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Understanding Energy: Kinetic Energy and Work Energy Theorems

Explore the fundamental concept of energy in physics through kinetic energy and work energy theorems. Learn how energy descriptions can equivalently replace force descriptions, leading to generalized and effective approaches. Derive equations of motion and understand the significance of kinetic energy in describing an object's state of motion. Discover the relationship between work and kinetic energy, including graphical representations and applications of forces on systems. Gain insights into power and its relation to work, as well as practical problem-solving in energy dynamics.

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Understanding Energy: Kinetic Energy and Work Energy Theorems

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  1. Chapter 7 Kinetic Energy and Work

  2. Energy • What is energy? • Energy - is a fundamental, basic notion in physics • Energy is a scalar, describing state of an object or a system • Description of a system in ‘energy language’ is equivalent to a description in ‘force language’ • Energy approach is more general and more effective than the force approach • Equations of motion of an object (system) can be derived from the energy equations

  3. Some calculus • In 1D case

  4. Some calculus • In 1D case • In 3D case, similar derivations yield • K – kinetic energy

  5. James Prescott Joule (1818 - 1889) • Kinetic energy • K = mv2/2 • SI unit: kg*m2/s2 = J (Joule) • Kinetic energy describes object’s ‘state of motion’ • Kinetic energy is a scalar

  6. Chapter 7 Problem 4

  7. Work–kinetic energy theorem • Wnet – work (net) • Work is a scalar • Work is equal to the change in kinetic energy, i.e. work is required to produce a change in kinetic energy • Work is done on the object by a force

  8. Work: graphical representation • 1D case: Graphically - work is the area under the curve F(x)

  9. Net work vs. net force • We can consider a system, with several forces acting on it • Each force acting on the system, considered separately, produces its own work • Since

  10. Work done by a constant force • If a force is constant • If the displacement and the constant force are not parallel

  11. Chapter 7 Problem 14

  12. Work done by a spring force • Hooke’s law in 1D • From the work–kinetic energy theorem

  13. Work done by the gravitational force • Gravity force is ~ constant near the surface of the Earth • If the displacement is vertically up • In this case the gravity force does a negative work (against the direction of motion)

  14. Lifting an object • We apply a force F to lift an object • Force F does a positive work Wa • The net work done • If in the initial and final states the object is at rest, then the net work done is zero, and the work done by the force F is

  15. Chapter 7 Problem 20

  16. James Watt (1736-1819) • Power • Average power • Instantaneous power – the rate of doing work • SI unit: J/s = kg*m2/s3 = W (Watt)

  17. Power of a constant force • In the case of a constant force

  18. Chapter 7 Problem 44

  19. Chapter 7 Problem 50

  20. Answers to the even-numbered problems Chapter 7: Problem 8 5.0 kJ

  21. Answers to the even-numbered problems Chapter 7: Problem 40 2.7 × 105 W

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