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
1+2=3
:you’ve got to move the 2 over
: 1+2-2=3-2
1=3-2  1 =1
:you’ve got to move the 1 over
: 1-1+2=3-1
: 2=3-1
:2=2
A+B=C
A+B=C
:move the B over
: A+B-B=C-B
: A=C-B
: move the A over
: A-A+B=C-A
: B=C-A
A=C :
B
: move what over?
: A x B=C x B
B 1
1
: A=C x B
A=C x B : move what over?
: 1 x A=C x B x 1
C
C
:A=B
C
CANCEL UNITS
CANCEL UNITS
D=M :
V
: D x V=M x V
1 V 1
: D x V=M
CANCEL UNITS
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
DxV
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)
Greater than
1g/mL
H2O (1g/mL)
Mass
(g)
Less than 1g/mL
Volume (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?)
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:
Velocity = 7.3 m/s
Time = 25 seconds
2. Unknown:
Distance
3. Formulas:
Base: v = d/t
Working: d = vt
4. show work: (cancel, sigfigs, units, circle answer)
d = vt
= 7.3 m/s x 25 s
= 182.5 m
= 180 m
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?