Lecture slides available at physics.ucdavis/physics7

1. Physics 7B - ABLecture 1Lecturer Dr. Yu Sato111 Phy/GeoWed 4-5pmsato@physics.ucdavis.edu** When using e-mail, please include “Physics7B” in the subject line. ** Lecture slides available athttp://physics.ucdavis.edu/physics7

2. Course Website http://physics.ucdavis.edu/physics7 Click on Physics 7B-A/B Lecturer 3 Dr. Kevin Klapstein

3. Course Policy Highlights • Text College Physics: A Models Approach, Part II by W. Potter •  Text •  Discussion/Lab Workbook • Final Examination June 9, Monday, 1pm – 3pm • Course Grading = Exam grade +/- DL grade. •  Exam grade (8 quizzes and the final) •  D/L grade • Your quiz grade is the average of five highest individual quiz grades. • Your Exam grade is then the higher of either of the two weighting schemes. • (a) 50% Quiz grade + 50% Final grade • (b) 20%Quiz grade + 80% Final grade Bring to your DL meetings!

4. Six Quizzes during lectures Go to your assigned lecture time Full schedule of Quizzes this quarter on the academic calendar on the website. Consult Quiz information on the website for (given) Quizzes, solution, rubrics, and grades. Q R S T Be sure to write your name, ID number & DL section!!!!! Rubric Codes We categorise/grade your responses based on : (1) your understanding of the problem (2) choice of appropriate model (3) logic to arrive at the (hopefully correct) answer.

5. Attendance in the DL(Discussion/Lab) section is MANDATORY • With two unexcused DL absences, your highest DL grade is a low pass (lowers your grade by 0.5 pts). • With three unexcused DL absences, your DL grade is unsatisfactory (lowers your grade by 2 pts). • In case of emergency… • As the space is limited in Walker Annex 114, you should also contact the make-up DL instructor before the make-up DL to ensure extra space will be available for you. Consult the link “DL Meeting Times” and the academic calendar on the website for the full schedule and the list of DL instructors/their e-mail addresses.

6. Academic Dishonesty • Copying during quizzes/final. • Taking a test for another student. • Modifying a quiz before asking for a re-grade. • Suspected cheating of any form is always reported to Student Judicial Affair for appropriate action.

7. Second DL (DLM 2) starts TODAY All DLs are in 114 Walker Annex This is 114 Walker TB

8. Second DL (DLM 2) starts TODAY All DLs are in 114 Walker Annex IMPORTANTOnly the DL instructor of the section you want to add is able to issue you a PTA number.DL meeting times (list of DL instructors with e-mail addresses) posted on the website Currently, 21 waitlisted.

9. What is physics 7? • Physics 7 is a 3-quarter series of physics classes, typically taken by bio-science and other non-physical science majors. • Physics 7A: Energy conservation, thermodynamics, particle models of matter… • Physics 7B: Fluids, Electricity,Classical Mechanics (Newtonian Model), rotational motion, conservation of angular momentum, common kinds of change. • Physics 7C: Wave phenomena, optics, electricity and magnetism, the atom and modern quantum mechanics.

10. ModelsUseful way to think of and address questions about phenomena(e.g. Energy interaction model)

11. Models in Physics 7BModels can help us organize our thinking, and can be very useful.Models also have limitations: experiment is the final judge. Hum…I already know this one! • Energy Density Model (Fluids) • Linear Transport Model (Fluids, Circuits) • Gallilean Space-Time Model • We can understand our universe in 3D + Time and 3 spatial dimensions and time are all independent of each other. We now know (Thanks to Einstein et al.) this is NOT true but very usefulto analyze many physical phenomena. • Force model • Momentum Conservation Model • Angular Momentum Model • Newtonian Model • Exponential Change Model

