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Chapter 8

Chapter 8. Potential Enegy. Introduction. Potential Energy- Energy associated with the configuration of a system of objects that exert forces on each other. Associated with conservative forces. No Energy is lost/gained across the system boundaries

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Chapter 8

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  1. Chapter 8 Potential Enegy

  2. Introduction • Potential Energy- Energy associated with the configuration of a system of objects that exert forces on each other. • Associated with conservative forces. • No Energy is lost/gained across the system boundaries • Any gain in potential energy is coupled with a loss of KE, and vice versa. • Conservation of Mechanical Energy

  3. 8.1 Potential Energy of a System • Look at a system of multiple particles that interact with internal forces only. • The KE of the system is the sum of KE of each of the particles. • In some cases the KE of an object within the system is negligible, and can be ignored. (Ex: object falling to earth) • Potential Energy is often considered an Energy storage mechanism

  4. 8.1 • Book/Earth System • Energy can be added to the system by an external force by lifting the object to a new height. (work is done)

  5. 8.1 • No Change in KE, no change in Temp (Eint) • Where did the energy go? • It must be stored somewhere. • If we let the book go and it returns to height A… The book now has KE at height A that it didn’t have before.

  6. 8.1 • The work done on the system to lift the object gave it the “Potential” to have kinetic energy. • Gravitational Potential Energy (Ug)

  7. 8.1 • Note that the work done is the same between lifting the object/pushing it up a ramp. (Dot product of lift force and displacement are only share j components) • Ug also depends on a reference “zero” height • This can be chosen at any level • Above is positive Ug, below is negative Ug

  8. 8.2 Isolated Systems (Cons. of ME) • The mechanical energy of a system is the sum of K and U (kinetic and stored potential) • The conservation of mechanical energy of a systems means the total MEinitial equals total MEfinal (assuming isolated, no outside work)

  9. 8.2 • Quick Quiz p. 220

  10. 8.2 • Elastic Potential Energy – energy stored in a stretched compressed spring. • Work done on spring = energy stored in it. • Energies for a spring system in Horizontal oscillation • At max compression, K = 0 J, Us = Etot • At equilibrium, K = Etot, Us = 0 J

  11. 8.2 • Conservation of Mech Energy

  12. 8.2 • Quick Quiz p. 223 • Example Problems 8.2-8.5

  13. 8.3 Conservative and Non-Conservative Forces • As an object moves down towards earth (near the surface) the work done by gravity is the same regardless of the path taken. • Falling vs. Sliding down an incline • Conservative Force- A force whose work is independent of the path taken (Gravity) • Also a conservative force does zero work for a closed path (same starting ending points).

  14. 8.3 • Spring Force – Conservative • Non-Conservative Force- a force whose work depends on the path taken. (Friction) • Conservative forces generally convert energy between potential and kinetic • Non-Conservative forces generally convert energy into a non-mechanical (non-recoverable form).

  15. 8.4 Changes in ME with Non-Conservative Forces • For a situation with a non conservative force (usually friction)- • Nonconservative forces reduce the amount of Mechanical Energy available as K or U. Quick Quizzes p 230 Examples 8.6-8.10

  16. 8.5 Conservative Forces and Potential Energy • Remember the work done by a conservative force is independent of path, only depends on initial/final configuration of the system. • Potential Energy Function U such that the work done by a conservative force equals the decrease in potential energy of the system.

  17. 8.5 • Work by a conservative force (remember the conservative force varies with postion) Rearranged… And over tiny displacements…

  18. 8.5 • Therefore, the conservative force is related to the potential energy function through… • That is, the x component of a conservative force acting on an object within a system equals the negative derivative of the potential energy of the systems with respect to x.

  19. 8.5 • Check with Us • Check with Ug Quick Quiz 8.11

  20. 8.6 • Energy Graphs (U vs. x) can be used to qualitatively interpret the motion of a system. • Consider a block spring system-

  21. 8.6 • For any slight displacement from x = 0 the block will accelerate back to equilibrium. • Stable Equilibrium • The natural tendency is to get to the lowest state of potential energy possible.

  22. 8.6 • Consider another scenario where an object is at equilibrium, but has Umax. (Unstable Eq) • A ball balanced on top of a hill • If it is displaced to either side of eq, the slope will allow the object to reduce its potential energy.

  23. 6.5 • Neutral Equilibrium- situation where a displacement does not allow for a decrease in potential energy (no change) • A ball resting on a horizontal surface. • The Potential energy function is a constant value. Example 8.11

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