PHY1033C/HIS3931/IDH 3931 : Discovering Physics:
The Universe and Humanity’s Place in It
Fall 2015
Prof. Peter Hirschfeld, Physics
Announcements
• HW 2 due Sept. 15
• Turn in lab writeups
• Reading: Gregory Chs. 2,3 Wertheim
(coursepack), Lindberg (coursepack)
Last time
Last time
• Review of position, velocity from modern perspective (slides on web)
• Development of medieval scientific thought: attempt to reconcile a
rediscovered Aristotle with church teachings.
• Medieval critiques of Aristotle’s theories of motion: idea of
“impressed force” to keep an arrow moving after it has left the bow.
•Possibility of “infinitite rectilinear motion” if one can remove
resistance understood in 1300s.
Clicker quickies
Which of the following mathematical devices for describing
planetary motions discussed in the Almagest was the
contribution of Ptolemy himself?
a.
b.
c.
d.
e.
homocentric spheres
epicycles on deferent
eccentric circles
equant point
all of the above
Introduction of mathematics into discussion of moving bodies (1300s):
Mertonians (Oxford) : definitions of velocity and acceleration
Nicole Oresme (U. Paris) graphical representation and theorems
Acceleration
Velocity was the rate of change of the position of an
object. What's the rate of change of the velocity called?
Def: acceleration-- rate of change of the velocity
of an object.
average acceleration
a = ∆v/∆t
Q: Can you have a=0 and v ≠ 0?
A: Yes, when object has constant velocity!
Q: Can you have a ≠ 0 and v = 0 ?
A: Yes, e.g. when you throw a ball up and it is at the very top
of its trajectory before starting back down: a=-9.8m/s2, v=0.
Q: Can you have a ≠ 0, v = constant?
A: Yes, when something is going in a circle at constant
speed, it is continuously changing the direction of its
velocity, so a ≠ 0.
In this course, we have referred to “uniform circular motion”
where a planet moves at constant speed
v
later time 2
time 1
v
From modern perspective, since it’s velocity direction is
changing, it is accelerating. Greeks & medievals
would not have called this acceleration.
Equations of motion
Already know one special equation for something
moving at constant velocity,
∆x = v ∆t.
If we measure with respect to the origin of the coordinate system at t=0
(choose xi=0 and ti=0), then we just write
x = v t.
What about if acceleration is constant? This would occur if you are keeping
the gas pedal depressed at a fixed angle for a few seconds, or when an object
is in free fall near the Earth's surface.
Constant acceleration a
The same kind of reasoning as above leads to
v = a t,
The velocity increases at a constant rate! You might be
tempted to substitute this into our x-equation, but
this is wrong, because x = v t is only good for constant
velocity, not changing velocity. It turns out for the special
case of constant a, we get
v =a t
x = ½ a t2
constant acceleration only!
Marco Polo’s journey
Pace of exploration quickened in the 1400s
1. New navigational techniques
2. Royal funding
Traditional Navigation techniques
If latitude of a location was known, it could be reached
The cross staff
N
New technique: The magnetic compass
Location 2
Location 1
A captain could not always control where the ship went
Numerous islands were discovered when
a ship was blown about by storms
Pace of exploration quickened in the 1400s
1. New navigational techniques
2. Royal funding
Why did kings start supporting travel?
Ottoman ruler
Sultan of Egypt
Food in medieval times was very bland
So the West began to be interested in exploration
Encouraged geographical
exploration
Heard of a gold trade south
along Africa’s coast
Wanted to find Prester John
Prince Henry of Portugal
1394-1460
Cape Nun
By 1450
A Portugal
new
kingwas
gotslave
secretive,
Popetrade
Sixtus
but
IVSpain
to issue
began
a bull
to in
be1481
interested
confirming
Lucrative
established
Portugals’s right to lands south of the Canary Islands
1487
Bartholomeu Diaz
Cape of Good Hope
The success of Columbus forced the creation of a new papal treaty
1494
Returned, 1499
Encountered Arabs
Vasco da Gamma
1497
By 1509 Portuguese were
in the Spice Islands
Now that India had been reached by sea,
was there another route to the East?
Columbus
studied
Ptolemy’s
Read had
Paolo
Toscanelli
–
Reduced
Began
trying
distance
to
persuade
to
3500
miles
Distance
from
Africa
to
China
not
great
After
rejection,
turned
to
Spain
Geography
and
Polo’s Travels
distance
= Marco
5000 miles
Portuguese in 1480s
UsedLeft
dead
forreckoning,
Canary the
Islands
not
celestial
August,
navigation
1492
Columbus
underreported
distances
he calculated
to the crew
Gold ornaments the of inhabitants of the islands
convinced him he had reached islands off China
Others became convinced
Inspired
that
what
by
thethese
voyages
of Columbus,
One
Other
who
voyages
used
to the
words
east
coast
was the
of South
Columbus had revealed was
he
visited
a new
the
world
Gulf and
the
eastern
Italian
America
geographer
convinced
Amerigo
him
that
Vespucci
this territory
coast
of the U.S.
in a continent
voyage of 1497
represented
a new
map of
of the
150716th century
The world at theWorld
beginning
Waldseemüller
was a differentMartin
place from
what it had been
The goals were the same as they had been in the East – spices, gold, and Christians
Ironically as theIn
Before
world
became
Copernicus
new,stumbled
there
Europeans
wasupon
another
looked
world
backwards
shaking
to event
regain
lost wisdom
the process
they
a new
vision
of the
cosmos
In 1505
he signed
on at 24
to athe
20-ship
Expected
resistance
from
Sultanfleet
From the lesser Portuguese nobility
the kingofcommissioned
take over
Egypt and theto
Indian
rajahsspice trade
Ferdinand Magellan
(~1480-1521)
Cannanore
Malacca
Back
inwas
Portugal
he fell
out
ofactions
favor
at
Was notFrustrated
able
Magellan
to
persuade
by
the
rejections,
promoted
the king
tofor
he
search
his
turned
forto
shorter
the
incourt
these
king
route
ofcampaigns
Spain
to the Spice Islands
Magellan claimed to have learned about the existence of
18-year
old Emperor
Charles
I found
the idea
intriguing
But after
He also
being
reported
disappointed
a geographer’s
with
Columbus,
conclusion
theabout
king’s
the
advisors
Treaty
were
of Tordesailles
against it
a pass from a document in the Portuguese archives
Afirst
fleet
of
5 ships
set
September
20,
with
Magellan
command
The
location
offarther
the off
supposed
passsouth
was
just
the
of
river
Magellan
pushed
and
farther
– he
was
caught
ina in
awide
bind
Other
4 ships
had
Spanish
captains
who
did
not
trust
the
Portuguese
admiral
But
the
farther
south
he
went,
the1519
more
hismouth
hopes
waned
Three
Heships
knewarrived
he could
in the
notPhilippines
be to
Magellan
determined
farintake
from
thethe
the
spring
Spice
offor
1521
Islands
land
Spain
Since those left behind in Malacca were later captured
When the Victoria
into port
Spain
there
were but 18 crew left
Thenstumbled
cargo of spices
did in
pay
for the
voyage
these were the only survivors of the original 265