4: Module 3 - Conservation Laws
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- Apr 10, 2024
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The application of Newton’s laws usually requires solving differential equations that relate the forces acting on an object to the accelerations they produce. Often, an analytic solution is intractable or impossible, requiring lengthy numerical solutions or simulations to get approximate results. In such situations, more general relations, like the work-energy theorem (or the conservation of energy), can still provide useful answers to many questions and require a more modest amount of mathematical calculation. In particular, you will see how the work-energy theorem is useful in relating the speeds of a particle, at different points along its trajectory, to the forces acting on it, even when the trajectory is otherwise too complicated to deal with. Thus, some aspects of motion can be addressed with fewer equations and without vector decompositions.
- 4.1: Objective 3.a.
- 4.1.1: Work
- 4.1.2: Kinetic Energy
- 4.1.3: Work-Energy Theorem
- 4.1.4: Power
- 4.1.5: Prelude to Potential Energy and Conservation of Energy
- 4.1.6: Potential Energy of a System
- 4.1.7: Conservative and Non-Conservative Forces
- 4.1.8: Conservation of Energy
- 4.1.9: Potential Energy Diagrams and Stability
- 4.1.10: Sources of Energy
Thumbnail: One form of energy is mechanical work, the energy required to move an object of mass m a distance d when opposed by a force F, such as gravity.
