1. Physics 218, Lecture XIII1 Physics 218 Lecture 13 Dr. David Toback

2. Physics 218, Lecture XIII2 The Schedule Today: Finish up Chapters 6&7 Chapter 6 in recitation if you haven’t already 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 Tues (reading questions due) Exam 2 on Thursday October 26 th

3. Physics 218, Lecture XIII3 Energy Potential Energy & Conservation of Energy problems The relationship between potential energy and Force Energy diagrams and Equilibrium

4. Physics 218, Lecture XIII4

5. 5 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

6. Physics 218, Lecture XIII6 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

7. Physics 218, Lecture XIII7 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 

8. Physics 218, Lecture XIII8 Force and Potential Energy If we know the potential energy, U, we can find the force This makes sense… For example, the force of gravity points down, but the potential increases as you go up

9. Physics 218, Lecture XIII9 Force and Potential Energy Draw some examples… –Gravity –Spring

10. Physics 218, Lecture XIII10 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)

11. Physics 218, Lecture XIII11 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?

12. Physics 218, Lecture XIII12 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

13. Physics 218, Lecture XIII13 Next Week… Chapter 8: Momentum –Reading Questions for Tuesday: Q8.6 and Q8.13 Homework 6 Due Monday Recitation on Chapter 7 Exam 2 is Thursday October 26 th

14. Physics 218, Lecture XIII14

15. Physics 218, Lecture XIII15 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?

16. Physics 218, Lecture XIII16 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|.

17. Physics 218, Lecture XIII17 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

18. Physics 218, Lecture XIII18 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

19. Physics 218, Lecture XIII19 Robot Arm A robot arm has a funny Force equation in 1-dimension where F 0 and X 0 are constants. What is the work done to move a block from position X 1 to position X 2 ?