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6 Work and Kinetic Energy

6 Work and Kinetic Energy. Work Done by a Constant Force Work Done by a Variable Force – Straight Line Motion The Scalar Product Work-Kinetic Energy Theorem – Curved Paths Hk: 27, 41, 49, 51. Some Definitions.

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6 Work and Kinetic Energy

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  1. 6 Work and Kinetic Energy • Work Done by a Constant Force • Work Done by a Variable Force – Straight Line Motion • The Scalar Product • Work-Kinetic Energy Theorem – Curved Paths • Hk: 27, 41, 49, 51.

  2. Some Definitions Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary) Energy: The capacity to do work. (Physics) What is Work?

  3. Work Transformation • Work is a usage of energy, e.g., • Burning gasoline produces heat & motion • battery running a car • /

  4. Work • Work is force x distance (N·m = joule), force parallel to motion (no work done by perpendicular component) • It takes energy to do work. • Less stored energy is available after productive work is done.

  5. Work by Constant Force Ex: F = 80N, Angle is 40°, Dx is 11m, Work = FcosqDx = (80N)(cos40)(11m) = 674 J

  6. Total Work on Object

  7. Kinetic Energy

  8. Example: 20kg moving at 5m/s. 250J of work (total) are done on it. What is its final speed?

  9. Negative Work (object slows down) Ex. A car moves 10 meters while a braking force of 500 newtons acts.

  10. Ex. Block pushed 3m with 75N of force while Friction of 50N. Total Work is,

  11. Work by a Variable Force, Straight Line Motion

  12. Hooke’s Law • Elastic restoring force proportional to deformation • F = -kx k = elastic constant (N/m) • Ex. Lab springs, k = 8N/m, 0.1kg mass: • mg = kx • (0.1kg)(9.8N/kg) = 8N/m(x) • x = 0.98N/(8N/m) = 0.1225 m

  13. Scalar (Dot) Product

  14. Ex: A = (1, 1, 0), B = (5, 0, 0)

  15. Example: Find the angle between A = (1, 1, 1) and B = (5, 0, 0)

  16. Power

  17. Ex: A car drives at 20m/s and experiences air-drag of 400N.

  18. What size motor needed when Operating Speed is 10cm/s? Cube of bricks ~ 1 ton 1 ton = 2000 lbs ~ 9000 N Minimum Power: P = Fv = (9000N)(0.1m/s) P = 900 W = 1.2 hp

  19. Work along Curved Path

  20. Summary • Work is force parallel to path x distance (force constant) • Negative total work (object slows down) • Work is integral of force·distance (Scalar Product) • Power is rate work is done • Total work = change in KE • /

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