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Unformatted text preview: Physics 7A2 (C/D) Professor Chertok Fall, 2008 Lecture 4
Original presentations copyright M. Chertok 2008. All rights reserved. Questions? Outline for today
Conservation of Energy: T or F? Recap of DLM 56 Ch. 3  the particle model Quiz 4 M. Chertok, Physics 7A 3 Which of the following can be valid? Use your clickers By the way... if you Which of the join the session before following c(forbe valid? an the 9am I restart it lecture) this might make your clickers not Use your clickers function properly Which of the following can be valid? Use your clickers Eth + Eb = Q M. Chertok, Physics 7A 5 Eth + Eb = W M. Chertok, Physics 7A 6 ΔEth + Eb = Q M. Chertok, Physics 7A 7 ΔEth + ΔEb = W M. Chertok, Physics 7A 8 ΔKE + ΔPE = W M. Chertok, Physics 7A 9 ΔKE + ΔPE = 0 M. Chertok, Physics 7A 10 ΔKE = W M. Chertok, Physics 7A 11 Eth + Eb = W M. Chertok, Physics 7A 12 KE = W M. Chertok, Physics 7A 13 ΔKE + ΔPE = Q+W M. Chertok, Physics 7A 14 ΔKE + ΔPE = QW M. Chertok, Physics 7A 15 Recap of DLM 5 & 6 DLM 5
2.1.3  FNTs from DLM 4
Rocks thrown in different directions cars launched from springs bucket of water on rope 2.1.4  Another new energy system
Rotational KE 2.2.1  Modeling with quantitative expressions...
linear vs. quadratic indicators modeling a thrown ball
M. Chertok, Physics 7A 17 DLM 6
2.2.2  Followup of FNTs from DLM 5
Modeling thrown ball  entire process vs. two subprocesses. Is the result the same? Show that for ball thrown upward, speed at some height going up = speed at same height going down Redeﬁne y=0 as hand, not ﬂoor. Any change in result? Water balloon dropped from building. Thermal energy plus mechanical energy Massspring: ﬁnd work, ﬁnd speeds at various points
M. Chertok, Physics 7A 18 DLM 6, (ii)
2.3.1  Graphically representing energy relationships
PE+KE=Etot is equivalent to ΔKE + ΔPE = 0 Falling ball: Graph PE, Etot, KE for different choices of y=0. What changes and what remains same? Why plot PE and Etot ﬁrst? Massspring: Can we set y=0 wherever we want? No! M. Chertok, Physics 7A 19 Changing (location of) y=0
y=5 y=2 y=0 By changing y=0, we change the PEg as well as Etot So, graphs of these will look different But: maximum height above ﬂoor unchanged!
M. Chertok, Physics 7A 20 Changing (location of) y=0
y=5 y=2 y=0 y=0 By changing y=0, we change the PEg as well as Etot So, graphs of these will look different But: maximum height above ﬂoor unchanged!
M. Chertok, Physics 7A 20 Changing (location of) y=0
y=5 y=3 y=2 y=0 y=0 By changing y=0, we change the PEg as well as Etot So, graphs of these will look different But: maximum height above ﬂoor unchanged!
M. Chertok, Physics 7A 20 Changing (location of) y=0
y=5 y=3 y=2 y=0 y=0 y=2 By changing y=0, we change the PEg as well as Etot So, graphs of these will look different But: maximum height above ﬂoor unchanged!
M. Chertok, Physics 7A 20 Changing (location of) y=0
y=5 y=3 y=2 y=0 } what is Etot here? y=0 y=2 By changing y=0, we change the PEg as well as Etot So, graphs of these will look different But: maximum height above ﬂoor unchanged!
M. Chertok, Physics 7A 20 DLM 6, (iii) 2.2.3  Checking understanding with a new phenomenon
Vertical pulley with string and two unlike hanging masses Which will accelerate faster? M=220 g, m=200 g or M=70 g, m=50 g M. Chertok, Physics 7A 21 Don’t call it “Atwood’s Machine”!
Q: which set of masses will win? Hint
initial state: just as you release masses ﬁnal state: masses have moved distance d and have speed v How many bubbles in the E.I.D.? Closed or open system? M m M. Chertok, Physics 7A 22 Chapter 3 Particle model of matter
Main idea of chapter: investigate “magic” spring
Try to apply as basis for bond energy Remember connection between force and PE
Which was...? M. Chertok, Physics 7A 24 Force: gravity
Potential Energy ( J ) PE height above ground (m) What is the strength and direction of force of gravity?
M. Chertok, Physics 7A 25 Force: gravity
Potential Energy ( J ) PE height above ground (m) What is the strength and direction of force of gravity?
M. Chertok, Physics 7A 25 Force: gravity
Potential Energy ( J ) PE height above ground (m) What is the strength and direction of force of gravity?
M. Chertok, Physics 7A 25 Force: gravity
Potential Energy ( J ) PE height above ground (m) What is the strength and direction of force of gravity?
M. Chertok, Physics 7A 25 Force: gravity
Potential Energy ( J ) PE height above ground (m) What is the strength and direction of force of gravity? Strength: constant. Direction: toward Earth M. Chertok, Physics 7A 25 Force: regular spring
Energy PE y displacement from equilibrium +y M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph!
