Theme Music: Blondie Atomic - UMD PhysicsFoothold ideas: Energies between charge clusters Atoms and...
Transcript of Theme Music: Blondie Atomic - UMD PhysicsFoothold ideas: Energies between charge clusters Atoms and...
1/29/16 1 Physics 132
■ Theme Music: Blondie Atomic
■ Cartoon: Bill Amend FoxTrot
January 29, 2016 Physics 132 Prof. E. F. Redish
Potential energy and force
Work energy theorem
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F = − dUdx
Δ 1
2 mv2( ) = !
F ⋅d!r∫
Foothold ideas: Conservation of Mechanical Energy
■ Mechanical energy – The mechanical energy of a system of objects
is conserved if resistive forces can be ignored.
■ Thermal energy – Resistive forces transform coherent energy
of motion (energy associated with a net momentum) into thermal energy (energy associated with internal chaotic motions and no net momentum)
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Δ KE + PE( ) = 0KEinitial + PEinitial = KEfinal + PEfinal
This is why we define the PE with a negative sign.
Foothold ideas: Energies between charge clusters ■ Atoms and molecules are made up of charges. ■ The potential energy between two charges is
■ The potential energy between many charges is
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U12elec = kCQ1Q2
r12
U12...Nelec =
kCQiQj
riji< j=1
N
∑
Foothold ideas: Forces from PE
■ For conservative forces, PE can be defined by ■ If you know U, the force can be gotten from
it via
■ In more than 1D need to use the gradient
■ The force always points down the PE hill.
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F ⋅ Δr = −ΔU
The extra potential energy from adding Q as a function of position r of charge Q
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-q
-q
r 2q Q
ΔU = kCQ
qi
rQ→qii=1
3
∑ = kCQq1
r1
+q2
r2
+q3
r3
⎛
⎝⎜⎞
⎠⎟
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Foothold ideas: Bound states
■ When two objects attract, they may form a bound state – that is, they may stick together.
■ If you have to do positive work to pull them apart in order to get to a separated state with KE = 0, then the original state was in a state with negative energy.
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The Gauss Gun: A classical analog of an exothermic reaction
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Sketch 1. What the potential energy curve
must look like between the magnet and a metal sphere as a function of distance. (Hint: think about the WEΘ)
2. Energy bar graphs that show the initial and final energies of each of the 4 spheres (when the moving one is far from the magnet)
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Energy conservation with chemical reactions: 1
■ Consider the collision of two molecules in isolation A + B → A + B
■ If the initial and final states both have the two molecules far apart, UAB ~ 0.
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KA + KB +UAB = constant
KA + KB = constant
Energy conservation with chemical reactions: 2
■ Consider the reaction of two molecules in isolation A + B → C + D
■ If the initial and final states both have the
two molecules far apart, UAB ~ UCD ~ 0.
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KA + EA( ) + KB + EB( ) +UAB = KC + EC( ) + KD + ED( ) +UCD
KA + EA( ) + KB + EB( ) = KC + EC( ) + KD + ED( )Note: The “E”s here are molecular internal energies and are negative since the molecules are bound. The (positive) bond energies from chemistry are given by E = -E > 0.