Lecture: Density(Mikey’s Lecture)

(video: https://www.youtube.com/watch?v=1PJTq2xQiQ0)

1,2,3 A,B,C Don’t You Know it’s:DENSITY!!!

How do you isolate the circled number/letter?:1+2=3 :you’ve got to move the 2 over

: 1+2-2=3-21=3-2 1 =1

1+2=3 :you’ve got to move the 1 over: 1-1+2=3-1 : 2=3-1: 2 = 2

A+B=C :move the B over: A+B-B=C-B : A=C-B

A+B=C : move the A over: A-A+B=C-A : B=C-A

A=C : : move what over?

B

: A x B=C x B CANCEL UNITS

B 1 1

: A=C x B

A=C x B : move what over?

: 1 x A=C x B x 1 CANCEL UNITS

C C

: A = B

C

D=M : V

: D x V=M x V CANCEL UNITS

1 V 1: D x V=M

Key point: what you do to one side of the equal sign,you must do to the other side too(that’s what equal means!!)

1. Density is mass per unit volume:

per = divide therefore it is a fraction

ie: price per pound: $/lb

: miles per gallon: mi/gal

So: density is a measure of two variables of the same substance:

it’s how much matter there is for the volume of the

same stuff !!!!!!!

Example:

Tear a piece of paper in half:

Each piece has half the volume and

half the mass, but

it is still paper with the same density no matter the size:

it’s called a characteristic property, like finger prints or

DNA sequences

2. Formula for density

Density = mass divided by volume

D = M (rise)

V (run)

density is a broken heart

or:

density is mountains over valleys: M

V

or: M

D x V

3. Density of pure water (H20) = 1.000g/ml

4. Density is a characteristic property: solids?, gasses?

5. unit for density =

g/cm3 (key point: two units! for same stuff)

mass: amount of matter present, its heft:

gram is the unit (must be dry, why?)

volume is space occupied by matter:

solid: cm3 is the unit,

measured LxWxH; or

with water displacement for irregular objects

liquid: use a graduated cylinder:

mL is the unit

remember: 1cm3 = 1mL (goal posts)

Mass (g)

Volume (mL)

H2O (1g/mL)

Less than 1g/mL

Greater than1g/mL

•Why are the axis labeled this way (hint: formula for slope)?•Where is the line for the Titanic before/after it hits the iceberg?•For the same substance, the density will be the same, no matter

how much you have = straight line.•Also, the density will be different for different substances because

it is a characteristic property: soda cans, density columns•What is the density: of all gases?

:almost all solids? (not ice/wood?):submarines/hot air balloons?

Required format for solving word problems:

4 steps:

• K: Know: state what you know: what is the given info

• ?K: unknown: state what you are trying to solve for: the unknown

• F: state the formulas which are needed for the solution, two types:

-base formula

-working formula

• Show work: apply working formula, show work, cancel units, k-b-c-m, circle answer, units

Word Problem Flow Chart

Question: A cart travels at a velocity of 7.3 m/s for 25 seconds. How far did the cart travel?

1. Know: 4. show work: (cancel, sigfigs, units, circle answer)

Velocity = 7.3 m/s d = vt

Time = 25 seconds = 7.3 m/s x 25 s

2. Unknown: = 182.5 m

Distance = 180 m

3. Formulas:

Base: v = d/t

Working: d = vt

Examples of word problems:

What is the density of a substance with a mass of 15.2g and a volume of 2.7 ml?

What is the volume of an unknown rock which has a density of 3.44 g/cm3 and a mass of 0.0039 kg?