1. Physics 218 Lecture 14
Dr. David Toback
Physics 218, Lecture XIV

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

3. The Schedule This week: (3/3) Chapter 7 due in WebCT
5th and 6th 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
Physics 218, Lecture XIV

4. Chapters 7, 8 & 9 Cont Before: Work and Energy
The Work-Energy relationship
Potential Energy
Conservation of Mechanical Energy
This time and next time:
Conservation of Energy
Lots of problems
Physics 218, Lecture XIV

5. Physics 218, Lecture XIV

6. Different Style Than the Textbook
I like teaching this material using a different style than the textbook
Teach you the concepts
Give you the important equations
Then we’ll do lots of problems
Physics 218, Lecture XIV

7. Mechanical Energy
We define the total mechanical energy in a system to be the kinetic energy plus the potential energy
Define E≡K+U
Physics 218, Lecture XIV

8. Conservation of Mechanical Energy
For some types of problems, Mechanical Energy is conserved (more on this next week)
E.g. Mechanical energy before you drop a brick is equal to the mechanical energy after you drop the brick
K2+U2 = K1+U1
Conservation of Mechanical Energy
E2=E1
Physics 218, Lecture XIV

9. Problem Solving E = K + U = ½mv2 + mgy
What are the types of examples we’ll encounter?
Gravity
Things falling
Springs
Converting their potential energy into kinetic energy and back again
E = K + U = ½mv2 + mgy
Physics 218, Lecture XIV

10. Falling onto a Spring Before After Z Z
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? Z Z C
Physics 218, Lecture XIV

11. Is mechanical energy conserved?
Quick Problem
A refrigerator with mass M and speed V0 is sliding on a dirty floor with coefficient of friction m.
Is mechanical energy conserved?
Physics 218, Lecture XIV

12. Non-Conservative Forces
We’ve talked about three different types of forces:
Gravity: Conserves mechanical energy
Normal Force: Conserves mechanical energy (doesn’t do work)
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 XIV

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 XIV

14. Conservative Forces Good examples: Gravity and Springs
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 XIV

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 XIV

16. Roller Coaster with Friction
A roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).
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 XIV

17. DUTotal = WPerson =-WGravity
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.)
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 XIV

18. EHeat+Light+Sound.. = -WNC
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)
K1+U1 = K2+U2+EHeat…
K1+U1 = K2+U2-WNC
Physics 218, Lecture XIV

19. 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 a total distance D.
Determine m
Physics 218, Lecture XIV

20. 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.
How far does the cord stretch, l in the picture?
What is the equilibrium point around which you will bounce? l
Physics 218, Lecture XIV

21. Coming up… Lectures: Last lectures on Chaps 7, 8 and 9
Chapter 7 was due in WebCT on Monday
For Recitation
Chap 8 problems due
Lab reading
Reading for Lecture next week
Chaps 10 & 11: Momentum
Physics 218, Lecture XIV

22. End of Lecture Notes
Physics 218, Lecture XIV

23. Roller Coaster
You are in a roller coaster car of mass M that starts at the top, height Z, with an initial speed V0=0. Assume no friction.
What is the speed at the bottom?
How high will it go again?
Would it go as high if there were friction? Z
Physics 218, Lecture XIV

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

25. DUTotal = WPerson =-WGravity
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.)
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 XIV

26. EHeat+Light+Sound.. = -WNC
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.
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)
K1+U1 = K2+U2+EHeat…
K1+U1 = K2+U2-WNC
Physics 218, Lecture XIV

27. 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)
Physics 218, Lecture XIV

28. 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?
Physics 218, Lecture XIV

29. Roller Coaster with Friction
A roller coaster car of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).
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 XIV

30. Roller Coaster with Friction
A roller coaster car of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2). 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|.
Physics 218, Lecture XIV

31. 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? l
Physics 218, Lecture XIV

32. A football is thrown
A 145g football starts at rest and is thrown with a speed of 25m/s.
What is the final kinetic energy?
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
Physics 218, Lecture XIV

33. Robot Arm A robot arm has a funny Force equation in 1-dimension
where F0 and X0 are constants.
What is the work done to move a block from position X1 to position X2?
Physics 218, Lecture XIV