12. “Learning” Physics 7B Do’s Learn how to use the model to find answers You learn music, soccer, ski,physics, etc. by practicing under the watchful eyes of your instructor/coach. You learn the basic ideas and practice with them, and then you go out there and apply them in complex situations. Physics 7 : 1.4 hours practice in lecture + 5 hrs of practice in DL + + 2-4 hrs of practice at home (FNTs/review) = 9-10 hrs OK… how do we “practice” ? Learn basic physical models Be able to explain physical ideas in common English, in technical scientific English, and in mathematics (calculate measurable quantities). Be able to use these models to explain/calculate in new situations Don’ts Don’t learn the answers

13. Lecture 1Steady-State Energy Density ModelApplied to Fluid CircuitElectrical Circuit

14. What is Fluid? Gasses, Liquids. Individual molecules do not have fixed positions relative to each other. How do we characterize Fluid? Volume, Temperature, Pressure… Mt.Everest, 8848m, 30 kPa UCDavis, sea level, 103 kPa, 1 Pascal = 1N/m2

15. How do we analyze a Steady-State Motion of a fluid?  Heart 

16. By conserving energy, Of Course!

17. Use energy conservation for this open system (we will always have Q = 0) ∆U = Uf – Ui but ∆U = Wtotal = Wfluid pushing on right +Wfluid being pushed on left = PiVi – PfVf ∆H = 0in this situation ) ∆U = ∆Eth (i.e., ∆Ebond = 0) ∆H = ∆Eth + V∆P = 0 ∆Eth + V∆P + ∆KE + ∆PEg = Epump ∆P + ∆KE/V + ∆PEg/V + ∆Eth/V= Epump/V ∆P + (1/2)∆(v2) +  g∆y + IR =  Volumetic flow rate I : [I] = [m3/s], Resistance R : [R] = [J s/m6],  : total energy/volume put in by pump

18. Our Model for Analyzing Fluid Flow (use these two ideas to analyze every fluid problem) Conservation of Energy (as applied to Fluids) a.k.a. Fluid Transport Equation/Energy Density Equation/Extended Bernoulli eq. ∆P + (1/2)∆(v2) +  g∆h + IR = Epump/V *Volumetic flow rate I : [I] = [m3/s], Resistance R : [R] = [J s/m6] Don’t’s : Since the fluid is in a steady state, you don’t pick two points in time to find the changes. Do’s : Instead, pick two points in the fluid circuit to calculate changes in the various quantities. (P2– P1) + (1/2)(v22 –v12) +  g( h2 –h1) + IR12 = 12 IR12: Resistance of the pipe between points 1 to 2 12: total energy/volume put in (or taken out) by all the pumps between points 1 to 2

19. Conservation of Matter can tell is about fluid speed (fluid speed is indicator for KE term) I1 = I2 I1 I2 A1v1 = A2v2 continuity equation (just a matter of conserving matter…)

20. Our Model for Analyzing Fluid Flow (use these two ideas to analyze every fluid problem) Conservation of Energy (as applied to Fluids) a.k.a. Fluid Transport Equation (P2– P1) + (1/2)(v22 –v12) +  g( h2 –h1) + IR12 = 12 IR12: Resistance of the pipe between points 1 to 2 12: total energy/volume put in (or taken out) by all the pumps between points 1 to 2 Don’t’s : Since the fluid is in a steady state, you don’t pick two points in time to find the changes. Do’s : Instead, pick two points in the fluid circuit to calculate changes in the various quantities. Conservation of Matter (as applied to Fluids) a.k.a. Continuity Equation I1 = I2, A1v1 = A2v2

21. Note :Closed circuits When you return to the same place in the circuit, ∆P, ∆v2 and ∆h are zero! Therefore the fluid transport equation reads IRtotal = all

22. Below is a fluid circuit that lies flat on a tabletop. The pipe has no resistance and is the same diameter all the way along, except for a one section of narrow pipe. A steady current flows at 1 m3/s. The pressure at point A is 101,300 Pa and at point B it is 101,100 Pa. Use the above information to answer the following questions: • What is the energy density the pump adds to the fluid? • What is the resistance of the pipe Rnarrow? 1 m3/s B A Rnarrow = ???? PA=101,300 Pa PB=101,100 Pa R=0

