Quiz information on the course website Include : Quiz answers (posted by ~5pm Tuesdays) Quiz problems Quiz rubrics (posted by 5pm following Tuesdays) Quiz

Quiz information on the course website Include :Quiz answers (posted by ~5pm Tuesdays)Quiz problemsQuiz 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 thatmeet after the following quiz. (I.e. Quiz3 will be returned later next week)

What about Quiz 1? Average 8.69Those who has not gotten them back will get them in the first DLM this week. Answer, rubrics are on the course web site.

Request regrade? => Submit your quiz along with Quiz Re-evaluation Request Form (available from the course website) to me AFTER the lecture by lecture 6 (Feb12)

What about Quiz 2?Quiz 2 will be returned in DLM 7 this week.

Quiz 3 8:30-8:50am TODAYHave your calculator ready

Closed book

Next lecture February 5Quiz 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 farEnergy systems so far

EEthermatherma

ll

TT

EEbondbond

PhasePhase

KEKESpeedSpeed

PEPEgragra

vv

heightheight

EEelectrelectr

icic

EEmass-springmass-spring

Distance from Distance from

the the

equilibrium equilibrium

positionposition

EEnucleanuclea

rr

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 EnergyConservation of Energy

5

2

Etot = 10 Joule

3

Nature happens…

Energy Interaction ModelEnergy Interaction ModelEtot = 10 Joule

7 1 2

Energy Interaction ModelEnergy Interaction Model

(-3J) + (+5J) + (-2J) = 0∆Eorange + ∆ Emelon + ∆ Egrape = 0

Etot = 10 Joule

7 1 2

Etotal = Eorange + Emelon + Egrape

X

Y

Z

2.1-1) Three rocks of equal mass are thrown with identical speeds from the top of thesame building. Rock X is thrown vertically downward, rock Y is thrown verticallyupward, and rock Z is thrown horizontally. Which ball has the greatest speed justbefore it hits the ground? Assume air resistance is negligible.

FNT 2.1.-1Equal mass, identical initial speedsWhich rock has the greatest speed just Before it hits the ground?


FNT 2.1.-1X

Y

Z

Increase in the KE system is the same as the decrease in the PEgrav system

∆PEgravX + ∆ KEX = 0

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

(KEX)initial = (KEY)initial = (KEZ)initial (PEgrav

X )initial= (PEgravY )initial= (PEgrav

Z )initial

(PEgravX)final - (PEgrav

X)initial + (KEX)final - (KEX)initial = 0

0 - (PEgravX)initial + (KEX)final - (KEX)initial = 0

=> (KEX)final = (KEX)initial + (PEgravX)initial

Wait a minute!


FNT 2.1.-1X

Y

Z

Total energy of the system remains unchanged

EtotX = PEgrav

X + KEX = Constant

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

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 BallBowling Ball

What is the height of the bowling ball after one full swing?

(a) Same

(b) Higher

(c) Lower


What is the height of the bowling ball after one full swing?

(a) Same

(Assume friction is negligable)


(a) Starting point

(b) When rope is vertical

(c) At point c.

When is the speed of the bowling ball maximum?

ab

c



When is the speed of the bowling ball maximum?

ab

c


(a) Starting point


(c) At point c

When is the PEgravity of the bowling ball maximum?

ab

c


(a) Starting point

(c) At point c.

When is the PEgravity of the bowling ball maximum?

ab

c


PEgravity = - KEmgh = - (1/2) m v2

Etotal = PEgrav + KE = constant

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 v2

Conservation of Energy dictates that:

All of the PE goes into KE, and then back again!

Consider a simple pendulum:


InitialFinal(Still in motion)PEgrav

Height

KESpeed


PEgrav

Height

KESpeed

Final

Initial

(In motion)


PEgrav

Height

KESpeed

Initial

Final (Still in motion)

Potential Energy: SpringsPotential 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!

PEspring = (1/2) kx2PEspring = (1/2) kx2

x

Mass-Spring SystemsMass-Spring Systems

• k is a property of the spring only• PEmass-spring does not depend on mass• PE = 0 arbitrary

PEmass- spring = (1/2) ky2 +CPEmass- spring = (1/2) ky2 +C

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.




PEmass-

spring

∆y

KESpeed




PEmass-

spring

∆y

KESpeed


PEspring-mass = - KE(1/2)k y2 = - (1/2) m v2

Etotal = PEspring-mass + KE = constant

Just like a simple pendulum:• At the peak of the amplitude, the object is at rest. PEmass-spring = (1/2) m y2(define y from the

equilibrium position)• At the equilibrium position, the object is moving quickly, and y =0. KE = (1/2) m v2

Conservation of Energy dictates that:

All of the PE goes into KE, and then back again!

Graphing EnergiesGraphing 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 Potential Energy and Forces: Forces:

Springs, GravitationalSprings, Gravitational

The indicator is how much the spring is stretched or compressed, x, from its equilibrium position.

PEspring = (1/2) kx2PEspring = (1/2) kx2

x

∆PEgrav =

€

mgh h

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)

PE vs displacement: Force

Displacement from equilibrium y[+][-]



direction of force


direction of force



On this side force pushes up

On this side force pushes down

Equilibrium

Forces from potentials point in direction

that (locally) lowers PE


Potential Energy vs r and Potential Energy vs r and ForcesForces

• 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

Why does it take more energy to vaporize than

to melt?Whst is Ebond?

We will model real atoms of liquids and solids as oscillating masses and springs

Particle Model of Matter

What does this to do with real What does this to do with real world??world??

• 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

r

Introduction to the Introduction to the Particle Model Particle Model

Potential Energy between two atomsPotential Energy between two atoms

separation

Flattening: atoms have negligible forcesat large separation.

Repulsive: Atoms push apart as they get too close

r

PE

Distance between the atoms

Closed Book

Make sure above boxes are filled!

Documents

Quiz information on the course website Include : Quiz answers (posted by ~5pm Tuesdays) Quiz problems Quiz rubrics (posted by 5pm following Tuesdays) Quiz