Physics 218 Lecture 12 Dr David Toback Physics

Physics 218 Lecture 12 Dr. David Toback Physics 218, Lecture XII 1

This week… • This week we will finish up Chapters 6 & 7 –Last set of topics for Exam 2 • Exam 2: Thurs, October • Covers chapters 1 -7 Physics 218, Lecture XII th 26 2

The Schedule This week: (10/9) • Finish up Chapters 6&7 in lecture • Chapter 6 in recitation Next week: (10/16) • Chapter 6 HW due • Chapter 8 in lecture (reading questions due) • Chapter 7 in recitation Following week: (10/23) • HW 7 due • Chapter 9 in lecture on Tuesday (reading questions due) • Chapter 8 in Recitation • Exam 2 on Thursday October 26 th Physics 218, Lecture XII 3

Energy • Conservation of Mechanical Energy problems • Conservative Forces • Conservation of Energy Physics 218, Lecture XII 4

Physics 218, Lecture XII 5

Potential Energy A brick held 6 feet in the air has potential energy • Subtlety: Gravitational potential energy is relative to somewhere! Example: What is the potential energy of a book 6 feet above a 4 foot high table? 10 feet above the floor? • DU = U 2 -U 1 = Wext = mg (h 2 -h 1) • Write U = mgh • U=mgh + Const Only change in potential energy is really meaningful Physics 218, Lecture XII 6

Other Potential Energies: Springs Last week we calculated that it took ½kx 2 of work to compress a spring by a distance x How much potential energy does it now have? U(x) = 2 ½kx Physics 218, Lecture XII 7

Problem Solving For Conservation of Energy problems: BEFORE and AFTER diagrams Physics 218, Lecture XII 8

Conservation of Energy Problems Before… Physics 218, Lecture XII 9

After Physics 218, Lecture XII 10

Falling onto a Spring We want to measure the spring constant of a certain spring. We drop a ball of known mass m from a known height Z above the uncompressed spring. Observe it compresses a distance C. What is the spring constant? Before Physics 218, Lecture XII Z After Z C 11

Roller Coaster You are in a roller coaster car of mass M that starts at the top, height Z, with an initial speed V 0=0. Assume no friction. a) What is the speed at the bottom? b) How high will it go again? c) Would it go as high if there were friction? Z Physics 218, Lecture XII 12

Non-Conservative Forces • In this problem there are three different types of forces acting: 1. Gravity: Conserves mechanical energy 2. Normal Force: Conserves mechanical energy 3. Friction: Doesn’t conserve mechanical energy • Since Friction causes us to lose mechanical energy (doesn’t conserve mechanical energy) it is a Non-Conservative force! Physics 218, Lecture XII 13

Law of Conservation of Energy • Mechanical Energy NOT always conserved • If you’ve ever watched a roller coaster, you see that the friction turns the energy into heating the rails, sparks, noise, wind etc. • Energy = Kinetic Energy + Potential Energy + Heat + Others… – Total Energy is what is conserved! Physics 218, Lecture XII 14

Conservative Forces If there are only conservative forces in the problem, then there is conservation of mechanical energy • Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another – Good examples: Gravity and Springs • Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc… Mechanical energy is lost. – Good example: Friction (like on Roller Coasters) Physics 218, Lecture XII 15

Law of Conservation of Energy • Even if there is friction, Energy is conserved • Friction does work – Can turn the energy into heat – Changes the kinetic energy • Total Energy = Kinetic Energy + Potential Energy + Heat + Others… – This is what is conserved • Can use “lost” mechanical energy to estimate things about friction Physics 218, Lecture XII 16

Roller Coaster with Friction A roller coaster of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Physics 218, Lecture XII 17

Energy Summary If there is net work on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up Work done. ) Wnet = DK If there is a change in the potential energy, some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball) DUTotal = WPerson =-WGravity Physics 218, Lecture XII 18

Energy Summary If work is done by a non-conservative force it does negative work (slows something down), and we get heat, light, sound etc. EHeat+Light+Sound. . = -WNC If work is done by a non-conservative force, take this into account in the total energy. (Friction causes mechanical energy to be lost) K 1+U 1 = K 2+U 2+EHeat… K 1+U 1 = K 2+U 2 -WNC Physics 218, Lecture XII 19

Next time… • More problems on Chapters 6 & 7 • Recitation on Chapter 6 problems Physics 218, Lecture XII 20

Physics 218, Lecture XII 21

Roller Coaster with Friction A roller coaster of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2). An odometer tells us that the total scalar distance traveled is d. Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Physics 218, Lecture XII 22

What if the Roller Coaster had Friction? • If there were no friction, the roller coaster would go back up to height Z and come to a stop (then come back down again) Physics 218, Lecture XII 23

Roller Coaster You are in a roller coaster car of mass M that starts at the top, height Z, with an initial speed V 0=0. Assume no friction. a) What is the energy at the top? b) What is the speed at the bottom? c) How much work is done by gravity in going from the top to the bottom? Z Physics 218, Lecture XII 24

Friction and Springs A block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed vo and compresses it by an amount D. Determine m Physics 218, Lecture XII 25

Bungee Jump A jumper of mass m sits on a platform attached to a bungee cord with spring constant k. The cord has length l (it doesn’t stretch until it has reached this length). How far does the cord stretch Dy? Physics 218, Lecture XII l 26