23. path under consideration 1 m3/s B A start end Rnarrow = ???? PA=101,300 Pa PB=101,100 Pa a) Use the fluid transport equation, starting at B and ending at A.We know that • The heights are the same: hA = hb (i.e. hA - hB = 0) • The velocities are the same: vA = vB • The resistence along the pipe from B to A is zero • There is one pump in the pipe from B to A

24. path under consideration 1 m3/s B A Rnarrow = ???? PA=101,300 Pa PB=101,100 Pa a) i.e. The pump adds 200 Joules per cubic metre of energy to the fluid.

25. 1 m3/s B A end start Rnarrow = ???? path considered PA=101,300 Pa PB=101,100 Pa b) Use the fluid transport equation, starting at A and ending at B.We know that • The heights are the same: hA = hb (i.e. hA - hB = 0) • The velocities are the same: vA = vB • The resistence along the pipe from A to B is Rnarrow • There are no pumps in the pipe from A to B

26. 1 m3/s B A end start Rnarrow = ???? path considered PA=101,300 Pa PB=101,100 Pa b)

27. Take home messages: • The energy (density) gained through the pumps was 200 J/m3. The energy lost to thermal energy is IR = (1 x 200) = 200 J/m3. • These numbers had to be the same, as there is no change between a point and itself! • We only include resistors between the points of interest; not all resistors in the circuit. • We only include pumps between the points of interest; not all the pumps in the circuit.

28. How else is our Steady-State Energy Density Model useful? Electrical circuits !

29. What flows in it? Electricity seems mysterious because we cannot touch it or see it. However, electricity is no more than a flow of charge from one point to the other. Positive charge travels this way I  Current  charge/time, [I] = [Ampere] = [ coulomb/sec] We are going to model the motion of positive charges in a way analogous to how we treated water molecules

30. + - Parameterising our ignornance • Charged particles in circuits feel very strong forces (electric forces). These forces are so strong that that we can safely neglect kinetic energy and gravitational potential energy. • In a fluid system, pressure was the energy stored in the fluid per unit volume. • In circuits, the voltage is the energy stored per unit charge. We have not developed a good idea for where voltage comes from (it involves electric forces, which we do not see until 7C), but we can still use it provided we just accept that charge leaving a battery has a different voltage + -

31. Ideas Fluid transport equation As applied to electrical circuit (V2– V1) + IR12 = 12

32. + - Conventions: Batteries are shown as a pair of lines, the longer of which is the positive terminal. Normal wires are shown as a solid line. These have resistance, but it is so small we neglect it. Things with high resistance are indicated by a zigzagging line, or in the special case of lightbulbs resistor lightbulb (special resistor)

33. Current (charge) conservation Just like the number of water molecules does not change, the number of charges do not change. As the charges push each other along, they cannot build up indefinitely. Current in = current out From rest of circuit To rest of circuit 1 2 3 I1 = I2 = I3, as the current cannot change and there is nowhere else for it to go

34. 2 Current into A = I1 Current out of A = I2 + I3 Current in = current out I1 = I2 + I3 4 From rest of circuit To rest of circuit 1 3 Current into B = I2 + I3 Current out of B = I4 I2 + I3 = I4 = I1 Current (charge) conservation A B

35. 2 4 From rest of circuit To rest of circuit 1 3 Important! A B Never apply the electric transport equation directly between points 1 and 2!(They have different currents, so you don’t know which I to use) Instead, we would use the fact that the voltage drop VB - VA is a fixed value, so it cannot depend on how we get from A to B.If we know the resistances, we can use this and conservation of current to find the current through each resistor.

36. DLM2&3 : Steady-State Density Model applied to Fluid/Electric Circuits Next weekApril10 Lecture 2Quiz1(20min) will cover:Today’s lecture (exclude electric circuit)Activities through DLM2 and FNTs from DLM1Bring Calculator!Closed-book, formulas will be provided.