Kepler’s Laws of Planetary Motion

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

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

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.

Chapter 8 Fluid Mechanics Section 1

What are the 3 States of Matter? Liquid Solid Gas

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

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

Liquids have definite volume but not a definite shape.

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

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

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

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

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

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

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.

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?

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?

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?

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?

Chapter 8 Fluid Mechanics Section 2

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

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

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.

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

Chapter 8 Fluid Mechanics Section 3

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

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

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

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.

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

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

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

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?