Work-KE theorem and net force....

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Discussion Overview

The discussion revolves around the work-kinetic energy theorem, exploring its implications for both conservative and nonconservative forces. Participants examine the relationship between work, kinetic energy, and potential energy, particularly in dynamic scenarios involving forces acting on objects, such as a rocket or a book. The conversation includes theoretical considerations as well as practical examples to clarify concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the work-kinetic energy theorem states that the work done by a force is equal to the change in kinetic energy, applicable for the net force acting on an object.
  • It is proposed that nonconservative forces can only change kinetic energy and not potential energy, leading to confusion about the role of potential energy in such contexts.
  • Examples are provided, such as a rocket climbing at constant speed, to illustrate that while forces may perform work, they do not necessarily result in a change in kinetic energy if the net force is zero.
  • Some participants express confusion regarding the relationship between work done by gravity and changes in potential and kinetic energy, suggesting that these concepts may be interrelated rather than distinct.
  • There is a discussion about the implications of displacement and net force, with some participants noting that displacement can occur without a net force affecting kinetic energy.
  • Concerns are raised about the application of the work-kinetic energy theorem to rigid extended objects versus point-like objects, questioning whether the theorem holds in different scenarios.
  • Participants discuss the nature of nonconservative forces, noting that their work depends on the path taken and can affect the total mechanical energy of a system.

Areas of Agreement / Disagreement

Participants express a range of views on the implications of the work-kinetic energy theorem, particularly regarding the roles of conservative and nonconservative forces. There is no clear consensus on how potential energy relates to nonconservative forces, and the discussion remains unresolved on several technical points.

Contextual Notes

Some limitations are noted, such as the dependence on definitions of conservative and nonconservative forces, and the complexities introduced when considering rigid versus point-like objects. The discussion highlights the need for clarity in distinguishing between work done by different types of forces and their effects on energy.

  • #31
fog37 said:
OK, the pucks on the air table...mechanical energy is conserved while it is not for the blocks with friction...

So, it IS important for the internal forces to be conservative for ME to be conserved!
Therefore, for ME to be conserved, two conditions must be satisfied:

a) The internal force pairs must be conservative
b) The net external force is either zero or conservative
A zero force does count (trivially) as conservative.
 
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  • #32
fog37 said:
Therefore, for ME to be conserved, two conditions must be satisfied:

a) The internal force pairs must be conservative
b) The net external force is either zero or conservative
Isn't that simply all forces then?
 
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  • #33
I guess so :)
 
  • #34
In general, when discussing conservation of mechanical energy for a system, the system is considered isolated which implies that no mass or energy can enter or exit the system. Isolated means that the system does not interact with the environment in any fashion. Lack of external interaction means lack of external force. The net external force ##F_{net}## must be automatically zero if the system is isolated since the system cannot receive or lose energy. I see how a net force can add or subtract energy to the system. How could an external force add or subtract mass to the system?

For an isolated system, energy can only transfer between different parts within the system itself...
 
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