Mr. Lowrie's Science Site
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  • Environmental Systems
    • First Week Stuff
    • 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

Kinetic Energy and Work


Kinetic Energy:  The kinetic energy K associated with the motion of a particle of mass m and speed v, where v is well below the speed of light, is:
Picture

Work:  Work W is energy transferred to or from an object via a force acting on the object.  Energy transferred to the object is positive work, and from the object, negative work.

Work Done by a Constant Force:  The work done on a particle by a constant force F during displacement d is:
Picture
in which theta is the constant angle between the directions of F and d.  Only the component of F that is along the displacement d can do work on the object.  When two or more forces act on the object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force F(sub)net of those forces.

Work and Kinetic Energy:  For a particle, a change (delta K) in the kinetic energy equals the net work W done on the particle:
Picture
in which K(sub)o is the original kinetic energy of the particle and K(sub)f is the final kinetic energy after the work is done.  Rearranging the previous equation gives us:
Picture

Work Done by Gravitational Force:  The work W(sub)g done by the gravitational force F(sub)g on a particle-like object of mass m as the object moves through a displacement d is given by:
Picture
in which theta is the angle between F(sub)g and d.
Picture
If K(sub)f = K(sub)o, then the above equation reduces to:
Picture
which tells us that applied force transfers as much energy to the object as the gravitational force transfers from it.

Spring Force:  The force, F(sub)s, from a spring is:
Picture
(continued from previous column) where d is the displacement of the spring's free end from its position when the spring is in its relaxed state (neither compressed nor extended), and k is the spring constant (a measure of the spring's stiffness).  If an x-axis lies along the spring, with the origin at the location of the spring's free end when the spring is in its relaxed state, the previous equation can be written as:
Picture
(Hooke's Law)
A spring force is thus a variable force:  It varies with the displacement of the spring's free end.

Work Done by a Spring Force:  If an object is attached to the spring's free end, the work, W(sub)s, done on the object by the spring force when the object is moved from an initial position x(sub)o to a final position x(sub)f ​is:
Picture
Picture

Work Done by a Variable Force:  When the force F on a particle-like object depends on the position of the object, the work done by F on the object while the object moves from an initial position r(sub)0 with coordinates x(sub)0, y(sub)0, and z(sub)0 to a final position r(sub)f with coordinates x(sub)f, y(sub)f, and z(sub)f must be found by integrating the force.  If we assume that component F(sub)x may depend on x but not on y or z, component F(sub)y may depend on y but not on x or z, and component F(sub)z may depend on z but not on x or y, then the work is:
Picture
If F has only an x component, then the equation above becomes:
Picture

Power:  The power due to force is the rate at which that force does work on an object.  If the force does work W during a time interval delta t, the average power due to the force over the time interval is:
Picture
Instantaneous power is the instantaneous rate of doing work:
Picture
For a force F at an angle theta to the direction of travel of the instantaneous velocity v, the instantaneous power is:
Picture

Files:
APCM Chapter 7 Presentation
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File Type: ppt
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