



When and where
 Thurs April 21 th , 5:45-7:00 pm
 Rooms: Same as Exam I and II, See course webpage.
 Your TA will give a brief review during the discussion session.
Coverage: Chapts 9 – 12 (4 chapters)
Format
 Closed book, 20 multiple-choices questions (format as in practice exams)
 1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc.
 Bring a calculator (but no lap-top computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron.
 Fill in your ID and section # !
Special requests:
 If different from Exam II, email me at than@hep.wisc.edu
 One alternative exam: 3:30pm – 4:45pm, Thurs Mar. 24, Cham 5280
(as before).
4/18/11 Phys 201, Spring 2011 1

 Density
 Pressure in fluids
 Variation of pressure with depth in a fluid
 Buoyancy and Archimedes’ principle
4/18/11 Phys 201, Spring 2011 2





Has a definite volume
No definite shape
Exist at a higher temperature than solids
The molecules “wander” through the liquid in a random fashion
 The intermolecular forces are not strong enough to keep the molecules in a fixed position
4/18/11 Phys 201, Spring 2011 3

 Has no definite volume
 Has no definite shape
 Molecules are in constant random motion
 The molecules exert only weak forces on each other
 Average distance between molecules is large compared to the size of the molecules
4/18/11 Phys 201, Spring 2011 4

4/18/11
 Density = Mass/Volume
 ρ = M / V
 units = kg/m 3
Phys 201, Spring 2011 5

Which will hurt more?
 If you are pricked by a nail with a force equal to your weight
 If your entire weight is supported by a bed of similar nails
 Both will hurt the same
4/18/11 Phys 201, Spring 2011 6

• Impulse to book:
(or raindrops on your umbrella) v
• Force is perpendicular to surface
Air molecule
• Force proportional to area of surface v
• pressure (p) p = Force/area [N/m 2 ]
1 N/m 2 = 1 Pascal (Pa)
F x book
4/18/11 Phys 201, Spring 2011 7

4/18/11
Even when there is no breeze, air molecules are continuously bombarding everything around - results in pressure.
Normal atmospheric pressure = 1.01 x 10 5 Pa
Phys 201, Spring 2011 8





 Examine the darker region, assumed to be a fluid ρ
 It has a cross-sectional area A
 Extends to a depth h below the surface
Three external forces act on the region
-P
1
A + P
2
A - Mg = 0
P
2
= P
1
+ Mg/A = P
1
+ Mgh/V = P
1
+ ρgh
At the surface compared to at depth h
 P o is normal atmospheric pressure
 1.013 x 10 5 Pa = 14.7 lb/in 2
4/18/11
P is the “absolute pressure”;
P - P o is the “gauge pressure”
Phys 201, Spring 2011 9

p
2
= p p atm
1
+ ρ
= ρ gh gh
Measure h, determine p atm example--Mercury
ρ = 13,600 kg/m 3 p atm
= 1.05 x 10 5 Pa
ρ h = 0.757 m = 757 mm (for 1 atm) p
1
=0 p
2
=p atm h
4/18/11 Phys 201, Spring 2011 10

Is it possible to stand on the roof of a five story (50 foot) tall house and drink, using a straw, from a glass on the ground?
1. No CORRECT
2. Yes
P=0
P a h
Evacuate the straw by sucking
How high will water rise?
no more than h = P a
8”
/ ρ g (= 1.05 x 10 5 /1000/9.8) = 33 ft no matter how hard you suck!
the glass is not enough to push all of the liquid up the
50ft through the straw.
Phys 201, Spring 2011 11 4/18/11

 Manometer
 If both sides of an U-tube are open to atmosphere the levels of the fluid are the same on both sides
 If one side is connected to a “pressurized side” the level difference between the two sides can be used to measure pressure.
4/18/11 Phys 201, Spring 2011 12



Blood pressure is quite high, 120/80 mm of Hg
Use higher density fluid in a manometer: Mercury
4/18/11 Phys 201, Spring 2011 13

F
1
A
A
1
1
F
2
A
2


The pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
This principle is used in hydraulic system
 P
1

= P
2
 (F
1
/ A
1
) = (F
2
/ A
2
)
Can be used to derive large gain by making A
2 much larger than A
1
» F
2
= F
1
(A
2
/ A
1
)
» Work done is the same: height by which the surface A
2 rises is smaller than the change in the height of surface with area A
1
.
4/18/11 Phys 201, Spring 2011 15

4/18/11
B = ρ f
V g
Phys 201, Spring 2011 16



King Hiero II asked Archimedes to check if his crown was pure gold.
Archimedes knew
ρ gold
= 19.3x10
3 kg/m 3 , ρ w
= 1.00x10
3 kg/m 3 weighed:
W c
W’ c
= F g
= F’ g
= 7.84 N in air
= 6.86 N in water

Archimedes’ principle:
B = W c
W’ c
= 0.98 N = F w
= V ρ w g

V g = 0.98 N/
ρ w
 Thus, the crown density:
ρ c
= M/V = W c
/ V g = (7.84 N /0.98 N)
ρ w
= 8 kg/m 3 < ρ gold
King Hiero II was cheated !
4/18/11 Phys 201, Spring 2011 17