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DENSITY. OR, WHY DO SOME THINGS FLOAT WHILE OTHERS SINK. What Is Density?. Density is how heavy something is for its size. Density is mass divided by volume or D=m/v Where D equals density, m equals mass and v equals volume. Another Way of Looking at It.

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density

DENSITY

OR, WHY DO SOME THINGS FLOAT WHILE OTHERS SINK.

what is density
What Is Density?
  • Density is how heavy something is for its size.
  • Density is mass divided by volume or

D=m/vWhere D equals density, m equals mass and v equals volume

another way of looking at it
Another Way of Looking at It.
  • You will often hear density referred to as “mass per unit volume.”
  • Let’s break this down:
  • Mass is how much matter the object has.
  • Per simply means divided by
  • Unit volume is a measure of how much space it takes up
slide4
So…
  • When you hear mass per unit volume, you should think…
  • Take the mass and divide by its volume!
what are the units of density
What Are the Units of Density?
  • Mass units would include
    • Grams for very small objects or
    • Kilograms for larger objects
  • Volume units would include
    • Cubic centimeters for small objects or
    • Cubic meters for large objects
    • Milliliters for small amounts of liquids
    • Liters for larger amounts of liquid
  • Lets stick to grams and cubic centimeters for now.
how to state density units
How to State Density Units
  • You have grams for mass
  • You have cubic centimeters for volume
  • These are not the same units, they don’t cancel so you have to include both units in your answer
how to state density units1
How to State Density Units
  • The units of density are:
  • Grams/Cubic Centimeter or

g/cm3

why cubic centimeters
Why Cubic Centimeters
  • Remember that volume is

length multiplied by width multiplied by height or

l X w X h

  • In each case, the distance is in cm and since you are multiplying it three times, you get cubic centimeters.
  • Easy huh!
now how about an example

Mass= 100 grams

l=10 cm

h=5 cm

w=2 cm

Now, How About an Example?

Use the information provided to calculate the density of the object

what did you get
What Did You Get?
  • If you got 1g/cm3, you are correct!
  • Lets see how this works:

V=l x w x h

V=10 cm X 5 cm X 2 cm

V=100cm3

Mass = 100 g (given)

D=m/v

D=100 g/100cm3=1g/cm3

a few words about the mass volume relationship of liquids and solids
A Few Words About the Mass/volume Relationship of Liquids and Solids.

When working with a sample of any liquid or solid - wood, steel, or peanut butter,

  • If you decrease the mass, you also decrease the volume
  • If you decrease the volume, you also decrease the mass
a few words about the mass volume relationship of liquids and solids1
A Few Words About the Mass/volume Relationship of Liquids and Solids.

When working with a sample of any liquid or solid - wood, steel, or peanut butter,

  • If you increase the volume, you also increase the mass
  • If you increase the mass, you also increase the volume
let s think about it for a second
Let’s Think About It for a Second.
  • If you add more peanut butter to the pile (more mass) it is going to take up more space (more volume)
  • If you remove peanut butter from the pile (less mass) it is going to take up less space (less volume)
what about volume
What About Volume?

The same holds true for volume.

  • If you start with the volume of peanut butter in the jar (lets say 16 oz) and you have to move it into another container (say 2 oz). You definitely have less peanut butter in the 2 oz jar than in the 16 oz jar therefore the mass of the 16 oz of peanut butter would be more than the mass of the 2 oz of peanut butter. Remember, we’re not massing the jars but the contents of the jars.
does the density change when mass and volume change
Does the Density Change When Mass and Volume Change?
  • The answer is NO and here is why:
  • Density is a proportional relationship meaning as long as mass and volume are in proportion to each other, the density of a liquid or solid remains the same. This is how we know that certain objects have a predictable density regardless of the sample size.
let me prove it to you

l=10 cm

h=5 cm

Mass= 100 grams

w=2 cm

What would happen to its density if we cut it in half?

