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Lecture #4

Lecture #4. Cassandra Paul Physics 7A Summer Session II 2008. Graphing. On Monday we didn’t get to finish talking about graphing, let’s do that now. Diving: Potential Energy. From board From floor. 2m or 5m. 0m or 3m. -2m or 1m. -3m or 0m.

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Lecture #4

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  1. Lecture #4 Cassandra Paul Physics 7A Summer Session II 2008

  2. Graphing On Monday we didn’t get to finish talking about graphing, let’s do that now.

  3. Diving: Potential Energy From board From floor 2m or 5m 0m or 3m -2m or 1m -3m or 0m At highest point, Tricia Woo is 2 meters above the board and 5 meters above the water, how should we calculate her PE? Where should we measure the height from?

  4. System: Diver Initial: Highest point Final: Just before hitting water How can it not Matter!? From board From floor 2m or 5 m 0m or 3m KEtrans PEgravity Speed Height -2m or 1m + - ΔKE +ΔPE= 0 -3m or 0m ½ m(vf2-vi2) + mg(hf-hi)= 0 (0 - 5) (0.5)(50kg)(vf2-0) + (50kg)(10m/s2)(hf-hi)= 0 (-3 - 2) Δh is the same! Δh=-5 so vf = 10m/s

  5. Instantaneous PE and KE ΔKE +ΔPE= 0 (KEf – KEi) + (PEf- PEi) = 0 KEf + PEf - KEi - PEi = 0 KEf + PEf = KEi + PEi = Etot The sum total of all of the energies at one point in time is equal to the total energy of the system. In a closed system that value is constant throughout the process. KEanytime + PEanytime = Etot

  6. Let’s graph our instantaneous energy…. 2m 0m -2m -3m Mass=50kg Say g = 10m/s2

  7. Practice this!!!! Energy in Joules X axis is height in meters

  8. Where have I set h=0? A 5m Energy in Joules B C X axis is height in meters D The answer is D! Potential Energy is 1 meter above the water. Why? Look at the Graph we can tell that PE is zero At letter D, and KE is zero at A. From there we should Be able to work backwards to interpret the graph. E

  9. h=0 at board (3 meters above water) Same and different? • PE can be negative • KE can’t be negative. (½ mv2) • Etot is NOT the same for both cases • KE line remains the same! (2500J just before hitting the ground) Energy in Joules h=0 (2 meters above water) X axis is height in meters Energy in Joules X axis is height in meters

  10. Springs! Intro to Spring-Mass Oscillator Model (another model in blue pages in course notes)

  11. Potential Energy: Springs • Springs contain energy when you stretch or compress them. We will use them a lot in Physics 7. • The indicator is how much the spring is stretched or compressed, x, from its equilibrium position. • k is a measure of the “stiffness” • of the spring, with units [k] = kg/s2. • x: Much easier to stretch a spring a little bit than a lot! ΔPEspring = (1/2) kΔx2 x

  12. Mass-Spring Systems ΔPEmass- spring = (1/2) kΔx2 • k is a property of the spring only • PEmass-spring does not depend on mass • PE = 0 arbitrary x x x

  13. Mass-Spring Systems KE Speed PEmass-spring ∆y initial final Δx = -2cm

  14. Mass-Spring Systems KE Speed PEmass-spring ∆x System: mass-spring Initial: mass at rest at 2cm Final: mass at x=0 initial X = 2cm final (x

  15. ∆PEgrav = x Potential Energy and Forces: Springs, Gravitational • The indicator is how much the spring is stretched or compressed, x, from its equilibrium position. ΔPEspring = (1/2) kΔx2 The indicator is the change in vertical distance that the object moved (I.e. change in the distance between the center of the Earth and the object) h

  16. PE vs displacement: Force [-] Displacement from equilibrium y [+]

  17. PE vs displacement: Force direction of force [-] Displacement from equilibrium y [+]

  18. PE vs displacement: Force direction of force [-] Displacement from equilibrium y [+]

  19. PE vs displacement: Force On this side force pushes down Forces from potentials point in direction that (locally) lowers PE Equilibrium On this side force pushes up [-] Displacement from equilibrium y [+]

  20. Graphing Energies • What are the x-axis, y axis? Units? • x axis (independent variable: height) • y axis (dependent variable: PEgrav) • Which quantity (energy) is the easiest to graph? • Etot ? PEgrav? What about KE? • Where should the origin (0) be placed? Where does it most make sense? • Should the floor be 0m?