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Force: regular spring
Energy PE F=0
y displacement from equilibrium +y Where is force greatest? Where is force weakest? What is the direction of the force? Force is negative of derivative of PE graph! (Force is in direction that tries to lower the PE)
M. Chertok, Physics 7A 26 Graphs of TwoObject system
Energy
y displacement from equilibrium +y ???
separation, r (m)
M. Chertok, Physics 7A Energy 27 Graphs of TwoObject system
Energy
y displacement from equilibrium +y ???
separation, r (m)
M. Chertok, Physics 7A Energy 27 Graphs of TwoObject system
Energy 0 separation, r (m) That’s better! Can’t have negative separation
M. Chertok, Physics 7A 28 DLM 7  Starts Today
2.3.2
FNTs from DLM 6: Ball thrown straight up, massspring, horizontal massspring with friction, skier, masses on pulley 2.4.1
Connection between Force and PE Graphing PE versus distance for PEgrav, massspring F = d(PE)/dr (“r” is direction coordinate) 2.4.2
Two objects connected by a spring
M. Chertok, Physics 7A 29 Twoobject system r M. Chertok, Physics 7A 30 Twoobject system r r: distance between objects M. Chertok, Physics 7A 30 Twoobject system r r: distance between objects r0: distance between objects when spring relaxed (equilibrium position) M. Chertok, Physics 7A 30 Twoobject system r r: distance between objects r0: distance between objects when spring relaxed (equilibrium position)
We will study this in great detail
M. Chertok, Physics 7A 30 Atomic hypothesis
... I believe it is the atomic hypothesis... that all things are made of atomslittle particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another...
M. Chertok, Physics 7A 31 PE for 2atom system
e en ship
Potential Energy (in units of well depth, ") Pairwise or AtomAtom Potential
(as modeled with the LennardJones Potential)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Pairwise Potential (as modeled with the LennardJones Potential) hat . tion um rticle 1.2 distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 32 PE for 2atom system
e en ship
Potential Energy (in units of well depth, ") Pairwise or AtomAtom Potential
(as modeled with the LennardJones Potential)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Pairwise Potential (as modeled with the LennardJones Potential) a/k/a LennardJones Potential hat . tion um rticle 1.2 distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 32 PE for 2atom system
e en ship
Potential Energy (in units of well depth, ") Pairwise or AtomAtom Potential
(as modeled with the LennardJones Potential)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Pairwise Potential (as modeled with the LennardJones Potential) a/k/a LennardJones Potential hat . tion um Think about 1.2 rticle strength and direction of force distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 32 PE for 2atom system
e en ship
Potential Energy (in units of well depth, ") Pairwise or AtomAtom Potential
(as modeled with the LennardJones Potential)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Pairwise Potential (as modeled with the LennardJones Potential) a/k/a LennardJones Potential Note location of 2.6 2.8 xaxis 3 hat . tion um Think about 1.2 rticle strength and direction of force distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 32 PE for 2atom system
e en ship
Potential Energy (in units of well depth, ") Pairwise or AtomAtom Potential
(as modeled with the LennardJones Potential)
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Pairwise Potential (as modeled with the LennardJones Potential) a/k/a LennardJones Potential Note location of 2.6 2.8 xaxis 3 hat . tion um Think about 1.2 rticle strength and direction of force Note location of PE minimum
distance between centers of atoms, r (in units of particle diameter, ! )
M. Chertok, Physics 7A 32 Particle Model of Matter
Feynman’s quote F = slope of PE(r)
Direction is such that it reduces the PE Pairwise PE: general form shown on graph
Strong repulsion when too close Attractive when separation greater than equilibrium Attractive force is short range. Attraction becomes weaker as particles separate further M. Chertok, Physics 7A 33 Particle Model, (ii)
For system of many particles, phase (s,l,g) depends on Etot
High energy: particles unbound  gas Average separation is much greater than r0 Low energy: particles bound  solid or liquid Average separation ~ r0 M. Chertok, Physics 7A 34 Particle Model, (iii)
Graph is 1D. However, every particle interacts with all its nearby neighbors.
Result is 3D PE for a given particle. Its minimum deﬁnes equilibrium position of particle in solid or liquid. “single particle PE” Each particle in solid or liquid oscillates in 3D about this equilibrium position
M. Chertok, Physics 7A 35 DLM 8 next week
2.4.3
Follow up from DLM 7  FNTs This is fair game for the next quiz FNTs are: PEgrav: Earth versus Moon Graph of Twomass system if k, r0 change Graph of PEelectrical Detailed graph of LennardJones potential Atomic spacing for solids, liquids and gasses M. Chertok, Physics 7A 36 DLM 8
3.1.1
Particle model: Feynman’s quote 3.1.2
PE graph: how particles interact. Force, PE versus separation 3.1.3
Particle separation for solids, liquids and gasses Water Liquid/gaseous nitrogen! M. Chertok, Physics 7A 37 Quiz 4 Quiz 4
Next Friday! Covers:
DLM 1 through... DLM 7 (including FNTs discussed in DLM08) M. Chertok, Physics 7A 39 ...
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Full Document
 Fall '08
 PARDINI
 Physics, Conservation Of Energy, Energy, Force, Potential Energy, General Relativity, Physics 7A, M. Chertok

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