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PHYS16 – Lecture 16

PHYS16 – Lecture 16. Ch. 8 Energy Conservation. Energy Pre-question.

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PHYS16 – Lecture 16

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  1. PHYS16 – Lecture 16 Ch. 8 Energy Conservation

  2. Energy Pre-question • Clyde, the dinosaur, is sick of his doll-sized roller coaster and decides to ride the 20-m tall roller coaster at Ohio’s Cedar Point. Since Clyde is a little scared he decides to start from a location on the track that is 10 m lower than the top. How does Clyde’s speed at the bottom compare to a rider that started from the top of the hill? A) It is slower by a factor of 4. B) It is slower by a factor of 2√2. C) It is slower by a factor of 2. D) It is slower by a factor of √10 E) None of the above

  3. Ch. 8 Energy Conservation • Conservative vs. Non-conservative Forces • Conservation of Energy • Basic Equations • Systems without Friction • Systems with Friction • Power

  4. Conservative Forces

  5. Conservative vs. Nonconservative Forces • Conservative Forces– force where work done over ANY closed path is zero WAtoB= -WBtoA WAtoB, path 1 = WAtoB, path 2 • Nonconservative force – not conservative

  6. Is Gravity a conservative Force? • Let’s assume two different paths and see if we get the same work… Path #1 Path #2 Yes, so gravity is conservative!

  7. Is the spring force conservative? • Let’s assume two different paths and see if we get the same work… Path #1 Path #2 Yes, so spring force is conservative!

  8. Is friction conservative? • Let’s assume two different paths and see if we get the same work… Path #1 Ff Ff Path #2 Ff No, so friction is nonconservative…

  9. Conservative vs. Nonconservative Forces • Conservative • Spring Force • Gravity • Buoyant Force • Nonconservative • Friction • Air resistance/Drag • Fluid resistance • Applied Forces Situation Dependent Tension Normal Force

  10. When is normal force conservative? Situation #1 Block slides down frictionless inclined plane at constant velocity. Situation #2 Block on table. Table is lifted by person at constant acceleration. FN FN Fapplied FG FG Conservative system – Normal force is Conservative, but not doing work anyway… Nonconservative system – Normal force is not conservative, normal force is doing work

  11. When is tension conservative? Situation #1 Block being lifted by weight at constant velocity. Situation #2 Block being lifted by person. T T Fapplied FG FG Conservative system – Tension is conservative Nonconservative system – Tension is not conservative

  12. Energy Conservation

  13. Energy Conservation • For Conservative Forces and an Isolated System: • For Nonconservative Forces:

  14. Sledding • Ignore friction. What is the velocity of our sledder at the current position if they started from top? 5 m 10 m 20 m Ground

  15. Clyde on the Rollercoaster • Our favorite green dinosaur, Clyde, wants to take a ride on the rollercoaster. What is his speed at the end, if he starts at 62 cm and ends at 18 cm? • Does it matter that he went over a loop? No

  16. Discussion Question 1 • Why is the second hill in a roller coaster ride always shorter than the first? (Hint: there could be two answers.)

  17. Discussion Question 2 • A 0.5 kg ball is on a 0.5 m platform. There is a straight ramp down to the bottom or a ramp that looks more like a slide. Ignore friction. • What is the velocity of the ball at the end of each ramp? • Which ramp will be the quickest way down?

  18. Conclusions • Conservative vs. Nonconservative Forces • Energy Conservation

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