HOW TO SOLVE DENSITY PROBLEMS

USING THE D.U.F.A.S. METHODEarth/Physical Science

Mr. Woodruff

Physical property is a property that can be observed without changing the identity of the substance.

Physical Properties

Examples: viscosity conductivity malleability hardness magnetism

melting point boiling point density color

THE D.U.F.A.S. METHOD“DON’T BE A DUMMY, USE

D.U.F.A.S.!”

• Data - what do you know from the problem? What is the unknown you are solving for?

• Units – What are the units of the data given? Does every number have a unit?

• Formula- What is the formula you need to use to solve your problem?

• Arrange- Plug in your data to the formula

• Solve - crank up your calculator and get the answer

THE FORMULA FOR DENSITY

• Density is equal to the Mass of the object divided by the Volume of the object.

• D=m/v

• Power Triangles for

Densitymass

Densityvolumex

m

D vor

xx

HOW DO YOU FIGURE OUT MASS?

• Place your object on the weighing pan of a metric scale.

• Read and record the object’s mass in grams

or

• Zero out a triple beam balance and then place the object on the weighing pan.

• Slide the weight tabs on the beams until the indicator is balanced again. Add the total masses and record the total.

HOW DO YOU CALCULATE VOLUME

• If you have a regular shaped object, measure the object’s width, height, and length in centimeters. Multiply the three lengths together and record the value.

L x W x H = Volume

• If the object is irregular in shape use the Water Displacement Method.

Put the object in a beaker with a measured level of water.

Record the new level after you place it in the beaker. Subtract

the old initial measure (Vi) from new final measure (Vf) and you have the object’s volume in mL or cm3. Vf – Vi = V (object)

SELECT THE FORMULA

• Use the power triangle. Cover the unknown, what’s is visible is the formula.

• In our examples:

• to solve for D use: D= m/v

• to solve for m use: m= D x v

• to solve for V use: V = m/D

The right Formula gets the right answer !!

WHAT ARE THE UNITS?

• Mass is measured in g

• Volume is measured in cm3 or mL

• Density is measured in g/cm3 or g/mL

Does every number have a Unit?

GET THE DATA FROM THE PROBLEM: MASS, VOLUME & DENSITY TYPE

• What is the density of a brick measuring 10 cm x 15 cm x 20 cm massing 6000g.?

• Density = ? g/cm3

• Mass = 6000g

• Volume = 10cm x 15 cm x 20 cm = 3000 cm3

• Density = m/v = 6000g/ 3000 cm3

Density = 2 g/cm3

MASS, VOLUME& DENSITY PROBLEM

• What is the mass of a block of granite that has density of 5 g/cm3 and volume of 40 cm3?

• Mass Formula is m= D x v

• Arrange the data in the formula:

• ?g = 5g/cm3 x 40cm3

• Solve the equation:

• ?g = 5g/cm3 x 40cm3 = 200g

The granite has a mass of 200g.

GET THE DATA FROM THE PROBLEM: MASS, DENSITY & VOLUME TYPE

• What is the volume of a 900 gram chunk of lead with a density of 15 g/cm3?

• Volume = ?cm3

• Mass = 900 g

• Density = 15 g/cm

• Formula for Volume is V= m/D Volume equals mass divided by Density

• Arrange ?cm3 = 900 g / 15 g/cm3 = 60 cm3

The volume of the chunk of lead is 60 cm3

DENSITY IS AN INTRINSIC PHYSICAL PROPERTY

• The density of a substance is unchanging as long as the substance does not change.

A lump of gold has a density of 19.3 g/cm3. If you cut the lump in half, the density of the gold is still 19.3 g/cm3. The mass and volume of the “half lumps” would be half the original mass and volume; but the density would still be 19.3 g/cm3.

“SEE HOW IT’S DONE” PROBLEMS

Don’t be a dummy!

Use D.U.F.A.S.Data

UnitsFormula

Arrange

Solution

What is the density of a piece of iron that has a mass of 70.0g and a volume of 20.0 cm3

m=v =D =

70.0 g20.0 cm3 ? g/cm3

Formula for Density:

D= m/vArrange: ? g/cm3 = 70g/20 cm3

Data Table & Units

Solution: D= 3.5 g/cm3D.U.F.A.S.

I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125 grams. What must the volume be to have a density of 0.500 g/cm3 ( I want it to float of course!)

Data Table & Units

125.0 g? cm3 . 500 g/cm3

m= v =D =

Formula for Volume:V=m/D

Arrange:

? cm3 = 125g/.500 g/cm3

Solution: v= 250 cm3

D.U.F.A.S.D.U.F.A.S.

A block of aluminum occupies a volume of 15.0 cm3 and density of 3.0 g/cm3? What is its’ mass?

Data Table & Unitsm= v =D =

? g15.0 cm3 3.0 g/cm3

Formula for Mass: m= D x v

Arrange: ? g = 15.0 g/cm3 x 3.0 cm3Solution:The aluminum’s mass is 45.0 g

D.U.F.A.S.D.U.F.A.S.