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Unit IV: Work, Energy, and Momentum

Unit IV: Work, Energy, and Momentum. Essential Questions:  What is work?  How is work related to energy?  What is power?  What are different types of energy?  How is energy conserved? Energy : The Ability To Do Work. I. Work.

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Unit IV: Work, Energy, and Momentum

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  1. Unit IV: Work, Energy, and Momentum Essential Questions:  What is work?  How is work related to energy?  What is power?  What are different types of energy?  How is energy conserved? Energy: The Ability To Do Work

  2. I. Work A. Work: transfer of energy to an object when the object moves due to a force 1. Work is scalar!  has magnitude only! 2. Symbol: 3. Work is also defined as a change in total energy of something

  3. 4. Work is also also defined mathematically as Force (F) x Displacement (d) 5. Units for Work:

  4. Example: Work A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right. How much work is done on this object?

  5. F B. Work Done at Angles 1. The only part of a force that does work is the part parallel to the direction of movement 2. Formula Becomes: For Horizontal Surfaces

  6. Example: Work at an Angle Calculate the work done by a 2.0-N force (directed at a 30° angle to the vertical) to move a 500 gram box a horizontal distance of 400 cm across a rough floor at a constant speed of 0.5 m/s.

  7. Journal #17 10/28 • Suppose you are dragged to school in the morning with a force of 282.8 N by a rope with angle of 45° off the ground. If 5000 J of work is done how far did you get dragged?. • Sketch the situation!

  8. II. Power A.Power: Amount of work done per unit time 1. Power is scalar!  has magnitude only 2. Symbol: 3. Power = rate at which work is done

  9. 4. Power is also also defined mathematically as Work (W) over time (t) 5. Units for Power: 1W  Note that kilowatts (kW) are often used to keep numbers smaller

  10. 6. There is one more way to express Power  Formulas In Your Reference Tables!!

  11. Example: Power A 60 kg box of squirrels is pushed for 10 meters toward a cliff with a force of 200 Newtons. It takes 20 seconds to reach the edge of the cliff.  What is the work done?  What is the average velocity of the box?  What is the Power generated during the push?  What is the Power generated during the push? (use a different formula!)

  12. B. Graphs of Work and Power 1. Work vs. Displacement  Relationship: “As the displacement increases, the work done increases” Work Done (J)  Type of Relationship: DIRECT Displacement (m)

  13.  Slope of Work vs. Displacement Work Done (J) Units: Displacement (m)

  14.  Relationship: “As time passes, the power generated decreases” 2. Power vs. Time Power (Watts)  Type of Relationship: INDIRECT Time (s)

  15. Journal #17 10/29 A jaguar does 3000 J of work dragging a capybara toward its den. • If the distance from the kill to the den is 30 meters, how much force was exerted? • How much power was developed if it took 40 seconds to move the rodent? • How could the power generated by the jaguar be increased?

  16. III. Forms of Energy A. Potential Energy: possessed by an object due to its position or condition 1. Gravitational: gained by doing work to raise an object to a height above Earth’s surface

  17. a. Work done lifting an object: b. The force exerted is equal to the weight of the object when lifted vertically Work Done (W)= Change in Potential Energy (ΔPE) So: Displacement is just height lifted (h)

  18. c. Units for Gravitational Potential Energy or

  19. Example: Potential Energy The jaguar from earlier decides to drag the dead 50 kg rodent up into a tree instead. • If the tree is 25 meters tall, how much potential energy does the rodent now have? • How much work did the jaguar do in dragging the rodent upward? • How much force was exerted in this process?

  20. Journal #18 10/30 A crane lifts a 90 kg box of chipmunks up to a height of 200 m. • How much potential energy does the box now have? • What is the work done by the crane? • What is the lifting force from the crane (tension)? • What is the weight of the box?

  21. 2. Elastic Potential Energy: energy stored in an object or device by stretching or compressingit (doing work) a. How much energy can be stored depends on the constant (k) of the material  Units: Newtons per meter (N/m) b. Stretch is directly proportional to force applied  Hooke’s Law

  22. Example: Hooke’s Law • A spring with a constant of 40 N/m is stretched 20 cm. What is the force that stretched the spring?

  23. c. Potential Energy of a Spring (PEs) is proportional to the constant (k) and the stretch/compression (x) squared  Small change in length = lots of potential energy change Potential Energy (J) Elongation (m)

  24. Example: Spring PE • A spring with a constant of 40 N/m is stretched 20 cm. What is the Potential Energy stored that in the spring? • What is the work done on the spring?

  25. B. Kinetic Energy: energy possessed by an object due to its movement 1. Dependent on mass and velocity! 2. Mathematic Definition: Formula In Your Reference Tables!!

  26. 3. Units for Kinetic Energy or

  27. 4. Graph of Kinetic Energy vs. Speed  Relationship: “As the speed of an object increases, its kinetic energy increases (by a lot)” Kinetic Energy (J)  Type of Relationship: DIRECT SQUARED Speed (m/s)

  28. Example 1: Kinetic Energy What is the kinetic energy of a 45.5 kg cannonball that is fired toward a nearby squirrel with a velocity of 50 m/s?

  29. IV. Conservation of Energy A. Energy changes forms between kinetic and potential B. Law of Conservation of Energy: Energy cannot be created nor destroyed C. When friction/air resistance are ignored, work done to change energy of an object or system is the SAME regardless of path taken

  30. D. Change in Potential Energy (ΔPE) is equal to the change in Kinetic energy (ΔKE) in an ideal system:  Total Energy (ET) Remains the SAME!

  31. Total Energy Is Conserved!

  32. Example: Pendulum!

  33. Example 2: Kinetic Energy A crane lifts a 90 kg box of chipmunks up to a height of 200 m.  What is potential energy of the box?  When the box is dropped, what will be the kinetic energy of the box before it hits the ground?  What will be the final velocity of the box?  Calculate the kinetic energy of the box.

  34. Journal #18 1/12 • Rico slides a 60 kg crate of pureed squirrels up an inclined ramp 2.0 m long onto a platform 1.0 m above floor level. A 400 N force parallel to the ramp is needed to slide the crate up the ramp at a constant speed. • How much work does Rico do in sliding the crate up the ramp? • How much work would be done if Rico simply lifted the crate straight up from the floor to the platform?

  35. C. Thermal Energy: Heat resulting from kinetic energy of particles within an object D. Internal Energy: total energy possessed by particles within an object E. Nuclear Energy: released by splitting or combining nuclei of atoms (fission & fusion) F. Electromagnetic Energy: associated with electric and magnetic fields Symbol:

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