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Understanding Work and Kinetic Energy: The Work-Energy Theorem Explained

This comprehensive review covers key concepts related to work and kinetic energy in physics, specifically focusing on constant forces, straight-line displacement, and varying forces. The work-energy theorem is a highlight, illustrating how the work done by net forces equates to changes in kinetic energy. The material includes evaluations of work done via varying forces, examples of motion, and the relationship between work and power. Engage with the foundational principles and mathematical concepts that govern the interactions of forces and work in mechanics.

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Understanding Work and Kinetic Energy: The Work-Energy Theorem Explained

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  1. PHYS 218sec. 517-520 Review Chap. 6 Work and Kinetic Energy

  2. Constant force Straight-line displacement Force and displacement are in the same direction. Work Displacement vector Unit of work

  3. Work Constant force in direction of straight-line displacement Constant force, straight-line displacement Varying x-component of force, straight-line displacement Work done on a curved path (general definition of work)

  4. Evaluation of Work Ex 6.1 Ex 6.2

  5. Work done by a varying force, straight-line motion m m Work is the area under the curve between the initial and final positions in the graph of force as a function of position.

  6. Evaluation of Work: Stretched spring Restoring force

  7. Evaluation of Work Varying x-component of force, straight-line displacement When Fx is constant

  8. Kinetic energy and work-energy theorem Kinetic energy (K) When v = 0, K = 0 Work-Energy Theorem The work done by the net force on a particle equals the change in the particle’s kinetic energy This is a very general theorem. This theorem is true regardless of the nature of the force. Kinetic energy at the initial point Kinetic energy at the final point

  9. Proof of the work-energy theorem Constant force in direction of straight-line displacement m m When a particle undergoes a displacement, it speeds upif W > 0, slows down if W < 0, and maintains the same speed if W = 0.

  10. Proof of the work-energy theorem Varying force, straight-line motion Eliminate time dependence since W is an integral over x.

  11. Examples Ex 6.3 Same as Ex 6.2: suppose that the initial speed v1 is 2 m/s. What is the final speed? Use Work-Energy Theorem to calculate speed.

  12. Ex 6.4 Forces on a hammerhead Falling hammerhead hammerhead Point 1 3 m Point 2 7.4 cm I-beam Point 3 Speed of the hammerhead at point 2

  13. Forces on a hammerhead Ex 6.4 (cont’d) Hammerhead pushing I-beami.e., Point 2 g Point 1 Using the previous result Work-energy theorem Be careful with the change of unit

  14. Ex 6.7 Motion with a varying force m Friction (mk)

  15. Ex 6.8 Motion on a curved path I

  16. Ex 6.9 Motion on a curved path II (another way to compute the line integral) We get the same answer as in Ex 6.8

  17. Power The time rate at which work is done. Average power (Instantaneous) power Unit of power Writing power in terms of F

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