Energy Potential Energy and Force Conservation Laws Isolated and Nonisolated Systems

Transcription

1 Energy Potential Energy and Force Conservation Laws Isolated and Nonisolated ystems Lana heridan De Anza College Oct 27, 2017

2 Last time gravitational and spring potential energies conservative and nonconservative forces

3 Overview force and potential energy stable and unstable equilibrium conservation laws isolated and nonisolated systems

4 Conservative and Nonconservative Forces Conservative force A force that has the property that the work done by the force when on a particle that moves between any give initial and final points is independent of the path taken by the particle. Equivalently, the work done by the force as the particle moves through a closed path is zero. Nonconservative force Any force that is not a conservative force.

5 Conservative Force: Definition 1 A conservative force is a force that does zero total work on any closed path. Nonconservative Force by friction W = µ k mgd Top View when an tance d is ork done by nonzero. In kmgd. D f k C f k W = µ k mgd W = µ k mgd f k d f k A B W = µ k mgd d W in the diagram is the work done by kinetic friction.

6 ates 2.80 cm points. (b) Repeat part (a), setting the zero configuration 5.00 with m the and car y at 5 point m as shown in Figure P7.43. Calculate the work done by 41. A 0.20-kg stone is held 1.3 m above F on the the top particle edge of as a it moves water along well (a) and the then purple dropped path, (b) the red path, and (c) the blue path. (d) Is into it. The well has a depth of 5.0 m. Relative to the Fconfiguration conservative with or nonconservative? (e) the Explain top edge your of the answer well, what to part is the (d). gravita- the stone tional potential energy of the stone Earth system 46. (a) An before object the moves stone is in released the xy and plane (b) when in Figure it reaches P7.43 and Q/C the experiences bottom of the a friction well? (c) What force is with the change constant in gravitational 3.00 N, potential always energy acting of in the the system direction from release opposite to the magnitude reaching object s the velocity. bottom Calculate of the well? the work that you must do 42. A to 400-N slide child the object is in a swing at constant that is attached speed against to a pair the friction ropes force 2.00 as m long. the object Find the moves gravitational along potential (a) the purple W of energy of the child Earth system relative to the child s path O to followed by a return purple path to O, lowest position when (a) the ropes are horizontal, (b) (b) the the ropes purple make path a O angle to with followed the vertical, by a return and blue (c) path the to child O, is and at the (c) bottom the blue of the path circular O to arc. followed by a return blue path to O. (d) Each of your three answers ection should 7.7 Conservative be nonzero. and Nonconservative What is the significance Forces of this 43. A observation? 4.00-kg particle moves y (m) M from the origin to posi- ection Q/C 7.8, Relationship having coordinates Between Conservative (5.00, 5.00) Forces and x 5 Potential 5.00 m and Energy y m (Fig. P7.43). One 47. force The potential on the particle energy is of a system of two particles separated gravitational by a distance force r is given by U(r) 5 A/r, where A the acting is a constant. in the negative Find the y radial force Fr that each x (m) particle direction. Using Equa- O exerts on the other. electron in Friction and Work Example of light over nergy of the ctrons carry creen where it glow. For the electron he constant the acceleraval the elecenergy thellel to Newences affect, solve parts ) and (e) so wo theories. o a speed of m. (a) Find ves the barrem to find (c) Use your the average it was in the rticle under acceleration s a speed of Page 208, #46 positive zero a points (b) Ind of stab and neu rium. ( curve fo 53. A right horizon three e position Additional P 54. The po is given tion of force F x values o sus x an unstabl 55. Review ball at a

7 The work done by Conservative Forces and Potential Energy We now return to conservative forces. y f the agent on the book Earth system is mgy f mgy i. y i r Physics F app Physics mg Figure 7.15 An external agent lifts a book slowly from a height y i to a height y f. Pitfall Prevention 7.7 W = U Potential Energy The phrase potential energy does not refer to something that has the potential to become energy. Potential energy is energy. Let us imagine a system co gravitational force. We do som rest through a vertical displac to our discussion of work as an appear as an increase in energ the work and is at rest after we the kinetic energy of the system Because the energy change the work-kinetic energy theore appear as some form of energ book, we could release it and l (and therefore, the system) no that was done in lifting the bo tem had the potential to possess allowed to fall. Therefore, we is released potential energy. W only be associated with specifi If an external agent does work W on a system without accelerating any piece of it: The amount of potential ener the system. Moving members may change the configuration Let us now derive an expres at a given location above the s ing an object of mass m from a where W is the work done on the system and U is the potential energy change of the system. y f as in Figure We assume applied force from the agent is object: the object is modeled a

8 Conservative Forces and Potential Energy 192 Chapter 7 Energy of a ystem y f The work done by the agent on the book Earth system is mgy f mgy i. y i r Physics F app Physics mg Figure 7.15 An external agent lifts a book slowly from a height y i to a height y f. W = U = W Let us int imagine a system consisting of a gravitational force. We do some work on th rest Inthrough this diagramed a vertical example, displacement D r 5 to our discussion of work as an energy tran appear as an increase F app = in mg energy of the syste the work and is at rest after we perform the the kinetic energy of the system. yf Because W = W the energy change of the syste app = F app dy = U g the work-kinetic energy y i theorem does not appear as some form of energy storage oth book, we could release it and let it fall back (and therefore, the system) now has kinetic that The was conservative done in lifting force the internal book. While th tem force had the is mg potential and to possess kinetic ener allowed to fall. Therefore, yf we call the ener is released Wpotential energy. We will find t int = ( mg) dy only be associated with y i specific types of for The amount of potential energy in the syst

9 Conservative Forces and Potential Energy In general, a conservative force F can be related to its potential energy: xf U = W int = F x dx x i (supposing the particle moves along the x-axis)

10 Conservative Forces and Potential Energy For conservative forces, when the particle moves along the x-axis, xf U = F x dx x i and F x = du dx

11 Conservative Forces and Potential Energy In general, for a conservative force F the particle might move along an arbitrary path s: U = F dr s and 1 F = U where: U = x U i + y U j + z U k 1 If you are not yet familiar with this vector calculus notation, you will not need it for this course.

12 The Zero of Potential Energy ince U = U f U i : F x = du dx U = U f = xf x i xf x i F x dx F x dx + U i The force F and its component F x are physically meaningful, as is the change in potential energy. However, U i can basically be thought of as an integration constant. We can pick U i = 0 or any other convenient value. It can even be negative.

13 Example Gravitational Potential Energy 192 Chapter 7 Energy of a F y = du dy = d (mgy + const.) dy F y = mg And we can call any point the zero of potential energy. For example, we can choose U i = mgy i = 0 and U f = mg(y f y i ). y f The work done by the agent on the book Earth system is mgy f mgy i. y i r Physics F app Physics mg Figure 7.15 An external agent lifts a book slowly from a height y i to a height y f. Pitfall Prevention 7.7 Le gravit rest t to ou appea the w the ki Be the w appea book, (and that w tem h allowe is rele only b The a the sy may c Le

14 ummary isolated and nonisolated systems Next Test Friday, Nov 3, Chapters 6-8, and friction/pulleys from Ch 5. (Uncollected) Homework erway & Jewett, Ch 7, onward from page 207. Probs: 49, 52 Read Chapter 8. Ch 8, onward from page 236. Probs: 5, 9, 13, 15, 17