1. Your Comments MK
I thought that buoyancy and pressure in relation to depth were the most confusing. I just don't understand where exactly all of the equations come from. Other that that, doesn't seem to be too complicated. I think this is Fairly easy compared to the previous material. Even though the homework was LONG I still managed to finish it! I just don't understand why you would make our last homework assignment that long. Oh yea will there be office hours after Monday? Why can't the rest of physics be this easy? AND THAT'S HOW TITANIC HAPPENED. THE END. (saw titanic right before i did the prelecture, connects very well with the floating and sinking part) I think one of my friends really wishes you were her grandpa. Do you get this kind of thing often? This stuff doesn't seem too bad, but I think I speak for most of us when I say that I'm feeling pretty burnt out. Please have mercy in regards to homework and the final. What do you call a pencil with a broken tip?? Nevermind.. It's pointless! haha.. Ha Can we prove that Leonardo DiCaprio would have fit on the door also, because that is just some foolishness. I'm sure you've been receiving more and more "ZOMGGGG TWO LECTURES LEFT, PLEASE PUT MY COMMENT UP B4 THE YEAR ENDS!!!!". Just wanted to let you know you can represent all of us underdogs by putting this one up :D

2. Make sure you don’t have a double confict
Combined final: Wednesday May 9 at 1:30 pm. Conflict final: Thursday May 10 at 8 am. 
“If what really matters in college is what you learn throughout the semester and not your grade, does that mean an A on the final will get you an A in this course?”
If you want to know how to calculate your grade look at the first lecture

3. Today’s Concepts: A) Static Fluids B) Archimedes Principle
Physics 211 Lecture 25
Today’s Concepts:
A) Static Fluids
B) Archimedes Principle

4. Pressure due to an Liquid or Gas
Forces are caused by the movement and collisions of molecules.

5. Pressure due to a Liquid or Gas
Pressure is the force per unit area due to these collisions.
“These concepts are understandable and not difficult. I was wondering, however, if the shape of a glass is related to this principle? I noticed that the shape of the glass tapers as it goes down. Is this to reduce the force of the liquid on the glass?”

6. Recall where this comes from
Doesn't depend on shape

7. Pressure changes with depth
Think of it like this: The pressure at some depth is due to the weight of everything above that depth.
“I dont understand how water has more weight as you go lower”

8. CheckPoint
A yacht floats in a large pool. Compare the water pressure directly below the hull of the yacht (point A) to the pressure at the same depth beside the ship (point B).
A) PA > PB
B) PA = PB
C) PA < PB
The weight of the ship is the same as the weight of the displaced water A B
In the last prelecture we began the study of waves. We saw that when a wave propagates through a medium, the elements of the medium only make small displacements from their equilibrium position while the distance traveled by the wave itself is unlimited. We studied the example of a wave on a string and we derived the wave equation [show it] – a differential equation that must be satisfied by whatever function describes the displacements of the medium as a function of both position and time – and we showed that the solution we guessed for a harmonic wave satisfied this equation [show Acos(kx-wt)] as long as the speed of the wave was given by w/k. We will now show that waves of any shape – not just harmonic waves – will satisfy this equation as long as the speed of the wave is constant.
We start by re-writing the argument of the cosine in our harmonic solution in terms of the velocity of the wave. This solution clearly has the general form shown – it is a function which depends on the argument x-vt. Now lets see if this more general functional form is a solution of the wave equation. Using the chain rule to calculate the derivatives [not sure how much to show] we find that this is also a solution. But we now realize that something interesting has happened. The function f(x-vt) does not have to be harmonic at all – it can represent a wave of any shape moving with speed v. To see this consider the shape shown which his described by the function y=f(x) [left diagram]. Shifting this to the right a distance d along the x axis is described by the same function if the argument is simply changed from x to x-d since the new argument will have the same value when x=d as the old one did when x=0 [center diagram]. This means that we can have the pulse move to the right with a constant speed v just by saying that d = vt [right diagram].
Since we have just shown that this is a solution to the wave equation, it must be the case that a single pulse, or any other shape wave, will move through the medium with the same speed as a harmonic wave. This is certainly consistent with our experience. Whether we wiggle end of a string harmonically or we just wiggle it once, we see the shape we create propagate down the string with the same speed. Of course, we could describe a pulse moving to the left in the same way just by changing the sign of v [show f(x+vt)], and this will also be a solution to the wave equation since the mathematics cant care which end of the string we are wiggling.
Points at the same depth have the same pressure 8

