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

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

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

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

Physics 218, Lecture XIV

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

End of Lecture Notes Physics 218, Lecture XIV

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

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

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

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

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

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

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

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

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

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

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