PHYS16 – Lecture 16 Ch. 8 Energy Conservation

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

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

Conservative Forces

Conservative vs. Nonconservative Forces Conservative Forces– force where work done over ANY closed path is zero W AtoB = -W BtoA W AtoB, path 1 = W AtoB, path 2 Nonconservative force – not conservative

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!

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!

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

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

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

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

Energy Conservation

For Conservative Forces and an Isolated System: For Nonconservative Forces:

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

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

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

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?

Conclusions Conservative vs. Nonconservative Forces Energy Conservation