Energy Energy and Friction

Transcription

1 Energy Energy and Friction Lana heridan De Anza College Oct 31, 2017

2 Last time energy conservation isolated and nonisolated systems

3 Overview Isolated system example Kinetic friction and energy Practice with friction and energy

4 Isolated ystems l Isolated ystem (Energy) e ystem m boundary nd Kinetic energy Potential energy stem Internal energy gy can m in etic, The total amount of energy tera Energy transforms among in the system is constant. h no the three possible types. e sysod. Then, the system is isolated; energy transforms Exam p e f t D w t t e

5 of thermodynamics, DE int 5 W 1 Q (Chapter 20) : DE int 5 T ET 1 T ER (Chapter 27) Isolated ystems DK 1 DU 5 Pick a system such that energy does not flow across the system boundary. eg. consider a book-earth system: solated ystem (Energy) ry common scenario in physics problems: a syscrosses the system boundary by any method. We l situation. Think about the book Earth system pter. After we have lifted the book, there is gravthe system, which can be calculated from the n the system, using W 5 DU g. (Check to see that ore, is contained within Eq. 8.2 above.) work done on the book alone by the gravitational ck to its original height. As the book falls from y i ional force on the book is 12mg j^2? 31y f 2 y i 2j^4 5 mgy i 2 mgy f (8.3) rem of Chapter 7, the work done on the book is energy of the book: on book 5 DK book ns for the work done on the book: ook 5 mgy i 2 mgy f (8.4) quation to the system of the book and the Earth. y i y f r The book is held at rest here and then released. Physics Physics At a lower position, the book is moving and has kinetic energy K. Figure 8.2 A book is released from rest and falls due to work done by the gravitational force on the book. The Earth s gravitational force does work on the book. 2(mgy f 2 mgy i ) 5 2DU g potential energy of the system. For the left-hand ook is the only part of the system that is moving, K book = U g

6 Isolated ystems In that case we have K book + U g = 0 and the mechanical energy is conserved: E mech = 0 This holds when only conservative forces act in an isolated system. If non-conservative forces are allowed to act in an isolated system, we must include the internal degrees of freedom in our system and E mech 0 ; E system = 0

7 Question Quick Quiz A rock of mass m is dropped to the ground from a height h. A second rock, with mass 2m, is dropped from the same height. When the second rock strikes the ground, what is its kinetic energy? (A) twice that of the first rock (B) four times that of the first rock (C) the same as that of the first rock (D) half as much as that of the first rock 2 erway & Jewett, page 216.

8 Energy of an Isolated ystem For the gravitational situation of the falling book, Equa 1 2mv f 2 1 mgy f 5 1 2mv i 2 1 mgy i As the book falls to the Earth, the book Earth system gains kinetic energy such that the total of the two type Quick Quiz Three identical balls are thrown from the top of a building, all with the same constant: initial speed. E total,i 5 As E total,f shown,. the first is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal. Neglecting air resistance, rank the speeds of the balls at the energy of the system as instant each hits the ground, from largest to smallest. The total energy of an isolated system is conserved. 2 1 If there are nonconservative forces acting within the is transformed to internal energy as discussed in ect forces act in an isolated system, the total energy of the sy the mechanical energy is not. In that case, we can e DE system 5 0 where E system includes all kinetic, potential, and interna the most general statement of the energy version of the equivalent to Equation 8.2 with all terms on the right-ha 3 (A) 2, 1, 3 (B) 3, 1, 2 Q uick Quiz 8.3 A rock of mass m is dropped to the gro second rock, with mass 2m, is dropped from the same rock strikes (C) 1, the 2, ground, 3 what is its kinetic energy? (a) (b) four times that of the first rock (c) the same as tha as much (D) as that all the of the same first rock (e) impossible to dete Q uick Quiz 8.4 Three identical balls are thrown from with the same initial speed. As shown in Figure 8.3, t Figure 8.3 (Quick Quiz 8.4) zontally, the second at some angle above the horizont 2 Three identical balls are thrown Adapted from erway & Jewett, angle page below 216. the horizontal. Neglecting air resistance,

9 Tracking Energy in a ystem In general we can express the conservation of energy for our system as: W = K + U + E int where W is the net work done by all external forces on the system K is the change in kinetic energy of the system U is the change in potential energy of the system E int is the change in internal energy of the system

10 Tracking Energy in a ystem where W = K + U + E int W covers energy transfers into or out of the system K is the change in motion of parts of the system U is the change configuration of the system E int is energy converted to heating effects from friction in the system (or other non-conservative effects)

11 Internal Energy and Kinetic Friction When E int is energy converted to heating effects from friction in the system only: E int = f k s where f k is the magnitude of the friction force and s is the total path length that the object travels with this friction force acting. The longer the path, the larger s, the larger E int.

