Schedule
April 19
8.8,9.1-9.3
April 21
9.1-9.3
April 23
Boardwork
Quiz 9
April 26
10.1-10.4
April 28
10.5-10.6
April 30
Boardwork
Quiz 10
May 3
11.1-11.4,
11.7
May 5
14.1-14.6
May 7
Review
May 12
Final Exam
May 14
May 10
Final Exam: Wednesday, May 12, 10:30 am.
The quiz Friday will be on chapter 10, sections 16.
Be able to do problems 10.3, 10.11, 10.15,
10.17, 10.23, 10.27.
The grade cutoffs as follows:
Letter Grade
New %
A
87
B
77
C
67
D
57
Old %
89.5
79.5
69.5
59.5
10-4 Pascal’s Principle
Pressure applied to a confined fluid increases the
pressure throughout by the same amount.
F2 = ?
F1
A1
A2
P2 = ?
P1 = F1 / A1
fluid
Pressure is same throughout, so P2 = F2/A2 = P1 = F1/A1.
Thus F2 = (A2 / A1) F1.
10-5 Measurement of Pressure:
Gauges and the Barometer
Interesting material. Please read. You won’t be tested on
this material.
10-6 Buoyancy and Archimedes’ Principle
Who remembers the story of
Archimedes* and the king’s
crown?
http://www.engineering.usu.edu/jrestate/workshop/buoyancy.htm:
“As the story goes, the king of
Syracuse had given a craftsman a
certain amount of gold to be made
into an exquisite crown.”
*If Archimedes was born and raised in Syracuse, Sicily, why do we consider him a Greek?
“When the project was completed, a rumor surfaced that the
craftsman had substituted a quantity of silver for an equivalent
amount of gold, thereby devaluing the crown and defrauding
the king.”
“Archimedes was tasked with determining if the crown was
pure gold or not. The Roman architect Vitruvious relates the
story…”
‘While Archimedes was
considering the matter, he
happened to go to the baths.
When he went down into the
bathing pool he observed
that the amount of water
which flowed outside the
pool was equal to the
amount of his body that was
immersed.’
‘Since this fact indicated the method of
explaining the case, he did not linger, but
moved with delight, he leapt out of the pool,
and going home naked, cried aloud that he
had found exactly what he was seeking.’
‘For as he ran he shouted in Greek: Eureka! Eureka! (Eureka
translated is "I have found it").’
“Although there is speculation as to the authenticity of this
story, it remains famous.”
“Probably no other tale in all of science combines the elements
of brilliance and bareness quite so effectively.”
“Whether the story is true or not, there is no doubt to the
truth of Archimedes understanding of buoyancy.”
Archimedes’ death also makes an interesting story:
“In 212 BC Syracuse surrendered to Rome. Before sending his
men to sack the city Marcellus told them ‘Spare that
mathematician.’ Plutarch records what happened next:”
‘As fate would have it, intent
upon working out some problem
by a diagram, and having fixed
his mind alike and his eyes upon
the subject of his speculation,
he [Archimedes] never noticed
the incursion of the Romans,
nor that the city was taken.’
“‘In this transport of study and contemplation, a soldier,
unexpectedly coming up to him, commanded him to follow
Marcellus; which he declining to do before he had worked out
his problem to a demonstration, the soldier, enraged, drew his
sword and ran him through.’ ”
Archimedes is remembered by most of us as a mathematician,
but he also invented fabulous war machines.
He also overcame our 34-foot straw problem (remember the
last lecture) by inventing the Screw of Archimedes.
www.nearingzero.net
What is not so well known about Archimedes is that he had a
career record of 40 wins and 28 losses while pitching for the
Cosmic Ionians. For proof, see here.
Finally, you can go here to read why the traditional story of
Archimedes and the king’s crown is probably not true:
http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html
What is important for us, and what Archimedes understood, is
that an object immersed in a fluid experiences a buoyant force
equal in magnitude to the weight of the fluid displaced.
Archimedes could have done this experiment:
The craftsman lives.
The craftsman dies.
Why a buoyant force? An object submerged in a fluid
experiences pressure. The pressure increases with depth.
Because P = F / A, the force per unit area on the object
also increases with depth.
Force on object by fluid
increases with depth.
Force is always  to
surface.
Horizontal forces cancel.
Upward force on bottom is
greater than downward
force on top.
Summary: an object submerged in a fluid experiences a
net upward force because the pressure in the fluid
increases with depth.
Your text shows how the net force is independent of the
shape of the object, and depends only on the weight of
the fluid displaced.
The weight of the fluid is mg = (g)V. The buoyant force
is
OSE:
B = fluid g Vdisplaced.
If the object is completely submerged, Vdisplaced = Vobject.
If the object is only partially submerged, Vdisplaced is the
volume of the submerged part of the object.
Example: a log having a volume of 2.0 m3 and a density
of 0.9 g/cm3 is held under water and released. What is
the acceleration of the log at the instant it is released?
First ask yourself: what kind of a problem is this?
“What is the acceleration…” so it must be a kinematics or
force problem. You are not given information about
positions, velocities, or times, so it sounds like a force
problem.
Draw a free body diagram!
B
a
OSE: Fy = may
By + wy = may
y
x
w = mg
Substitute for generic quantities:
fluid g Vlog + (-mg) = +ma
Solve:
a = (fluid g Vlog - mg) / m
B
a
y
x
w = mg
Use the density and volume of the log to get its mass:
m = log Vlog
a = (fluid g Vlog - log Vlog g) / log Vlog
a = (fluid - log) g / log
a = ( 1.0 - 0.9) g / 0.9
(using water = 1 g/cm3)
(I admit--a bit sloppy with units here.)
a = (1/9) g
The rest of chapter 10.
This is good physics. It’s a shame we don’t have time to
study it. Some of the material may be useful for life
science students. I suggest you skim the material so
that you know where to look if the need arises in the
future.
I will demonstrate Bernoulli’s Principle: “where the
velocity of a fluid is high, the pressure is low, and where
the velocity of a fluid is low, the pressure is high.
Demonstrations: collapse the bridge (done), put the
dime in the cup (skip), soda rollers, atomizer (done),
loud sound.