1. Kepler’s Laws of Planetary Motion

2. Kepler’s First Law
Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points

3. Kepler’s Second Law
An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals.

4. Kepler’s Third Law
The square of a planet’s orbital period is proportional to the cube of the average distance between the planet and the sun.

5. Chapter 8 Fluid Mechanics
Section 1

6. What are the 3 States of Matter?
Liquid
Solid
Gas

7. What do liquids and gases have in common?
They are both fluids

8. What is a fluid?
Fluid- a nonsolid state of matter in which the atoms or molecules are free to move past each other

9. Liquids have definite volume but not a definite shape.

10. Gases do not have a definite shape or a definite volume.

11. Why are solids not considered a fluid?
Solids have both a definite shape and volume. The arrangement of their particles keeps them from flowing.

12. What’s density got to do with it??
Property of a fluid
A.K.A. “Mass Density”
How much stuff there is in a certain space

13. Density Symbol: rho (looks like a small caps “p”) Formula:
Density = Mass
Volume
SI Unit: kg/m³

14. Archimedes’ Principle
Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object
An immersed object is buoyed up by a force equal to the weight of the fluid it displaces
*True for liquids and gases

15. Buoyant Force
The upward force exerted by a liquid on an object immersed in or floating on the liquid
Buoyant forces can keep objects afloat

16. Buoyant Force Equation
FB = Density x gravity x Volume
Find the buoyant force exerted on a diver who has a volume of 0.90 m³ and a density of 1020 kg/m³, swimming in Lay Lake.

17. Practice
A 1-liter container filled with mercury has a mass of 13.6 kg and weighs 133 N. When it is submerged in water, what is the buoyant force on it?

18. Practice
A block is held suspended beneath the water in three positions. Near the top, in the middle, at the bottom. In which position is the buoyant force on it greatest?

19. Practice
A stone is thrown into a deep lake. As it sinks deeper and deeper into the water, does the buoyant force on it increase, decrease, or remain unchanged?

20. HW
What is the difference between a solid and a fluid? What is the difference between a gas and a liquid? (Particle level)
Many kayaks are made of plastics and other composite materials that are denser than water. How are such kayaks able to float in water?

21. Chapter 8 Fluid Mechanics
Section 2

22. Pressure The magnitude of the force on a surface per unit area
SI unit is pascal (Pa)

23. Pressure Applied pressure is transmitted equally throughout a fluid
Pressure = force or P = F
area A

24. Example
A 1.5 m wide by 2.5 m long water bed weighs 1025 N. Find the pressure that the water bed exerts on the floor. Assume that the entire lower surface of the bed makes contact with the floor.

25. Pascal’s Principle
Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container

26. Chapter 8 Fluid Mechanics
Section 3

27. Mass Density
The concentration of matter of an object, measured as the mass per unit volume of a substance
Ρ= m mass density= mass
V Volume

28. Fluid Flow
Two Types:
Laminar- when every particle passes a particular point and moves along the same smooth path as the particles that passed that point earlier
-Ex: Smooth stretches of river
Turbulent Flow- irregular flow
-Ex: When obstacles or turns are in a river

29. Ideal Fluid
A fluid that has no internal friction or viscosity and is incompressible
Have steady flow: the velocity, density, and pressure are constant at every point in the fluid

30. Principle of Fluid Flow
The speed of fluid flow depends on cross-sectional area
Ex:
A river flows more rapidly in shallow or narrow places than in places where the river is deep and wide.

31. Principle of Fluid Flow
The pressure in a fluid is related to the speed of flow
Water moves faster through the narrow part of a tube than through the wider part of a tube

32. Bernoulli’s Principle
The pressure in a fluid decreases as the fluid’s velocity increases
Fast-moving fluids exert less pressure than slower-moving fluids

33. Example
Find the density of a basketball with a mass of 2 kg and a volume of 0.01 m³.

34. Example
You have a rock with a volume of 30 m³ and it exerts a force of 58,800 N. What is the density of the rock?