PHYS16 – Lecture 18 Energy Conservation: Sleds and Rollercoasters October 20, 2010

Administration TA Help Sessions – Su 8-9 pm, W 8-9 pm, Sa 3-5pm – Merrill 116 (around the corner from my office) Course Website – Lectures posted – Assignments + Solutions posted – Announcements posted (in class, by , on website)

This Week Spring Force and Energy Conservative vs. Nonconservative Forces Conservation of Energy – Sleds and Rollercoasters – Springs – Pendulums

Questions from Last time

When is work negative? Work is (+) when done on system, (-) when done by system Work is (+) when force and displacement in the same direction, (-) when in opposite directions Examples of some problems with Work…

P16 is Bulking up… Becca decides to move couches and applies 200 N of force and moves a couch 5 m. – What is the work done by Becca to the couch? 1000 J – What is the work done by gravity to the couch? 0 J – What is the work done by the normal force to couch? 0 J – What is the work done by friction to couch if couch moves at constant speed? J

P16 is Bulking up… Peter builds a weight system where he has to move a weight attached to a spring 5 m. He applies 5 N of force. – What is the work done by Peter to the weight? 25 J – Let’s say that the spring constant is variable so that Peter ends up moving the weight at a constant speed, then what is the work done by the spring? -25 J In this instance the spring force would be constant so W=-F spring x where the magnitude of F spring equals 5 N

P16 is Bulking up… Tim uses Peter’s weight system except he applies 10 N of force to move the weight 5 m. – What is the work done by Tim to the weight? 50 J – The weight system hasn’t changed so what is the work done by the spring? -25 J, the weight is accelerating, so the rest of Tim’s work goes to increasing kinetic energy of weight!

P16 is Bulking up… Jorge decides to slow down large moving crates. He pushes a crate with 500 N of force for 100 m, slowing the crate down. – What is the work done by Jorge to the crate? -50,000 J

P16 is Bulking up… Who did the most work? – Becca = 1000 J – Peter = 25 J – Tim = 50 J – Jorge = -50,000 J – Jorge used the most calories, so if you asked which person did the most biological work within their body, it would be Jorge… – However, if you asked who did the most mechanical work to their particular system, it would be Becca

Zero point of Gravitational Potential For gravitational potential energy where you set the zero point is arbitrary. However, once choice is made you have to stick with it. Examples for Gravitational Potential

Sledding… 5 m 10 m 20 m What is the change in energy for the sledder from the top to current position?

Energy Conservation

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

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 are 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?