12 g along a freeway at 65 mi/h. Your car has kinetic stop Kinetic because Friction: of congestion Twoin Views traffic. Where is ce had? Consider (a) It block is all sliding in internal on a surface. energy in the road. in the tires. (c) ome of it has transformed to View 1: The system is the only mass of the block, modeled as a t transferred away by mechanical waves. (d) It is all point particle. r by various mechanisms. The internal degrees of freedom are part of the environment. AM n v f ntal surface by a f k F faces in contact x mg a uppose there is one applied force F app : W F net = F app dr + f v f n k dr + 0 n dr + mg 0 dr

13 Kinetic Friction: Two Views View 1: W net = F app dr + f k dr

14 Kinetic Friction: Two Views View 1: W net = F app dr + f k dr Net work equals to the sum of the work done by the applied force and the work done by friction. o, swapping the LH for the RH: W app + W fric = W net = K Then, W app + W fric = K where W fric = f k ds = f k s because the friction force points opposite to the direction of motion.

15 Kinetic Friction: Two Views View 1: In general the single applied force could be replaced by a collection of applied forces, to give: (Wother-ext-forces ) + W fric = K where W fric = f k s Translation: input work becomes kinetic energy of the system, or is lost to the environment as work done against friction.

16 g along a freeway at 65 mi/h. Your car has kinetic Kinetic Friction: Two Views stop because of congestion in traffic. Where is ce had? (a) It is all in internal energy in the road. in the View tires. 2: (c) Theome systemof isit the has mass transformed of the block, to modeled as a point t transferred particle, plus away the by internal mechanical degrees waves. of freedom (d) It of is the all block and the r by various surface. mechanisms. (But not the mass of the surface.) The internal degrees of freedom are part of the system. AM n v f ntal surface by a f k F faces in contact a mg x n F v f

17 Kinetic Friction: Two Views View 2: For the system (the moving object and the surface): F net dr = F app dr + f k dr

18 Kinetic Friction: Two Views View 2: For the system (the moving object and the surface): F net dr = F app dr + f k dr On the LH we have the net work. This will equal to the sum of the work done by the applied force and the work done by friction. o, swapping the LH for the RH: W app + f k dr = W net W app f k s = K

19 Kinetic Friction: Two Views View 2: In general the single applied force could be replaced by a collection of applied forces, to give: (Wext-forces ) f k s = K and since E int = f k s: (Wext-forces ) = K + E int

20 Internal Energy and Friction ummary View 1: W + W fric = K where W fric = f k s View 2 (Textbook s view): where E int = f k s. W = K + E int These give equivalent results.

21 Internal Energy and Friction ummary View 1: W + W fric = K where W fric = f k s View 2 (Textbook s view): where E int = f k s. W = K + E int These give equivalent results. If no other work is being done on the system: K = f k s

22 Question Example A car traveling at an initial speed v slides a distance d to a halt after its brakes lock. (This means the car is in a skid.) If the car s initial speed is instead 2v at the moment the brakes lock, what is the distance it slides? (A) d (B) 2d (C) 4d (D) 8d 1 Drawn from erway and Jewett, page 225.

23 tic energy in the system. 2m % 2 gh 1 1 2kh 2 1m k m 1 gh 5 0 is Energy moving. The Distribution bar chart 100 Isolated ly gravitational potential 50 m system: k 5 m 2g 2 1 2kh which corresponds to the ks in Figure 8.12 and reptem is of released. measuring the coefficient of kinetic friction between an object and some ethod tains the examples four types in of this energy. chapter using b the energy approach. We begin with Equation otential situation. energy This process bar is may at include % deleting terms, such as the kinetic energy term de ng of block Equation has moved 8.2 in halfding to energy Figure in 8.13a this example. and this example. 100 It can also include expanding terms, such as tential 50 0 refore, in this configurathe dark and light images energy pot. pot. energy energy Kinetic Elastic Grav. Internal Total energy energy 2. The system has gained c are moving, elastic potenstretching, and internal Figure 8.13 (Conceptual Example 8.10) Three energy bar Question. Would you 0 expect tom 1 see g an evolution of an total isolated Kinetic Elastic Grav. Internal Total energy system in a mechanicsenergy problem pot. to pot. go from energyaenergy state with constant this energy energy energy distribution: Interpreting to this the one? Energy Bars charts are shown for the system in Figure the block of mass m 1 and.13 show three instants in % 100 re gravitational 8.12 and described potential in energy bar is zero, telling us that the hanging block is at y 5 50 dentify etic energy the bar configuration is zero, indicating 0that the blocks have stopped moving momentarily. e system chart. is that shown by the light images Kinetic of the Elastic blocks Grav. in Figure Internal8.12. Total The height of energy pot. pot. energy energy igh because the spring is stretched its maximum amount. The height of the internal energy energy 8.13b because the block of mass ma 1 has continued to slide over the surface after the tic b. energy in the system. % is moving. (A) The Yes, bar you chart might. 100 Isolated ly gravitational potential 50 system: (B) No, you would which corresponds to the 0not. total Kinetic Elastic Grav. Internal Total energy

24 Mechanical Energy Decreasing due to Nonconservative Forces E int is always positive or zero. (Increases with time!) A system s mechanical energy can increase only if work is done on it by an external force. If no work is done (isolated system) the system s mechanical energy decreases (or stays the same) over time.

