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```									Quiz information on the course website
Include :
Quiz answers (posted by ~5pm Tuesdays)
Quiz problems
Quiz rubrics (posted by 5pm following Tuesdays)
Quiz score will also be posted by the end of the
following week.

Quizzes will be returned in your DL section that
meet after the following quiz. (I.e. Quiz3 will be
returned later next week)
What about Quiz 1?              Average 8.69
Those who has not gotten them back will get them in the first
DLM this week. Answer, rubrics are on the course web site.

evaluation Request Form (available from the course
website) to me AFTER the lecture by lecture 6 (Feb12)

Quiz 2 will be returned in DLM 7 this week.
Quiz 3 8:30-8:50am TODAY
Closed book

Next lecture February 5
Quiz 4 will cover the material from today’s
lecture, FNT’s from DLM 5, material from
DLM6&7 this week, including FNTs for DLM7
but NOT FNT’s for DLM8.
Energy systems so far

Emass-spring
KE                Etherm         Ebond            Distance from
Speed                  al         Phase           the equilibrium
T                              position

PEgra
Eelectri              v              Enuclea
c                height                r

Energy is converted from one form to another, but
NEVER created nor destroyed.
If the energy of an object increases, something else must have
given that object its energy.
Conservation of Energy
Etot = 10 Joule

5
3
2

Nature happens…
Energy Interaction Model
Etot = 10 Joule

7
2                        1
Energy Interaction Model
Etot = 10 Joule

7
2                                        1

(-3J) + (+5J) + (-2J) = 0
∆Eorange + ∆ Emelon + ∆ Egrape = 0
Etotal = Eorange + Emelon + Egrape
Conservation of Energy

FNT 2.1.-1
Equal mass, identical initial speeds
Which rock has the greatest speed just
Before it hits the ground?
Conservation of Energy
FNT 2.1.-1

Equal mass, identical initial speeds
Which rock has the greatest speed just
Before it hits the ground?

Increase in the KE system is the same as the decrease in the PEgrav system
∆PEgravX + ∆ KEX = 0
(PEgravX)final - (PEgravX)initial + (KEX)final - (KEX)initial = 0
0           - (PEgravX)initial + (KEX)final - (KEX)initial = 0
=>
(KEX)final = (KEX)initial + (PEgravX)initial

Wait a minute! (KEX)initial = (KEY)initial = (KEZ)initial
(PEgravX )initial= (PEgravY )initial= (PEgravZ )initial
Conservation of Energy
FNT 2.1.-1

Equal mass, identical initial speeds
Which rock has the greatest speed just
Before it hits the ground?

Total energy of the system remains unchanged
EtotX = PEgravX + KEX = Constant

How do the total energies of the three rocks compare initially?

Same

How do the total energies of the three rocks compare finally
(or at anytime) ?
Same
Bowling Ball

What is the height of
the bowling ball after one full swing?
(a) Same
(b) Higher
(c) Lower
Bowling Ball

What is the height of
the bowling ball after one full swing?
(a) Same
(Assume friction is negligable)
Bowling Ball

c               a
b
When is the speed of the bowling ball
maximum? (a) Starting point

(b) When rope is vertical
(c) At point c.
Bowling Ball

c                a
b
When is the speed of the bowling ball
maximum?

(b) When rope is vertical
Bowling Ball

c               a
b
When is the PEgravity of the bowling ball
maximum? (a) Starting point

(b) When rope is vertical
(c) At point c
Bowling Ball

c            a
b
When is the PEgravity of the bowling ball
maximum? (a) Starting point

(c) At point c.
Conservation of Energy
Consider a simple pendulum:
At the height (peak) of the amplitude, the object is
at rest. PEgravity = mgh (define h above the low point)

At the bottom of the motion, the object is moving
quickly, and h=0. KE = (1/2) m Dv2

Conservation of Energy dictates that:
DPEgravity = - DKE
mgDh = - (1/2) m Dv2
Etotal = PEgrav + KE = constant
All of the PE goes into KE, and then back again!
Bowling Ball

Initial
Final
(Still in
KE      PEgrav   motion)
Speed   Height
Bowling Ball

Final
Initial

KE      PEgrav           (In motion)
Speed   Height
Bowling Ball

Initial
Final
(Still in
KE      PEgrav             motion)
Speed   Height
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, Dx, from its equilibrium position.

DPE spring = (1/2) kDx 2
x
• k is a measure of the “stiffness”
of the spring, with units [k] = kg/s2.

• Dx: Much easier to stretch a spring a little bit than a lot!
Mass-Spring Systems

DPEmass- spring = (1/2) kDy2 +C
• k is a property of the spring only
• PEmass-spring does not depend on mass
• PE = 0 arbitrary
Mass-Spring Systems

KE      PEmass-
spring
Speed
∆y
Mass-Spring Systems

KE       PEmass-
Speed     spring
∆y
Conservation of Energy
Just like a simple pendulum:
• At the peak of the amplitude, the object is at
rest. PEmass-spring = (1/2) m Dy2(define y from the
equilibrium position)
• At the equilibrium position, the object is moving
quickly, and Dy =0. KE = (1/2) m Dv2

Conservation of Energy dictates that:
DPEspring-mass = - DKE
(1/2)k Dy2 = - (1/2) m Dv2
Etotal = PEspring-mass + KE = constant
All of the PE goes into KE, and then back again!
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?
Potential Energy and Forces:
Springs, Gravitational

The indicator is how much the spring is stretched or compressed,
Dx, from its equilibrium position.
x
DPEspring = (1/2) kDx2

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)

∆PEgrav =                     h
PE vs displacement: Force

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

direction of force

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

direction of force

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

On this side
force
pushes
down
Forces from potentials
point in direction
Equilibrium                        that (locally) lowers PE

On this side     [-]   Displacement from equilibrium y [+]
force
pushes up
Potential Energy vs r and Forces

• Force is always in direction that decreases PE
• Force is related to the slope -- NOT the value of PE
• The steeper the PE vs r graph, the larger the force
What does this to do with real world??
Why does it take more
• Three-phase model of matter               energy to vaporize than
to melt?
Whst is Ebond?
• Energy-interaction model
r
• Mass-spring oscillator

• Particle model of matter
 Particle model of bond energy
 Particle model of thermal energy
We will model real atoms of liquids
and solids as oscillating masses and springs
•Thermodynamics            Particle Model   of Matter
• Ideal gas model
• Statistical model of thermodynamics
Introduction to the Particle Model
Potential Energy between two atoms
P
E

Repulsive:
Atoms push apart as they
get too close

Flattening:
atoms have negligible forces
at large separation.

separation

r

Distance between the atoms
Closed Book

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