WOE - Introduction to Work and Energy

Work and Energy

Introduction

Work and Energy are introduced and related to motion and forces. We will discuss different types of mechanical energy such as gravitational potential energy and kinetic energy. The law of conservation of energy will be introduced and the concepts of conservative and non-conservative force. The work-kinetic energy theorem will allow us to bridge the concepts of energy and those of force. Finally the rate of work, or power, will be addressed.

Essential Questions

  1. What is the work done by a constant force on an object that undergoes a specified displacement?
  2. What is the relationship between the work done by a force and the area under a graph of force as a function of time and what is the value for this work when the force is a linear function of position?
  3. What is the work performed by a force F(x) on an object that undergoes a specified displacement in one dimension?
  4. What is the work performed by a specified constant force F on an object undergoing displacement in a plane?
  5. What is the change in kinetic energy or speed that results from performing work on an object?
  6. What is the work done by the net force or by the forces that act on an object that undergoes a change in speed or kinetic energy?
  7. Using the work-kinetic energy theorem, what is the force that is needed to bring an object to rest in a period of time?
  8. What are the different definitions of the "conservation of force" and why are these definitions equivalent?
  9. What are examples of conservative and non-conservative forces?
  10. What is the general relationship between force and potential energy, and why is potential energy associated only with conservative forces?
  11. What is the potential energy function associated with a specified one-dimensional force F(x)?
  12. What is the magnitude and direction of a one-dimensional force that can be calculated from the potential energy function U(x) for the force?
  13. What is the force exerted by an ideal spring and what is the potential energy of a stretched or compressed spring?
  14. What is the potential energy of one or more objects in a uniform gravitational field?
  15. What is the relationship between the work performed on an object by a non-conservative force and the change in that object's mechanical energy?
  16. What are situations in which mechanical energy is converted to other forms of energy?
  17. What happens to mechanical energy that is changed by friction or by externally applied forces?
  18. When is mechanical energy conserved and not conserved?
  19. How can conservation of energy be used to predict the motion of systems of connected objects?
  20. How can conservation of energy be used to to predict the motion of objects moving under the influence of springs?
  21. How can conservation of energy be used to predict the motion of objects that move under the influence of non-constant one-dimensional forces?
  22. How can problems be solved that require an application of both conservation of energy and Newton's Laws?
  23. What is the power required to maintain the motion of an object with constant acceleration?
  24. What is the work performed by a force that supplies constant power or what is the power supplied by a force that performs work?

Key Terms

  1. Mechanical Energy - The sum of the energy due to position or motion of a particle.
  2. Gravitational Potential Energy - Energy due to the position of an object within a gravitational field.
  3. Kinetic Energy - Energy due to the motion of an object.
  4. Spring Potential Energy - Energy due to the displacement of a spring from its equilibrium position.
  5. Power - The rate at which energy is transferred.

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