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Chapter 10. Energy

Chapter 10. Energy. This pole vaulter can lift herself nearly 6 m (20 ft) off the ground by transforming the kinetic energy of her run into gravitational potential energy.

arthur-dickson
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Chapter 10. Energy

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  1. Chapter 10. Energy This pole vaulter can lift herself nearly 6 m (20 ft) off the ground by transforming the kinetic energy of her run into gravitational potential energy. Chapter Goal: To introduce the ideas of kinetic and potential energy and to learn a new problem-solving strategy based on conservation of energy.

  2. Chapter 10. Energy Topics: • A “Natural Money” Called Energy • Kinetic Energy and Gravitational Potential Energy • A Closer Look at Gravitational Potential Energy • Restoring Forces and Hooke’s Law • Elastic Potential Energy • Elastic Collisions • Energy Diagrams

  3. Kinetic and Potential Energy There are two basic forms of energy. Kinetic energy is an energy of motion Gravitational potential energy is an energy of position The sum K + Ug is not changed when an object is in freefall. Its initial and final values are equal

  4. Kinetic and Potential Energy

  5. The Zero of Potential Energy • You can place the origin of your coordinate system, and    thus the “zero of potential energy,” wherever you choose    and be assured of getting the correct answer to a problem. • The reason is that only ΔU has physical significance, not   Ug itself.

  6. The Zero of Potential Energy

  7. The Zero of Potential Energy

  8. Quick Quiz 1 • A block slides down a frictionless ramp of height h. It reaches velocity v at the bottom. To reach a velocity of 2v, the block would need to slide down a ramp of height • A. 1.41h • B. 2h • C. 3h • D. 4h • E. 6h

  9. Quick Quiz 2 • A block is shot up a frictionless 40° slope with initial velocity v. It reaches height h before sliding back down. The same block is shot with the same velocity up a frictionless 20° slope. On this slope, the block reaches height • 2h • h • ½ h • > h, but I can’t predict an exact value • < h, but I can’t predict an exact value

  10. Quick Quiz 3 Two balls, one twice as heavy as the other, are dropped from the roof of a building. Just before hitting the ground, the heavier ball has • one half • the same amount as • twice • four times the kinetic energy of the lighter ball.

  11. Conservation of Mechanical Energy The sum of the kinetic energy and the potential energy of a system is called the mechanical energy. Here, K is the total kinetic energy of all the particles in the system and U is the potential energy stored in the system. The kinetic energy and the potential energy can change, as they are transformed back and forth into each other, but their sum remains constant.

  12. Hooke’s Law If you stretch a rubber band, a force appears that tries to pull the rubber band back to its equilibrium, or unstretched, length. A force that restores a system to an equilibrium position is called a restoring force. If s is the position of the end of a spring, and se is the equilibrium position, we define Δs = s – se. If (Fsp)s is the s-component of the restoring force, and k is the spring constant of the spring, then Hooke’s Law states that The minus sign is the mathematical indication of a restoring force.

  13. Hooke’s Law

  14. Elastic Potential Energy Consider a before-and-after situation in which a spring launches a ball. The compressed spring has “stored energy,” which is then transferred to the kinetic energy of the ball. We define the elastic potential energyUs of a spring to be

  15. Quick Quiz 4 • A block sliding along a frictionless horizontal surface with velocity v collides with and compresses a spring. The maximum compression is 1.4 cm. If the block then collides with the spring while having velocity 2v, the spring’s maximum compression will be 0.35 cm 2.0 cm 0.70 cm 2.8 cm 1.0 cm 5.6 cm 1.4 cm

  16. Quick Quiz 5 • A block sliding along a frictionless horizontal surface with velocity v collides with and compresses a spring. The maximum compression is 1.4 cm. If this spring in is replaced by a spring whose spring constant is twice as large, a block with velocity v will compress the new spring a maximum distance 0.35 cm 2.0 cm 0.70 cm 2.8 cm 1.0 cm 5.6 cm 1.4 cm

  17. EXAMPLE 10.6 A spring-launched plastic ball QUESTION:

  18. EXAMPLE 10.6 A spring-launched plastic ball

  19. EXAMPLE 10.6 A spring-launched plastic ball

  20. EXAMPLE 10.6 A spring-launched plastic ball

  21. Elastic Collisions

  22. Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m1 having initial velocity (vix)1, with a ball of mass m2 that is initially at rest. The balls’ velocities after the collision are (vfx)1 and (vfx)2.These are velocities, not speeds, and have signs. Ball 1, in particular, might bounce backward and have a negative value for (vfx)1.

  23. Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m1 having initial velocity (vix)1, with a ball of mass m2 that is initially at rest. The solution, worked out in the text, is

  24. Energy Diagrams A graph showing a system’s potential energy and total energy as a function of position is called an energy diagram.

  25. Energy Diagrams

  26. Tactics: Interpreting an energy diagram

  27. Tactics: Interpreting an energy diagram

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