Energy Work vs Potential Energy Energy and Friction

Transcription

1 Energy Work vs Potential Energy Energy and Friction Lana heridan De Anza College Feb 19, 2019

2 Last time conservation

3 Overview work vs. potential kinetic friction and

4 Two Views: Isolated vs Nonisolated ystem Models Imagine a rock is dropped from rest a height h. We want to find an expression for how fast it is moving just before it hits the ground by considering.

5 Two Views: Isolated vs Nonisolated ystem Models Imagine a rock is dropped from rest a height h. We want to find an expression for how fast it is moving just before it hits the ground by considering. We have two choices for how to set up our conservation equation, depending on what we call our system.

6 Isolated ystem Approach A rock is dropped from rest a height h. ystem: rock + Earth The Earth is in our system, so the weight of the rock F g is an internal force. Let point i be the moment it is dropped; f be just before it strikes the ground. Let y = 0 be the ground level. 0 W net,ext = K + U

7 Isolated ystem Approach A rock is dropped from rest a height h. ystem: rock + Earth The Earth is in our system, so the weight of the rock F g is an internal force. Let point i be the moment it is dropped; f be just before it strikes the ground. Let y = 0 be the ground level. 0 W net,ext = K + U 0 0 = (K f K i ) + ( U 0 f U i ) K f = U i 1 2 mv 2 = mgh v = 2gh

8 Nonisolated ystem Approach A rock is dropped from rest a height h. ystem: rock ince the system does not include the Earth, we can t define a gravitational potential here. The weight of the rock F g is an external force. Let point i be the moment it is dropped; f be just before it strikes the ground. Let y = 0 be the ground level. W net,ext = K

9 Nonisolated ystem Approach A rock is dropped from rest a height h. ystem: rock ince the system does not include the Earth, we can t define a gravitational potential here. The weight of the rock F g is an external force. Let point i be the moment it is dropped; f be just before it strikes the ground. Let y = 0 be the ground level. W net,ext = K 0 W g = (K f K i ) ( F g ĵ) ( hĵ) = K f mgh = 1 2 mv 2 v = 2gh

10 Two Views: Isolated vs Nonisolated ystem Models Either approach gave us the correct result. The only difference is how we defined our system.

11 Two Views: Isolated vs Nonisolated ystem Models Either approach gave us the correct result. The only difference is how we defined our system. ometimes it is not practical to include enough things in the system to make it isolated.

12 Isolated and Nonisolated system example ystem: ball + spring + Earth 8.3 continued a y v y b y 0 % c % d % e % f Kinetic Kinetic Kinetic Kinetic Elastic pot. Elastic pot. Elastic pot. Elastic pot. Grav. pot. Grav. pot. Grav. pot. Grav. pot. 8.2 Analysis Model: Isolated ystem (Energy) Total Total Total Total Nonisolated system: total changes Isolated system: total constant External work is done by person loading gun. Figure 8.6 (Example A spring-loaded popgun firing and (b) when the extends to its relaxed le (c) An bar chart popgun projectile Ear before the popgun is lo The in the system (d) The popgun is load means of an external ag work on the system to p spring downward. Ther the system is nonisolate this process. After the p loaded, elastic potentia stored in the spring and tational potential energ system is lower because jectile is below point. projectile passes throug, all of the of t system is kinetic. (f) Wh projectile reaches point the of the isolate gravitational potential.

13 Isolated system example Page 237, # m 2.00 m Figure P Two objects are connected M by a light string passing over a light, frictionless pulley as shown in Figure P8.7. The object of mass m kg is released from rest at a height h m above the table. Using the isolated system model, (a) determine the speed of the object of mass m kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table to which the 3.00-kg object rises. 8. Two objects are connected by a light string passing over a light, frictionless pulley as shown in Figure P8.7. m 2 m 1 h Figure P8.7 Problems 7 and 8. cord, l blocks block B leys. T rest so height are the block separa ection A sled kick im The co is the sle 13. A sled kick im ficient Use en moves 14. A crate M an init paralle

14 Tracking Energy in a ystem, now with Internal Energy In general we can express the conservation of 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 of the system U is the change in potential of the system E int is the change in internal of the system

15 Tracking Energy in a ystem where W = K + U + E int W covers 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 converted to heating effects from friction in the system (or other non-conservative effects)

16 Internal Energy and Kinetic Friction When E int is 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.

17 Kinetic Friction Just as we had two choices for how treat a conservative force acting on our system (depending on what we call our system) we have two choices for how to think of the effect of friction.

18 Kinetic Friction g along a freeway at 65 mi/h. Your car has kinetic stop because of congestion in traffic. Where is ce had? Just(a) as we It is had all two in internal choices for how treat in the a conservative road. force in the acting tires. on (c) our ome system of it (depending has transformed on what we to call our system) we t transferred have two away choices by for mechanical how to think waves. of the(d) effect It is of all friction. r by various mechanisms. Consider block sliding on a surface. AM n v f ntal surface by a f k F faces in contact a mg x v

19 Kinetic Friction: Two Views View 1 (textbook s approach) ystem: block (mass) + internal degrees of freedom of the block and the surface By internal degrees of freedom we mean all of the ways could be stored in the molecules making up the block; molecular vibrations, etc. W net,ext = K + E int

20 Kinetic Friction: Two Views View 1 (textbook s approach) ystem: block (mass) + internal degrees of freedom of the block and the surface By internal degrees of freedom we mean all of the ways could be stored in the molecules making up the block; molecular vibrations, etc. W net,ext = K + E int W app = K + f k s W app f k s = K

21 Kinetic Friction: Two Views View 2: ystem: block (as a point mass) The internal degrees of freedom are part of the environment. W net,ext = K

22 Kinetic Friction: Two Views View 2: ystem: block (as a point mass) The internal degrees of freedom are part of the environment. W net,ext = K W app + W fs = K W app f k s = K (same as view 1)

23 Kinetic Friction The textbook does not ever refer to W fs. interface between two identical teeth projecting from the book and the surface. a d 2 d Book urface The point of application of the friction force moves through a displacement of magnitude d/2. as in Fi teeth m of appl In re sliding magnit vidual s placem displace friction The modele work do system formab straight tart book, w Let us s

24 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 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

25 Example 8.4

26 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

27 Example 8.4

28 Example 8.4

29 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.

30 tic 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. chapter using b the approach. We begin with Equation otential situation. This process bar is may at include % deleting terms, such as the kinetic term de ng of block Equation has moved 8.2 in halfding to 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 pot. pot. Kinetic Elastic Grav. Internal Total 2. The system has gained c are moving, elastic potenstretching, and internal Figure 8.13 (Conceptual Example 8.10) Three bar Question. Would you 0 expect tom 1 see g an evolution of an total isolated Kinetic Elastic Grav. Internal Total system in a mechanics problem pot. to pot. go from a state with constant this 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 bar is zero, telling us that the hanging block is at y 5 50 dentify etic 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 pot. pot. igh because the spring is stretched its maximum amount. The height of the internal 8.13b because the block of mass ma 1 has continued to slide over the surface after the tic b. 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

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

32 ummary work vs. potential kinetic friction and Next Test Monday, Feb 25, Chapters 5-8. (Uncollected) Homework erway & Jewett, Ch 8, onward from page 236. Prob: 2 (isolated vs nonisolated) Ch 8. Probs: 13, 15, 17, 21, 23 (friction)