l=5 cm

l=5 cm

h=5 cm

h=5 cm

50 grams

50 grams

w=2 cm

w=2 cm

Let Me Prove It to You.
  • Let’s start with the object from a previous slide
  • Recall that the density was 1.0 g/cm3
let me prove it to you1

l=5 cm

l=5 cm

h=5 cm

h=5 cm

50 grams

50 grams

w=2 cm

w=2 cm

Let Me Prove It to You.
  • The new volume of either half is:5 cm x 5 cm x 2 cm = 50 cm3
  • The new mass of either half is:100g ¸ 2 = 50g
  • So, the new density of either is:50g/50cm3 or still 1.0 g/cm3
what about gases
What About Gases?
  • By definition, gases have no specific volume and no specific shape
  • They expand or contract to entirely fill the vessel containing them
  • So, gases can have different densities, depending on their conditions
  • In fact, that is what distinguishes them from liquids
  • For this class, you will be given the density of a gas, as opposed to having to calculate it
a word about irregularly shaped objects
A Word About Irregularly Shaped Objects.
  • If you are given an irregularly shaped object and told to find the density, you might have a problem.
  • If the length, width, and height of the object are not uniform (the same), you cannot use l X w X h to determine volume.
a word about irregularly shaped objects1
A Word About Irregularly Shaped Objects.
  • To determine the volume of an irregularly shaped object, start with a graduated cylinder of water filled about half full
  • Record the volume of water in the cylinder
  • Drop in the irregularly shaped object
  • Record the volume of water in the cylinder with the object in it
  • Subtract the original volume from the second volume to determine the volume of the object
a word about irregularly shaped objects2
A Word About Irregularly Shaped Objects.
  • You are measuring the amount of water displaced by the object which is equal to the volume of that object
  • This is called:

volume by displacement

  • Cool!!
liquids
Liquids
  • So far we have been talking mostly about solids. Solids have densities that can be easily expressed in g/cm3
  • Liquids tend to be measured in milliliters or liters. This is not a problem because you can convert milliliters or liters into grams per cubic centimeter using a metric conversion factor
liquids1
Liquids
  • You can also weigh a liquid to determine its mass. Now we are going to use the word massing for weighing to avoid confusion
  • To do this, measure your cylinder in grams and record its empty mass
  • Add your liquid
  • Now mass the cylinder again
  • Subtract the mass of just the cylinder and you have the mass of your liquid
liquids2
Liquids
  • To determine the volume, simply look at where the liquid measures in your cylinder and record the amount
  • In order to convert your volume reading (milliliters or liters) you would use a conversion factor to change milliliters or liters to cubic centimeters.
liquids3
Liquids
  • For this class, you will be given liquid densities already converted to g/cm3
  • Whew!
ever notice
Ever Notice…
  • When you fill a glass with water, there isn’t a large bubble of air at the bottom of your cup.
  • When you put ice in your water it floats to the top.
that s because
That’s Because
  • Air is less dense than water and will naturally be displaced by the water and the air will be at the top.
  • Ice is also less dense than water by just a little bit. That is why your ice floats to the top of your water.
  • Now you know!!!
some general comments about density
Some General Comments About Density
  • In order to compare the density of two objects, they must first be in the same units (g/cm3)
  • The material with the lower density will always float to the top of the material with the higher density (think ice and water), as long as the materials don’t react with each other and mix
sink or float
Sink or Float?
  • Solids can float or sink in a liquid.

Can you guess what kind of solid would sink in water?

answer
Answer:
  • Any solid will sink in water if it has a density greater than the density of water.
  • Water has a density of 1g/cm3. Any solid with a density greater than 1g/cm3 will sink in water!
sink or float1
Sink or Float?
  • Comparing densities to determine if something will float, only makes sense if at least one of the materials is a liquid
  • A piece of steel (high density) can sit on top of a piece of wood (low density) because the wood cannot float through the steel!