Physics 218 Lecture 13

Transcription

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

2 Checklist for Today Things due for Last Thursday: Read Chapters 7, 8 & 9 Things that were due Last Monday: Chap 5&6 turned in on WebCT Things that were due for Wednesday s Recitation: Problems from Chap 7 Things due for this coming Monday: Problems from Chap 7 on WebCT Chaps 5&6 if you haven t done them already Physics 218, Lecture XIII 2

3 The Schedule This week: (2/25) HW on Chaps 5&6 on WebCT 3 rd and 4 th lectures (of six) on Chapters 7, 8 & 9 Chapter 7 in recitation Next 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 Following 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 XIII 3

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

5 Physics 218, Lecture XIII 5

6 Different Style Than the Textbook I like teaching this material using a different style than the textbook 1. Teach you the concepts 2. Give you the important equations 3. Then we ll do lots of problems Physics 218, Lecture XIII 6

7 Potential Energy Things with potential: COULD do work This woman has great potential as an engineer! Here we kinda mean the same thing E.g. Gravitation potential energy: If you lift up a brick it has the potential to do damage Physics 218, Lecture XIII 7

8 Example: Gravity & Potential Energy You lift up a brick (at rest) from the ground and then hold it at a height Z How much work has been done on the brick? How much work did you do? If you let it go, how much work will be done by gravity by the time it hits the ground? We say it has potential energy: U=mgZ Gravitational potential energy Physics 218, Lecture XIII 8

9 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 how have? U(x) = ½kx 2 Physics 218, Lecture XIII 9

10 Force and Potential Energy If we know the potential energy, U, we can find the force x = du dx This makes sense For example, the force of gravity points down, but the potential increases as you go up Physics 218, Lecture XIII 10

11 Force and Potential Energy Draw some examples Gravity Spring Physics 218, Lecture XIII 11

12 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 XIII 12

13 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 K 2 +U 2 = K 1 +U 1 Conservation of Mechanical Energy E 2 =E 1 Physics 218, Lecture XIII 13

14 Problem Solving 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 = ½mv 2 + mgy Physics 218, Lecture XIII 14

15 Problem Solving For Conservation of Energy problems: BEFORE and AFTER diagrams Physics 218, Lecture XIII 15

16 Conservation of Energy Problems Before Physics 218, Lecture XIII 16

17 After Physics 218, Lecture XIII 17

18 Quick Problem We drop a ball from a height D above the ground Using Conservation of Energy, what is the speed just before it hits the ground? Physics 218, Lecture XIII 18

19 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? ΔU = U 2 -U 1 = W ext = mg (h 2 -h 1 ) Write U = mgh U=mgh + Const Only change in potential energy is really meaningful Physics 218, Lecture XIII 19

20 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 Z After Z C Physics 218, Lecture XIII 20

21 Coming up Lectures: Last lectures on Chaps 7, 8 and 9 HW due in WebCT on Monday Chapter 7 Reading for Lecture next week Chaps 10 & 11: Momentum Recitation next week Chapter 8 Physics 218, Lecture XIII 31