Mr. Lowrie's Science Site
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    • Key Terms Glossary
    • Unit 1: Introduction to Environmental Science >
      • Chapter 1: Science and the Environment >
        • Section 1: Understanding Our Environment
        • Section 2: The Environment and Society
      • Chapter 2: Tools of Environmental Science >
        • Section 1: Scientific Methods
        • Section 2: Statistics and Models
        • Section 3: Making Informed Decisions
      • Chapter 3: The Dynamic Earth >
        • Section 1: The Geosphere
        • Section 2: The Atmosphere
        • Section 3: The Hydrosphere and Biosphere
    • Unit 2: Ecology >
      • Chapter 4: The Organization of Life >
        • Section 1: Ecosystems: Everything is Connected
        • Section 2: Evolution
        • Section 3: The Diversity of Living Things
      • Chapter 5: How Ecosystems Work >
        • Section 1: Energy Flow in Ecosystems
        • Section 2: The Cycling of Materials
        • Section 3: How Ecosystems Change
      • Chapter 6: Biomes >
        • Section 1: What is a Biome?
        • Section 2: Forest Biomes
        • Section 3: Grassland, Desert, and Tundra Biomes
      • Chapter 7: Aquatic Ecosystems >
        • Section 1: Freshwater Ecosystems
        • Section 2: Marine Ecosystems
    • Unit 3: Populations >
      • Chapter 8: Understanding Populations >
        • Section 1: How Populations Change in Size
        • Section 2: How Species Interact with Each Other
      • Chapter 9: The Human Population >
        • Section 1: Studying Human Populations
        • Section 2: Changing Population Trends
      • Chapter 10: Biodiversity >
        • Section 1: What is Biodiversity?
        • Section 2: Biodiversity at Risk
        • Section 3: The Future of Biodiversity
    • Unit 4: Water, Air, and Land >
      • Chapter 11: Water >
        • Section 1: Water Resources
        • Section 2: Water Use and Management
        • Section 3: Water Pollution
      • Chapter 12: Air >
        • Section 1: What Causes Air Pollution?
        • Section 2: Air, Noise, and Light Pollution
        • Section 3: Acid Precipitation
      • Chapter 13: Atmosphere and Climate Change >
        • Section 1: Climate and Climate Change
        • Section 2: The Ozone Shield
        • Section 3: Global Warming
      • Chapter 14: Land >
        • Section 1: How We Use Land
        • Section 2: Urban Land Use
        • Section 3: Land Management and Conservation
      • Chapter 15: Food and Agriculture >
        • Section 1: Feeding the World
        • Section 2: Crops and Soil
        • Section 3: Animals and Agriculture
    • Unit 5: Mineral and Energy Resources >
      • Chapter 16: Mining and Mineral Resources >
        • Section 1: Minerals and Mineral Resources
        • Section 2: Mineral Exploration and Mining
        • Section 3: Mining Regulations and Mine Reclamation
      • Chapter 17: Nonrenewable Energy >
        • Section 1: Energy Resources and Fossil Fuels
        • Section 2: Nuclear Energy
      • Chapter 18: Renewable Energy >
        • Section 1: Renewable Energy Today
        • Section 2: Alternative Energy and Conservation
      • Chapter 19: Waste >
        • Section 1: Solid Waste
        • Section 2: Reducing Solid Waste
        • Section 3: Hazardous Wastes
    • Unit 6: Our Health and Future >
      • Chapter 20: The Environment and Human Health >
        • Section 1: Pollution and Human Health
        • Section 2: Biological Hazards
      • Chapter 21: Economics, Policy, and the Future >
        • Section 1: Economics and International Cooperation
        • Section 2: Environmental Policies in the United States
        • Section 3: The Importance of the Individual
  • AP Environmental Science
    • First Week Stuff
    • Unit I: Humans and Sustainability: An Overview >
      • Chapter 1: Environmental Problems, Their Causes, and Sustainability
    • Unit II: Science, Ecological Principles, and Sustainability >
      • Chapter 2: Science, Matter, Energy, and Systems
      • Chapter 3: Ecosystems: What are They and How Do They Work?
      • Chapter 4: Biodiversity and Evolution
      • Chapter 5: Biodiversity, Species Interactions, and Population Control
      • Chapter 6: The Human Population and Its Impact
      • Chapter 7: Climate and Biodiversity
      • Chapter 8: Aquatic Biodiversity
    • Unit III: Sustaining Biodiversity >
      • Chapter 9: Sustaining Biodiversity: Saving Species and Ecosystem Services
      • Chapter 10: Sustaining Terrestrial Biodiversity: Saving Ecosystems and Ecosystem Services
      • Chapter 11: Sustaining Aquatic Biodiversity and Ecosystem Services
    • Unit IV: Sustaining Natural Resources >
      • Chapter 12: Food Production and the Environment
      • Chapter 13: Water Resources
      • Chapter 14: Nonrenewable Mineral Resources
      • Chapter 15: Nonrenewable Energy
      • Chapter 16: Energy Efficiency and Renewable Energy
    • Unit V: Sustaining Environmental Quality >
      • Chapter 17: Environmental Hazards and Human Health
      • Chapter 18: Air Pollution
      • Chapter 19: Climate Disruption
      • Chapter 20: Water Pollution
      • Chapter 21: Solid and Hazardous Waste
      • Chapter 22: Urbanization and Sustainability
    • Unit VI: Sustaining Human Societies >
      • Chapter 23: Economics, Environment, and Sustainability
      • Chapter 24: Politics, Environment, and Sustainability
      • Chapter 25: Environmental Worldviews, Ethics, and Sustainability
  • Chemistry
    • First Week Stuff
    • Matter

