much soda the cup could hold so he measures the volume of the cup. What is the volume?

hrV 2

d = 4 cm

h = 10 cm ALWAYS REMEMBER

UNITS!

d

π has a numerical value of 3.14. The Formula can be written V = 3.14 x r 2 x h

Before we attempt this problem here are some clarification:

What’s the area of a circle?

A = π x r 2

= π x r x r

The volume is just the area of the base times the height.

V = π x r 2 x h

d is twice the radius so: d = 2 x r

r = d/2

d = 4 cm

h = 10 cm

d

Frank has a cup for soda. He wants to know how much soda the cup could hold so he measures the volume of the cup. What is the volume?

hrV 2

d = 4 cm

h = 10 cm

Given:

Formulas:

Solve:

Answer:

V = ?

r = ? Cm

d = 4 cm

h = 10 cm

r = 4 cm/2

= 2 cm

V = 3.14 x (2cm)2x 10 cm

= 3.14x (2cm) x (2cm) x 10 cm

= 3.14 x 40 cm3

= 125.6637 cm3 = 125.66 cm3

125.66 cm3

ALWAYS REMEMBER

UNITS!

d

= 3.14 x r 2 x hd = 2 x r, r = d/2

r2 =r x r

V = 3.14 x r 2 x h

r = d/2

That’s where volume by displacement comes into play.

When you think of displacement, what do you think of?

In real life, most objects only resemble these shapes.

Most objects are odd shaped.

It is almost impossible to accurately calculate the volume of most objects.

The object takes a certain amount of space.

The water particles rises to a new final volume. VF

The difference in the water levels from before and after will give you the volume of the object.

In volume by displacement, the displacement of water or any other liquid is involved.

In a graduated cylinder, we measure the initial volume of water. V1

Then we drop our object in.

What is the volume of this object?

Vo= ?

Vf =

Vi =

Vo =

The equation for volume of displacement

Volume of the object = Volume of water after –

Volume of water before

Vo = Vf-Vi

9 mL

7 mL

9mL – 7mL

2mL

Measuring Accuracy There many type of errors

Instrumental: The balance is not calibrated right Human Error: mathematical, looking at the ticks on the

instruments, eyes play trick on you.

When measuring Volume of liquids: Meniscus: Bottom arch water of used for measuring

volume.

Liquid Layers

If you pour together liquids that don’t mix and have different densities, they will form liquid layers.

When liquids don’t mix that means they’re _____________The liquid with the highest density will be

on the bottom.The liquid with the lowest density will be

on the top.

insoluble

Liquid Layers Which layer has the highest

density? Which layer has the lowest

density? Imagine that the liquids on the

left have the following densities: 10g/cm3. 3g/cm3. 6g/cm3. 5g/cm3.

Which density would go with which layer?

Liquid Layers – Try with your neighbor

Which liquid has the highest density?

Which liquid has the lowest density?

Which liquid has the middle density?

Liquid Layers – Try on your own!

Imagine that the liquids on the right have the following densities: 15g/cm3 10g/cm3

3g/cm3 9g/cm3

7g/cm3 12g/cm3

Match the colors to the correct densities.

3g/cm3

7g/cm3

9g/cm3

10g/cm3

12g/cm3

15g/cm3

Review

What is the formula for density?What two methods can be used to

measure volume?What is a meniscus?What happens if you pour together liquids

that have different densities?Will the liquid on the top have the highest

or lowest density?Will the liquid on the bottom have the

highest or lowest density?

Super Scientist Question of the Day

Jake has a book, a ruler, and a balance. How can Jake find the density of the

book with the tools he has?

Practice Volume by displacement and density at:

http://www.sciencejoywagon.com/explrsci/media/density.htm

Website is on the Homework page under Friday 6th.