2/19/03Physics 103, Spring 2004, U. Wisconsin1 Physics 103: Lecture 9 Energy Conservation, Power Today’s lecture will cover Potential Energy Conservation of Energy Power Usefulness of these concepts in problem solving. Reminders: çHour Exam I, Tuesday February 24, 5:45 PM çMaterial from Chapters 1-4 inclusive çOne page of notes (8.5” x 11”) allowed ç20 multiple choice questions çScantron will be used - bring #2 HB pencils + calculator

2/19/03Physics 103, Spring 2004, U. Wisconsin2  Summary of Previous Lecture Work, W = |F| |  x| cos  Kinetic Energy, KE = mv 2 /2 Work-Kinetic Energy Theorem: > change in kinetic energy of an object = net work done on the object by all the forces Gravitational Potential Energy: mgh Spring Potential Energy: kx 2 /2

2/19/03Physics 103, Spring 2004, U. Wisconsin3 Lecture 9, Preflight 1&2 Which of the following statements correctly define a Conservative Force: 1. A force is conservative when the work it does on a moving object is independent of the path of the motion between the object's initial and final positions. 2. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point. 3. Both of the above statements are correct. 4. Neither of the above statements is correct. Gravity is a conservative force Define PE=0 on ground. PE=PE max at the top of the path. When it returns PE=0. Net work done is zero.

2/19/03Physics 103, Spring 2004, U. Wisconsin4 Conservation of Energy Work-Energy Theorem: net W =  KE Conservative forces net W = -  PE (total work done) -  PE=  KE  KE +  PE = 0 (no net change in energy) Conservation of Energy w/ only Conservative Forces: E = total energy = KE + PE (a constant) KE i + PE i = KE f + PE f

2/19/03Physics 103, Spring 2004, U. Wisconsin5 Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball get to the bottom first? 1. Dropping 2. Slide on ramp (no friction) 3. Swinging down 4. All the same correct Free fall versus constrained fall Question 1 The acceleration is different for the three cases a y =-g |a x |<g |a y (t)|<g time varying x

2/19/03Physics 103, Spring 2004, U. Wisconsin6 Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed? 1. Dropping 2. Slide on ramp (no friction) 3. Swinging down 4. All the same In all three cases, the work done by the gravitational force is the same since the change in vertical distance is the same correct Question 2

2/19/03Physics 103, Spring 2004, U. Wisconsin7 Non-conservative Forces l Work depends on the path çFriction »Longer path n More area erased l Adds or removes mechanical energy from a system çOpen system »Erasing results in heat generated »Dissipated to the paper + air system

2/19/03Physics 103, Spring 2004, U. Wisconsin8 Open versus Closed System Total energy is constant in any process. It may change forms. Energy leaving the open system is transformed into other energy (OE) heat, sound, deformation of the ground, …

2/19/03Physics 103, Spring 2004, U. Wisconsin9 Suppose the initial kinetic and potential energies of a system are 200J and 100J respectively, and that the final kinetic and potential energies of the same system are 100J and -100J respectively. How much work was done on the system by non-conservative forces? J J J 4. Work done must be positive W nc = E f - E i = (KE f + PE f ) - (KE i + PE i ) = (100J -100J) - (200J + 100J) = 0J - 300J = -300J correct The change in kinetic energy plus the change in potential energy equals the work done on the system by non-conservative forces Question 3

2/19/03Physics 103, Spring 2004, U. Wisconsin10 A stone is launched upward into the air. In addition to the force of gravity, the stone is subject to a frictional force due to air resistance. The time the stone takes to reach the top of its flight path is 1. larger than 2. smaller than 3. equal to the time it takes to return from the top to its original position. If there were no friction, the sum of PE+KE is constant, E max Due to friction, the energy at the top of the trajectory is E max -fd Due to friction, on the way down the total kinetic energy when it returns to the bottom is E max - fd - fd It takes longer to go down because it has smaller average kinetic energy on the way down. Velocity is getting smaller continuously because of friction - average velocity on the way down is smaller than on the way up. Question 4

2/19/03Physics 103, Spring 2004, U. Wisconsin11 Power Power when running up stairs

2/19/03Physics 103, Spring 2004, U. Wisconsin12 Preflight Question 3 & 4 A sports car accelerates from zero to 30 mph in 1.5 s. How long does it take for it to accelerate from zero to 60 mph, assuming the power of the engine to be independent of velocity and neglecting friction? 1. 2 s2. 3s s4. 6 s 5. 9s6. 12 s

2/19/03Physics 103, Spring 2004, U. Wisconsin13 Preflight Question 5 & 6 A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel before coming to rest? 1. 1 m2. 2 m 3. 3 m4. 4 m 5. 5 m6. Impossible to determine

2/19/03Physics 103, Spring 2004, U. Wisconsin14Efficiency

2/19/03Physics 103, Spring 2004, U. Wisconsin15 Preflight Question 7&8 Do you do work on the outside world when you rub your hands to keep them warm? 1. No, very little work on outside world 2. Yes, a lot of work is done on the outside world Due to friction, heat is generated and your hands warm up The heat dissipates to the rest of your body. Very little goes to warming up the environment.

2/19/03Physics 103, Spring 2004, U. Wisconsin16 Preflight Question 9&10 What is the efficiency of the activity of rubbing hands to keep warm? 1. Efficiency is very low 2. Efficiency is very high Due to friction, heat is generated and your hands warm up The heat dissipates to the rest of your body. Very little goes to warming up the environment. Therefore, efficiency is very high