1. Group Work
When a 40.0-kg diver stands at rest at the end of a diving board, the board deflects downward 10.0 cm. When she jumps up and lands back on the board, it deflects downward 25.0 cm. What is her acceleration when the board is defected 25.0 cm downward?

2. Pressure and Fluids
We’re surrounded
Chapter 11

3. Relating “how big” to “how much”
Density
Relating “how big” to “how much”
§ 11.1

4. Density Mass per volume r = m/V SI units kg/m3; conventionally g/cm3
Intensive quantity
Depends on substance and conditions, not amount

5. Some Densities Substance kg/m3 g/cm3 Air 1.20 0.0012 Plain water 1,000
1.000
Sea water
1,030
1.03
Lead
11,300
11.3

6. Pressure
One type of stress
§ 11.2

7. Pressure Force per unit area p = F/A
F is component perpendicular to surface
Scalar quantity

8. Units of Pressure SI Units: N/m2 = pascal = Pa
Bar = 100,000 Pa; mbar = hPa = 100 Pa
Atmosphere = atm = mean sea level pressure = 101,325 Pa = 1.01 bar
Torr: Height in mm of a mercury barometer (760 torr = 1 atm)
lb/in2 = psi ( psi = 1 atm)

9. Gauge and Absolute Pressure
Gauge: increase above surrounding atmosphere
e.g. tire pressure 32 psig
Absolute: total

10. Question
When a molecule bounces elastically off a frictionless surface, what is the direction of its momentum change? A. B. C. D.

11. Question
When a molecule bounces elastically off a surface, what is the direction of the force it applies to the surface? A. B. C. D.

12. Collisions Collision exerts a force into surface
Pressure from force averaged over time and area

13. Pressure in a fluid
Pascal’s Principle: pressure in a fluid is exerted uniformly in all directions throughout the fluid.
§ 11.5

14. just another simple machine
Hydraulics
just another simple machine
§ 11.5

15. Quick Question
If a force F1 is applied to the small piston with area A1, what is the pressure increase in the fluid?
Dp = F1A1.
Dp = F1 + A1.
Dp = A1/F1.
Dp = F1/A1. 1 2

16. Question
If a force F1 is applied to the narrow piston with area A1, How does the magnitude of the force F2 exerted by the fluid on the wide piston compare to F1?
F2 = F1.
F2 < F1.
F2 > F1. 1 2

17. Hydraulics Pistons have different areas
Pressure p = F/A for both pistons F1 A1 F2 A2 =
rearranges to F1 F2 A1 A2 =

18. Question
If the narrow piston with area A1 is moved a distance Dx1, How does the distance Dx2 that the wide piston moves compare to Dx1?
Dx2 = Dx1.
Dx2 < Dx1.
Dx2 > Dx1.
Dx2 ?
Dx1 1 2

19. Hydraulics are Simple MachinesF1 A1 F2 A2 =
Volume changes DV are opposites
DV = A1Dx1, so Dx1 = DV/A1; Dx2 = –DV/A2 = DV A1 F1 A2 F2
F1Dx1 = –F2Dx2
input, output work equal and opposite

20. Example Problem
In an auto shop a hydraulic jack is used to lift vehicles for service. If the radius of the cylinder below piston 1 is r1 = 0.02 m, and the radius of the cylinder below the piston holding the car is r2 = 0.1 m, what force F1 must be exerted on the small piston to lift a 1500-kg car?

21. Pressure with Depth
Why does it increase?
§ 11.6

22. Pressure within a fluid
Force comes from weight of fluid above
Pressure increases with depth
Supports weight above

23. Pressure in a liquid weight of fluid above cross-section p = F/A = =
mass  g A h
density  volume  g A = A
rAhg =
= rgh
p = pressure here

24. Depth Pressure Formula
p0 = pressure here
p = p0 + rgh h
p0 = pressure at depth 0
p = pressure at depth h
r = constant density of liquid
h = depth under top of liquid
p = pressure here

25. Whiteboard Work
What is the water pressure at the bottom at the deepest point of Lake Superior? Lake depth = 406 m, density of water = 1000 kg/m3.

26. Buoyancy
How do things float? Why?
§ 11.6

27. What forces are present?

28. What forces are present?

29. What forces are present?

30. What forces are present?

31. Pressure in a fluid Pressure increases with depth
Greater pressure at bottom than top of an immersed object
Results in upward buoyancy force that is the (vector) sum of all pA forces
F =  p dA A

32. Buoyancy Force Area A Force F = F1 + F2 P1 = rgh = P1A + P2A↑
= rghA + rg(h+L)A↑
= rg(h+L–h)A↑
= rgLA↑
= rgV↑
P1 = rgh
P2 = rg(h+L)
Length L
Volume V = LA

33. Buoyancy Force Principle of Archimedes:
Buoyancy force = weight of fluid displaced
F = rVg
r = constant density of fluid
V = volume of fluid displaced = volume of object submerged
g = 9.8 N/kg

34. Quick example The density of fresh water r = 1000 kg/m3.
What is the buoyancy force on a 1-m3 parcel of water?
What is the buoyancy force on a 1-m3 rock submerged under water?
What is the buoyancy force on a 1-m3 chunk of Styrofoam submerged under water?

35. Quick Questions All blocks are cubes with 1-m sides. Which ones float?
Which one makes the water level change the most?
Which one makes the water level change the least?

36. Buoyancy and Density
If an object is more dense than the surrounding fluid, it sinks
If an object is less dense than the surrounding fluid, it rises
A floating object displaces exactly enough fluid to support its weight

37. Quick Question Which boat (with cargo) has the greatest volume?
The high boat (left).
The low boat (right).
Both have the same volume.

38. Quick Question
Which boat (with cargo) has the greatest volume under the water line?
The high boat (left).
The low boat (right).
Both have the same volume under water.

39. Quick Question
Which boat (with cargo) experiences the greatest buoyancy force?
The high boat (left).
The low boat (right).
Both experience the same buoyancy force.

40. Quick Question Which boat (with cargo) has the greatest mass?
The high boat (left).
The low boat (right).
Both have the same mass.

41. Discussion Question After a boat sinks, it displaces
more water than when it floated.
less water than when it floated.
the same volume and weight of water as when it floated.