Force and Motion II


Friction:  When a force F tends to slide a body along a surface, a frictional force from the surface acts on the body.  The frictional force is parallel to the surface and directed so as to oppose the sliding.  It is due to bonding between the body and the surface.  
     If the body does not slide, the frictional force is a static frictional force f(sub)s.  If there is sliding, the frictional force is a kinetic frictional force f(sub)k.
  1.  If a body does not move, the static frictional force f(sub)s and the component of F parallel to the surface are equal in magnitude, and f(sub)s is directed opposite that component.  If the component increases, f(sub)s also increases.
  2.  The magnitude of f(sub)s has a maximum value f(sub)s,max given by:
Picture
where mu(sub)s is the coefficient of static friction and F(sub)N is the magnitude of the normal force.  If the component of F parallel to the surface exceeds f(sub)s,max, the body slides on the surface.
  3.  If the body begins to slide on the surface, the magnitude of the frictional force rapidly decreases to a constant value f(sub)k given by:

Picture
where mu(sub)k is the coefficient of kinetic friction.

Drag Force:  When there is relative motion between air (or some other fluid) and a body, the body experiences a drag force D that opposes the relative motion and points in the direction in which the fluid flows relative to the body.  The magnitude of D is related to the relative speed v by an experimentally determined drag coefficient C according to:
Picture
where rho is the fluid density (mass per unit volume) and A is the effective cross sectional area of the body (the area of a cross section taken perpendicular to the relative velocity v).

Terminal Speed:  When a blunt object has fallen far enough through air, the magnitudes of the drag force D and the gravitational force F(sub)g on the body become equal.  The body then falls at a constant terminal speed v(sub)t, given by:
Picture

Uniform Circular Motion:  If a particle moves in a circle or a circular arc of radius R at constant speed v, the particle is said to be in uniform circular motion.  It then has a centripetal acceleration a with a magnitude given by:
Picture
This acceleration is due to a net centripetal force on the particle, with a magnitude given by:
Picture
where m is the particle's mass.  The vector quantities a and F are directed toward the center of curvature of the particle's path.

Files:
APCM Chapter 6 Presentation
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File Type: ppt
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