9. Clicker Question
Two dams of equal height and width prevent water from entering a central basin. Compare the net force due to the water on the two dams.
A) FA > FB B) FA= FB C) FA< FB
“As a scuba diver, I find a lot of this rather interesting. As a student I kind of just want to be studying for finals.”

10. Atmospheric Pressure The weight of atmosphere.
Air molecules are colliding with you right now!
Patm = 1x105 N/m = 14.7 lbs/in2
Example: Sphere with r = 0.1 m
A = 4pr2 = .125 m2
F = 12,000 Newtons (over 2,500 lbs)!
Hemisphere Demo
Crush can
Glass

11. Does Air Really Weigh That Much?
8 km high stack weighs 105 N
Patm at 16 km its only 10% of Patm at sea level
1 m3 N2 at STP
M = 1.25 kg
1 mole N2 = 28 g
1 mole = 22.4 liters at STP
1 m
1 m
Weight = 12 N

12. Measuring Patm Hwater ~ 10 m (33 ft) for normal Patm
Hmercury ~ 30” for normal Patm

13. Clicker Question
Can you drink water through a long straw from a platform 40 feet above a glass of water.
A) Yes – you just have to suck hard enough.
B) No – it cant work no matter how hard you suck.
40 feet

14. Buoyancy
A floating object displaces its own weight

15. Excellent Question
Alright, call me naive, but why does the buoyant force always point up? I understand it perfectly whenever the object is floating or suspended in the liquid, but not when the object is at the bottom of the container. Since the buoyant force is caused by the collisions of the molecules of liquid on the object, wouldn't the buoyant force at the bottom not face upward since there's no liquid molecules to collide in the upward direction? Would the buoyant force then just be the normal force given off by the container?

16. CheckPoint
Suppose you float an ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will:
A) Go up, causing the water to spill out of the glass.
B) Go down.
C) Stay right at the brim.
“Bring some icecubes and lets have some drinks :)”

17. CheckPoint
When the ice melts, the level of the water in the glass will:
A) Go up, causing the water to spill out of the glass.
B) Go down.
C) Stay right at the brim.
A) The water level will rise. I learned that from Al Gore in "An Inconvenient Truth"
B) volume of ice is greater than volume of water
C) The melted water has exactly the same mass as the ice cube, and the volume of water displaced is equal to the mass of the ice cube.
“The ice melting in cup of water question confuses me. So if the water level doesn't change, why worry about global warming?”

18. Weight of ship = Buoyant force = Weight of displaced water
Clicker Question
Which weighs more:
A) A large tub filled to the brim with water.
B) A large tub filled to the brim with water with a battle-ship floating in it.
C) They will weigh the same.
Tub of water + ship
Tub of water
Overflowed water weighs the same as the ship
Weight of ship = Buoyant force = Weight of displaced water

19. CheckPoint
When you float an ice cube in water you notice that 90% of it is submerged beneath the surface.
Now suppose you put the same ice cube in a glass of some liquid whose density is less than that of water. How much of the ice cube will be submerged?
A) More than 90%
B) 90%
C) Less than 90%
A) It must displace more of the liquid to equal its weight
B) lower density meant that the ice cube will be heavier
C) If the density of the the liquid is less than the density of water than there will be less buoyant force on the ice cube and it will sink farther.

20. PATM PI PB

21. PATM PB

22. PI PB

23. PATM PI

24. PATM PI

25. h1 + h2 = 0.5 (same as before) d = h1 - h2 - h3 PATM h1 PI h2 PB
Solve for h1, h2
So we know h1, h2, h3
d = h1 - h2 - h3

26. PI h2 PB
We know both PI and h2 (prev. slides)