Physics 218 Lecture 14 Dr. David Toback Physics 218, Lecture XIV 1
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 2
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 Physics 218, Lecture XIV 3
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 4
Physics 218, Lecture XIV 5
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 XIV 6
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 7
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 XIV 8
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 XIV 9
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 XIV 10
Quick Problem A refrigerator with mass M and speed V is sliding 0 on a dirty floor with coefficient of friction μ. Is mechanical energy conserved? Physics 218, Lecture XIV 11
Non-Conservative Forces We ve talked about three different types of forces: 1.Gravity: Conserves mechanical energy 2.Normal Force: Conserves mechanical energy (doesn t do work) 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 XIV 12
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 13
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 XIV 14
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 15
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 XIV 16
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 = ΔK 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) ΔU Total = W Person =-W Gravity Physics 218, Lecture XIV 17
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 Physics 218, Lecture XIV 18
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 μ Physics 218, Lecture XIV 19
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? l l Physics 218, Lecture XIV 20
Lectures: Coming up 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 21