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Schedule. Final Exam: Wednesday, May 12, 10:30 am. The quiz Friday will be on chapter 10, sections 1-6. . 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 % Old % A 87 89.5 B 77 79.5 C 67 69.5

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slide1

Schedule

Final Exam: Wednesday, May 12, 10:30 am.

slide2

The quiz Friday will be on chapter 10, sections 1-6.

  • 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 % Old %

A 87 89.5

B 77 79.5

C 67 69.5

D 57 59.5

slide3

F2 = ?

F1

A1

A2

P2 = ?

P1 = F1 / A1

fluid

10-4 Pascal’s Principle

Pressure applied to a confined fluid increases the pressure throughout by the same amount.

Pressure is same throughout, so P2 = F2/A2 = P1 = F1/A1.Thus F2 = (A2 / A1) F1.

slide4

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

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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?

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“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…”

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‘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.’

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‘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.”

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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.’

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“‘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.’ ”

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Archimedes is remembered by most of us as a mathematician, but he also invented fabulous war machines.

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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.

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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.
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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.

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OSE: B = fluid g Vdisplaced.

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

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.

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B

a

y

w = mg

x

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!

OSE: Fy = may

By + wy = may

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B

a

y

w = mg

x

Substitute for generic quantities:

fluid g Vlog + (-mg) = +ma

Solve:

a = (fluid g Vlog - mg) / m

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

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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.