25 a nonconservative force acts. Example: Block pulled across surface g along a freeway at 65 mi/h. Your car has kinetic stop Example because of 8.4, congestion Page 224 in traffic. Where is ce had? (a) It is all in internal energy in the road. in the Atires. 6.0 kg(c) block ome initially of it at has rest transformed is pulled to the to right along a t transferred horizontal away surface by mechanical by a constantwaves. horizontal (d) force It is all of 12 N. r by various mechanisms. Find the speed of the block after it has moved 3.0 m if the surfaces in contact have a coefficient of kinetic friction of µ k = AM n v f ntal surface by a f k F faces in contact a mg x

26 Example 8.4

27 surface Example by a 8.4 f k F es in contact x uppose the force F is applied mg at an angle θ. At what angle should the force be applied to achieve the largest possible speed after the a block has moved 3.0 m to the right? Example 8.4) lled to the right face by a conal force. (b) The s at an angle u tal. b f k n mg F u x v f

28 Example 8.4

29 Example 8.4

30 is k 5 50 N/m as shown in Figure sion AM Example 8.8: pring Collisions and Friction calculate the maximum compression of the spring after the collision. initial Avelocity block having v a m/s massto of the 0.80 right kgand is given collides an with initial a spring velocity whose is k 5 50 N/m as shown in Figure x 0 v = 1.2 m/s to the right, just as it collides with a spring whose re 8.11 (Example v, calculate massthe is maximum negligible compression and whose force of the constant spring after is k the = 50 collision. N/m. A block sliding on a 1 E mv 2 ionless, horizontal a 2 ce collides with a x 0 re spring (a)(example Initially, v v A echanical block sliding energy on a is 1 ionless, horizontal a E mv 2 1 inetic energy. (b) The kx 2 b 2 2 ce anical collides energy with is a the of spring. the kinetic (a) Initially, energy x e v echanical block and energy the elasotential 1 is E mv 2 1 inetic energy. energy (b) in The the v kx 2 b hanical g. (c) The energy energy is the is 1 E kx 2 ely of the potential kinetic energy. c 2 max x e he block energy and is the transed back energy to the kinetic the elasotential x max v v gy 0 g. of (c) the The block. energy is v 1 E 2 kx 2 total ely potential energy of energy. the c max 1 E mv he energy is transed back the to the motion. k = What is the maximum compression x in the x m remains constant d mv 2 2 surface, µ ughout kinetic spring? gy of the block. v v total, the energy total mechanical of the energy of the system before the collision is just 1 mv 2. A constant force of kinetic friction acts between the block and the

31 Example 8.8

32 Example 8.7: Box liding Down an Incline A 3.00 kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it AMleaves the ramp. 0 m in length and he crate starts from f magnitude 5.00 N, zontal floor after it v i m 0 d 1.00 m 30.0 v f e crate at the bot- Use energy methods Figure to8.10 determine (Example the 8.7) A speed crate slides of the crate at the amp in Figure down a ramp under the influence of gravity. will slide. bottom of the ramp. The potential energy of the system decreases, whereas the kinetic energy increases. Earth as an isolated

33 Example 8.7: Box liding Down an Incline

34 Example 8.7: Part 2 A 3.00 kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of The crate starts from rest at the top, experiences a constant friction force of magnitude 5.00 N, and continues to move a short distance on the horizontal floor after it AMleaves the ramp. 0 m in length and he crate starts from f magnitude 5.00 N, zontal floor after it v i m 0 d 1.00 m 30.0 v f e crate at the bot- How far does the Figure crate8.10 slide (Example on the8.7) horizontal A crate slides floor if it continues amp in Figure down a ramp under the influence of gravity. will slide. to experience a The friction potential force energy of magnitude of the system decreases, 5.00 N? whereas the kinetic energy increases. Earth as an isolated

35 Example 8.7

36 ummary Friction and kinetic energy Friction and mechanical energy Next Test Friday, Nov 3, Chapters 6-8, and friction/pulleys from Ch 5. (Uncollected) Homework erway & Jewett, Read Chapter 8. Look at Example 8.6. PREV: Ch 8, onward from page 236. Probs: 5, 9, 13, 15, 17 Ch 8, onward from page 236. Probs: 21, 23, 29, 31, 41