PHYS 16 Lecture 18 Energy Conservation Sleds and

PHYS 16 – Lecture 18 Energy Conservation: Sleds and Rollercoasters October 20, 2010

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

P 16 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? -1000 J

P 16 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=-Fspringx where the magnitude of Fspring equals 5 N

P 16 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!

P 16 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

P 16 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… What is the change in energy for the sledder from the top to current position? 5 m 10 m 20 m

Energy Conservation

Conservative vs. Nonconservative Forces • Conservative Forces– force where work done over ANY closed path is zero WAto. B = -WBto. A WAto. B, path 1 = WAto. B, path 2 • Nonconservative force – not conservative

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

When is normal force conservative? Situation #1 Block slides down frictionless inclined plane at constant velocity. FN Situation #2 Block on table. Table is lifted by person at constant acceleration. 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

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

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?