Physics 103: Lecture 9 Hooke’s Law, Energy Conservation, Power

1. Physics 103: Lecture 9Hooke’s Law, Energy Conservation, Power • Reminder: • Midterm Exam I, Thursday October 7, 5:45 - 7 PM – Locations: • Sections 302, 308, 311, 325, 327, 328 (TAs Cho & Hart ): 145 Birge • Sections 305, 306, 309, 313, 314, 315 (TAs Feintzeig & Hinojosa) : 2103 Chamberlin • Sections 303, 304, 310, 316, 322, 330 (TAs Belknap & Yip): B102 Van Vleck • Sections 307, 312, 317, 321, 329 (TAs Parker & Walker): B130 Van Vleck • Sections 301, 318, 319, 323, 324, 326 (TAs Hostetter & Hu): 1310 Sterling Physics 103, Fall 2010, UW-Madison

2.  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 • Gravitational Potential Energy: mgh Physics 103, Fall 2010, UW-Madison

3. F Work = Area x Hooke’s Law • Force exerted to compress a spring is proportional to the amount of compression or extension. Work of the spring: k - is the force constant (or spring constant) Units: "N·m-1" or "kgs-2" Physics 103, Fall 2010, UW-Madison

4. Question The potential energy of a stretched spring is 1. proportional to the amount the spring is stretched. 2. proportional to the square of the amount the spring is stretched. 3. proportional to the amount the spring is compressed. Physics 103, Fall 2010, UW-Madison

5. Conservation of Energy Total Energy = (1/2) mv2 (kinetic energy) + mgh(gravitational potential energy) + (1/2) kx2 (spring potential energy) Physics 103, Fall 2010, UW-Madison

6. Conservative & Non-Conservative Forces • A force is conservative if work it does on an object moving between two points is independent of the path the objects take between the points • Work depends only upon initial and final positions of the object • Examples of conservative forces: • Gravity • Spring force • Electromagnetic forces • A force is non-conservative if work doneon an object depends on path taken byobject between its final and starting points. • Examples of non-conservative forces: • Kinetic friction • Air drag • Propulsive forces Work required is less on shorter blue path than on longer red path Friction depends on the path and so is a non-conservative force Physics 103, Fall 2010, UW-Madison

7. Lecture 9, Preflight 1&2 Which of the following statements correctly define a Conservative Force: • 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. • 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. • Both of the above statements are correct. • Neither of the above statements is correct. Gravity is a conservative force Define PE=0 on ground.PE=PEmax at the top of the path. When it returns PE=0. Net work done is zero. Physics 103, Fall 2010, UW-Madison

8. Conservation of Energy(with conservative forces) • 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) • KEi + PEi = KEf + PEf Physics 103, Fall 2010, UW-Madison

9. correct 1 3 2 x 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. Dropping2. Slide on ramp (no friction)3. Swinging down4. All the same |ay(t)|<gtimevarying ay=-g |ax|<g Free fall versus constrained fall The acceleration is different for the three cases Physics103, Fall 2010, UW-Madison

10. correct 1 3 2 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. Dropping2. Slide on ramp (no friction)3. Swinging down4. 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 Physics 103, Fall 2010, UW-Madison

11. 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 Physics 103, Fall 2010, UW-Madison

12. 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, … Physics 103, Fall 2010, UW-Madison

13. correct 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? 1. -300 J2. -200 J3. -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 Wnc = Ef - Ei = (KEf + PEf) - (KEi + PEi) = (100J -100J) - (200J + 100J) = 0J - 300J = -300J Physics 103, Fall 2010, UW-Madison

14. Power Average power when running up stairs starting from stationary: after 2.5 sec moving at 2 m/s and 3 m high: Physics 103, Fall 2010, UW-Madison

15. Unit Conversion: Power & Velocity A car of mass 1200 kg requires 20 hp to move at a constant velocity of 50 km/hr on a level road. Find the force of friction. Physics 103, Fall 2010, UW-Madison

16. 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 4. 6 s 5. 9s6. 12 s Physics 103, Fall 2010, UW-Madison

17. Efficiency Physics 103, Fall 2010, UW-Madison

18. 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. Physics 103, Fall 2010, UW-Madison

19. 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 Physics 103, Fall 2010, UW-Madison

20. Summary: Non-conservative Forces and Energy Conservation • When non-conservative forces are present, the total mechanical energy of the system is not constant • The work done by all non-conservative forces acting on parts of a system equals the change in the mechanical energy of the system • Wnc = Energy • If all forces are conservative, Wnc = 0 = Energy • In equation form:Energy = Wnc = (KEf - KEi) + (PEi - PEf) = (KEf + PEf) - (PEi + KEi) • The energy is not really lost but is generally transformed into a form of non-mechanical energy such as thermal energy Physics 103, Fall 2010, UW-Madison