1. Physics 218, Lecture XV1 Physics 218 Lecture 15 Dr. David Toback

2. Physics 218, Lecture XV2 Checklist for Today Things due awhile ago: –Read Chapters 7, 8 & 9 Things that were due Monday: –Problems from Chap 7 on WebCT Things that are due Yesterday in Recitation –Chapter 8 –Reading for Lab

3. Physics 218, Lecture XV3 The Schedule This week: (3/3) Chapter 7 due in WebCT 5 th and 6 th lectures (of six) on Chapters 7, 8 & 9 Chapter 8 in recitation Next week: (3/10) Spring Break!!! Following Week: (3/17) Chapter 8 due in WebCT Reading for Chapters 10 & 11 Lecture on Chapters 10 & 11 Chapter 9 and Exam 2 Review in recitation Following Week: (3/24) Chapter 9 due in WebCT Exam 2 on Tuesday Recitation on Chapters 10 & 11 Reading for Chapters 12 & 13 for Thursday Lecture 12 & 13 on Thursday

4. Physics 218, Lecture XV4 Before: –Work and Energy –The Work-Energy relationship –Potential Energy –Conservation of Mechanical Energy –Conservation of Energy This time: –Summary –More Problems Chapters 7, 8 & 9 Cont

5. Physics 218, Lecture XV5

6. 6 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!

7. Physics 218, Lecture XV7 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

8. Physics 218, Lecture XV8 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?

9. Physics 218, Lecture XV9 Energy Summary If there is net work done on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up  Work done.) W net =  K 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)  U Total = W Person =-W Gravity

10. Physics 218, Lecture XV10 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. E Heat+Light+Sound.. = -W NC 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 +E Heat… K 1 +U 1 = K 2 +U 2 -W NC

11. Physics 218, Lecture XV11 Friction and Springs A block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed V o and compresses it a total distance D. Determine 

12. Physics 218, Lecture XV12 Robot Arm A robot arm has a funny Force equation in 1- dimension where F 0 and X 0 are constants. The robot picks up a block at X=0 (at rest) and throws it, releasing it at X=X 0. What is the speed of the block?

13. Physics 218, Lecture XV13 l l Bungee Jump You are standing on a platform high in the air with a bungee cord (spring constant k) strapped to your leg. You have mass m and jump off the platform. 1.How far does the cord stretch, l in the picture? 2.What is the equilibrium point around which you will bounce?

14. Physics 218, Lecture XV14 Coming up… Next week: Spring Break Week after Spring Break –Homework in WebCT Monday: Chapter 8 –Reading for Lecture: Chaps 10 & 11: Momentum –Recitation: Chap 9 and Exam review

15. Physics 218, Lecture XV15

16. Physics 218, Lecture XV16 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

17. Physics 218, Lecture XV17 Energy Potential Energy & Conservation of Energy problems The relationship between potential energy and Force Energy diagrams and Equilibrium

18. Physics 218, Lecture XV18 Energy Review 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.) W net =  K 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)  U Total = W Person =-W Gravity

19. Physics 218, Lecture XV19 Energy Review If work is done by a non-conservative force it is negative work (slows something down), and we get heat, light, sound etc. E Heat+Light+Sound.. = -W NC 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 +E Heat… K 1 +U 1 = K 2 +U 2 -W NC

20. Physics 218, Lecture XV20 Potential Energy Diagrams For Conservative forces can draw energy diagrams Equilibrium points –Motion will move “around” the equilibrium –If placed there with no energy, will just stay (no force)

21. Physics 218, Lecture XV21 Stable vs. Unstable Equilibrium Points The force is zero at both maxima and minima but… –If I put a ball with no velocity there would it stay? –What if it had a little bit of velocity?

22. Physics 218, Lecture XV22 Roller Coaster with Friction A roller coaster car 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?

23. Physics 218, Lecture XV23 Roller Coaster with Friction A roller coaster car 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? Assuming that the magnitude and angle of the force of friction, F, between the car and the track is constant, find |F|.

24. Physics 218, Lecture XV24 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  y? l

25. Physics 218, Lecture XV25 A football is thrown A 145g football starts at rest and is thrown with a speed of 25m/s. 1.What is the final kinetic energy? 2.How much work was done to reach this velocity? We don’t know the forces exerted by the arm as a function of time, but this allows us to sum them all up to calculate the work