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Physics 103: Lecture 9 Energy Conservation, Power Reminders: Hour Exam I, Tuesday February 24, 5:45 PM Material from Chapters 1-4 inclusive One page of notes (8.5” x 11”) allowed 20 multiple choice questions Scantron will be used - bring #2 HB pencils + calculator Today’s lecture will cover Potential Energy Conservation of Energy Power Usefulness of these concepts in problem solving. 2/19/03 Physics 103, Spring 2004, U. Wisconsin 1 Summary of Previous Lecture • Work, W = |F| |Dx| cos • Kinetic Energy, KE = mv2/2 • Work-Kinetic Energy Theorem: change in kinetic energy of an object = net work done on the object by all the forces net W mv mv 1 2 2 1 2 2 0 • Gravitational Potential Energy: mgh • Spring Potential Energy: kx2/2 2/19/03 Physics 103, Spring 2004, U. Wisconsin 2 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 60 50 40 A B C D 30 20 Define PE=0 on ground. PE=PEmax at the top of the path. When it returns PE=0. Net work done is zero. 10 0 Preflight 9.1 2/19/03 Pretty Sure Not Quite Sure Just Guessing Physics 103, Spring 2004, U. Wisconsin 3 Conservation of Energy • Work-Energy Theorem: •net W = DKE • Conservative forces •net W = -DPE (total work done) •-DPE= DKE •DKE + DPE = 0 (no net change in energy) • Conservation of Energy w/ only Conservative Forces: •E = total energy = KE + PE (a constant) •KEi + PEi = KEf + PEf 2/19/03 Physics 103, Spring 2004, U. Wisconsin 4 Question 1 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 correct 2. Slide on ramp (no friction) 3. Swinging down 4. All the same 1 ay=-g 2 |ax|<g Free fall versus constrained fall x 3 |ay(t)|<g time varying The acceleration is different for the three cases 2/19/03 Physics 103, Spring 2004, U. Wisconsin 5 Question 2 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. 2. 3. 4. Dropping Slide on ramp (no friction) Swinging down correct All the same 1 2 3 In all three cases, the work done by the gravitational force is the same since the change in vertical distance is the same 1 2 mgh mv f v f 2gh 2 2/19/03 Physics 103, Spring 2004, U. Wisconsin 6 Non-conservative Forces Work depends on the path Friction » Longer path More area erased Adds or removes mechanical energy from a system Open system » Erasing results in heat generated » Dissipated to the paper + air system net W Wnc Wc DKE Wc DPE W nc DKE DPE KE i PEi W nc KE f PE f 2/19/03 Physics 103, Spring 2004, U. Wisconsin 7 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, … KE i PEi W nc OE i KE f PE f OE f 2/19/03 Physics 103, Spring 2004, U. Wisconsin 8 Question 3 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? correct 1. -300 J 2. -200 J 3. -100 J 4. Work done must be positive The change in kinetic energy plus the change in potential energy equals the work done on the system by non-conservative forces 2/19/03 Wnc = Ef - Ei = (KEf + PEf) - (KEi + PEi) = (100J -100J) - (200J + 100J) = 0J - 300J = -300J Physics 103, Spring 2004, U. Wisconsin 9 Question 4 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 Velocity is getting smaller continuously because of friction - average velocity on the way down is smaller than on the way up. 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, Emax Due to friction, the energy at the top of the trajectory is Emax-fd Due to friction, on the way down the total kinetic energy when it returns to the bottom is Emax - fd - fd It takes longer to go down because it has smaller average kinetic energy on the way down. 2/19/03 Physics 103, Spring 2004, U. Wisconsin 10 Power W Joules(J) P , Watts (W) t second(s) Power when running up stairs W KE PE 12 mv 2 mgh P t t t m 60 kg, v 2 m/s, h 3 m, t 2.5 s ( 12 )(60)(2) 2 (60)(9.8)(3) 120 1794 P W W 754 W 2.5 2.5 2/19/03 Physics 103, Spring 2004, U. Wisconsin 11 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 s 2. 3s 3. 4.5 s Pretty Sure Not Quite Sure Just Guessing 5. 9s 6. 12 s v1 v 0 v1 d (because v 0 0), v1 1 t1 t1 t1 v v0 v2 d a2 2 (because again v 0 0), v 2 2 t2 t2 t2 a1 70 60 50 A B C D E F 40 30 20 10 0 Preflight 9.3 2/19/03 4. 6 s P W1 F1d1 ma1d1 v v2 ma1v1 m 1 v1 m 1 t1 t1 t1 t1 t1 Power is constant, P m t 2 1.5s v12 v2 v2 m 2 t 2 t1 22 t1 t2 v1 60 60 1.5s 4 6s 30 30 Physics 103, Spring 2004, U. Wisconsin 12 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 m 2. 2 m 3. 3 m 4. 4 m 5. 5 m 6. Impossible to determine KE1 12 mv12 ; KE 2 12 mv22 70 KE 2 v 22 v 22 KE 2 KE1 2 KE1 v12 v1 60 KE1 Fd1 ; KE 2 Fd2 d2 d1 12 d2 1m 2 4m 0.5 2/19/03 Pretty Sure Not Quite Sure Just Guessing 50 A B C D E F 40 2 2 2 1 v v 30 20 10 0 Preflight 9.5 Physics 103, Spring 2004, U. Wisconsin 13 Efficiency W out Efficiency of getting work done : Eff E in E Efficiency of energy conversion : Eff out E in P Efficiency of power conversion : Eff out Pin W out mgh Eff E in E in Energy used by weight lifter : 8 kcal = (8 kcal) (4186 J/kcal) J Potential energy of the weight lifted 2705 Eff 0.0833 8.33% 33488 2/19/03 : mgh = (120 kg) (9.8 m/s 2 ) (2.3 m) J Physics 103, Spring 2004, U. Wisconsin 14 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 70 60 50 40 A B 30 The heat dissipates to the rest of your body. Very little goes to warming up the environment. 20 10 0 Preflight 9.7 2/19/03 Pretty Sure Not Quite Sure Just Guessing Physics 103, Spring 2004, U. Wisconsin 15 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. 60 50 40 A B 30 20 Therefore, efficiency is very high 10 0 Preflight 9.9 2/19/03 Pretty Sure Not Quite Sure Just Guessing Physics 103, Spring 2004, U. Wisconsin 16