  21. Practice: Pendulum Cassandra, how can we do a practice problem with a pendulum? We’ve never learned anything about pendulums!!!!!!!! Yes you have! Just use the Model, You’ll be surprised How much it will tell you.

  22. Practice: Pendulum A 2kg pendulum swings to a maximum height of 3 meters. At it’s lowest point it is one meter above the floor. Find the maximum speed of the pendulum, and then graph Etot, PE and KE as a function of distance. • 6.32 m/s • 7.74 m/s • 60m/s • None of these Initial 2m 3m Final (Still in motion)

  23. Let’s use the instantaneous method instead of the Energy Diagram SUM OF ALL ENERGIES PRESENT = Etot PEanytime + KEanytime = Etot Initial 2m PEtop + KEtop = Etot 3m Final (Still in motion) mgh + 0 = Etot Set h=0 at floor (2)(10)(3)J + 0 = Etot =60J PEbottom + KEbottom = Etot mgh + ½ mv2 = 60J (2)(10)(1) + ½ 2v2 = 60J  v=6.32m/s

  24. Initial 2m 3m Energy  Height 

  25. Back to Springs…

  26. r OK so springs are cool for physicists, but does understanding the spring help us understand anything else?? What is Ebond anyway?? • Three-phase model of matter • Energy-interaction model • Mass-spring oscillator • Particle model of matter • Particle model of bond energy • Particle model of thermal energy • Thermodynamics • Ideal gas model • Statistical model of thermodynamics We will model real atoms of liquids and solids as oscillating masses and springs Particle Model of Matter

  27. Intro to Particle Model of Matter This model helps us understand how particles interact with each other at the molecular level. (another blue page in your course notes)

  28. Goal : To understand macroscopic phenomena (e.g. melting, vaporizing) and macrocopic properties of matter such as phases, temperature, heat capacities, in terms of microscopic constituents and its behavior. r We will model real atoms of liquids and solids as oscillating masses and springs Particle Model of Matter

  29. ~ two atomic size particles interacting via“pair-wise potential” a.k.a. Lennard-Jones Potential Model Bonded Atoms as Masses on Spring Atom 2 (bonded or un-bonded) Atom 1 (anchored)

  30. r0 Ro the distance that the particles are at equilibrium We observe the system oscillating. At one instance we take a snapshot of the oscillation and see this: r > r0 2 1 Which way is the force on particle #2? • To the right because the particle is traveling to the right.  • We can’t tell because we don’t know which way the particle is traveling • To the left because the spring is pulling from the left.  • We can’t tell which way it’s traveling but we know the force is to the right.  • There is no force acting particle 2.

  31. Lennard-Jones Potential(pair-wise potential) Energy  IT’S JUST A WEIRD SPRING! Equilibrium separation ro Distance  Not to scale (particles are just about touching at equilibrium)

  32. Link to Applet: • http://polymer.bu.edu/java/java/intermol/index.html Don’t worry about this graph on the right.

  33. r Introduction to the Particle Model Potential Energy between two atoms PE Repulsive: Atoms push apart as they get too close Flattening: atoms have negligible forcesat large separation. separation Distance between the atoms

  34. Equations to memorize, and more importantly know how to use for Monday’s Quiz mcΔT= ΔEth ±lΔmΔHl= ΔEb ½ mΔ(v2)= ½ m (vf2-vi2) = ΔKEtrans ½ k (Δxf2-Δxi2) = ΔPEspring mgΔh= ΔPEgrav Also, we don’t use an equation for rotational energy, but know how to tell if it’s there.

  35. DL sections • Swapno: 11:00AM Everson Section 1 • Amandeep: 11:00AM Roesller Section 2 • Yi: 1:40PM Everson Section 3 • Chun-Yen: 1:40PM Roesller Section 4

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