Physics 7A -- Lecture 3 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg...

Physics 7A -- Lecture 3

Winter 2008

Physics 7A -- Lecture 3

Winter 2008

Prof. Robin D. Erbacher343 Phy/Geo Bldg

[email protected]

Prof. Robin D. Erbacher343 Phy/Geo Bldg

[email protected]

AnnouncementsAnnouncementsAnnouncementsAnnouncements• Join this Class Session with your PRS clicker! (Credit begins today.)

• Quiz 2 is today! Lecture 1-2, DLMs 1-5. Must take it in your correct lecture time slot.

• Quiz 1 Rubric posted, and grading scale is linked.

• Check Physics 7 website frequently for calendar &Announcements.

• Turn off cell phones and pagers during lecture.

Energy ConservedEnergy ConservedEnergy ConservedEnergy Conserved

Etherma

l

EbondEmovement

(KE)

Egravit

y

Eelectri

c

Esprin

g

........

Energy is converted from one form to another, but never created or destroyed!

Steam engine

EEnuclearnuclear

Nuclear power plant

There are many different forms of energy (energy systems):

Energy System ExpressionsEnergy System ExpressionsEnergy System ExpressionsEnergy System Expressions

•Ethermal = C T = mcpT, Temperature is the indicator.

• Between phase changes, only thermalenergy changes.

• Ebond = |m H|, m is the indicator.

• At a physical phase change, only the bond-energy system changes. H is the heat of the particular phase change. m is the amount that changed phase.

• In a chemical reaction, there are several bond energy changes corresponding to diff. molecular species (reactants or products). Here H is the heat of formation for a particular species.

Etherma

l

Ebond

Energy Interaction Diagrams - Energy Interaction Diagrams - Closed SystemClosed System

Energy Interaction Diagrams - Energy Interaction Diagrams - Closed SystemClosed System

Ea Eb Ec

Conservation of EnergyThe total energy of a closed physical system must remain constant. So, the change of the energies of all energy systems associated with the physical system must sum to zero.

Change in closed system energy = ∆Ea + ∆ Eb + ∆ Ec = 0

Energy Interaction Diagrams - Energy Interaction Diagrams - Open SystemOpen System

Energy Interaction Diagrams - Energy Interaction Diagrams - Open SystemOpen System

Ea Eb Ec

Conservation of EnergyThe change of the energies of all systems associated with an open physical system must sum to the net energy added or removed. Energy is added or removed as Heat or Work.

Change in open system energy = ∆Ea + ∆ Eb + ∆ Ec

= (Energy added) - (Energy removed) = Q + W.

Energy added Energy removed

Example for Open SystemExample for Open SystemExample for Open SystemExample for Open System

Ea

Energy added = + 100 J

Suppose we have a system where 100J of heat comes in from the outside. Joe claims that the only energy system that changes is Ea and that Ea is negative (Ea decreases).

Can Joe be correct?1) Yes, its possible that he is correct.2) Yes, Joe is definitely correct.3) No way is Joe’s description correct.

Clicker!

Energy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsExample: Melting IceTi= 0°C Tf = room temperature

Tem

pera

ture

Energy of substance

solid

liquid

gas

l-g coexist

s-l coexist

Initial

TMP

TBP

Final

Energy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsEnergy Interaction DiagramsExample: Melting Ice

Process 1: Ice at T=0ºC Water at T=0ºCProcess 2: Water at T=0ºC Water at room temperature

Tem

pera

ture

Energy of substance

solid

liquid

gas

l-g coexist

s-l coexist

Process 1Initial

TMP

TBP

Process 1Final /

Process 2Initial

Process 2Final


Process 1: Ice at T=0ºC Water at T=0ºC

Ice

∆T=0

∆Eth=0

Initial phase Solid, Final phase Liquid

Etherm

al

Ebond



Ice

∆T=0

∆Eth=0


Etherm

al

EbondHeat



Ice

∆T=0

∆Eth=0


∆Eth + ∆Ebond= Q+W

∆Ebond= Q

Etherm

al

EbondHeat


Process 2: Water at T=0ºC Water at room temperature

Ice

Initial phase Liquid, Final phase Liquid

Etherm

al

Ebond


Process 2: Water at T=0ºC Water at room temperature

Ice

Initial phase Liquid, Final phase Liquid

∆Ebond= 0

Etherm

al

Ebond

T

Heat

∆Eth + ∆Ebond= Q+W

∆Eth= Q


Ice

Initial phase Liquid, Final phase Solid

Etherm

al

Ebond

Freezing (Water at T=0°C Ice at T=0°C)

∆T=0

∆Eth=0

Heat

NOTE: Heat is released when bonds are formed! (In general E is negative)

EIM Algebra ReviewEIM Algebra ReviewEIM Algebra ReviewEIM Algebra Review• For a closed system:

(Is it clear why there’s no Q or W for a closed system?)

• For an open system:

(Q and W can be positive or negative, as can Es.)

€

E total = ΔE1 + ΔE 2 + ΔE 3 + ... = 0

€

E total = ΔE1 + ΔE 2 + ΔE 3 + ... = Q + W

Three New Energy Systems

Three New Energy Systems

Examples: Mechanical Examples: Mechanical PhenomenaPhenomena

Examples: Mechanical Examples: Mechanical PhenomenaPhenomena

EEmovementmovement

(KE)(KE)

EEgravitgravit

yy

EEsprinsprin

gg

Rear shock absorber and spring of

BMW R75/5Motorcycle

Kinetic Energy System (KE)Kinetic Energy System (KE)Kinetic Energy System (KE)Kinetic Energy System (KE)

• Kinetic energy is simply Emoving.

• For translational energy, the indicator is speed; the faster an object moves, the more KE it has.

•There is a quantitative relationship between KE and speed. Also, it is proportional to the mass of the object:

• The direction of motion of the object is unimportant.

KEtrans = ½ m v2KEtrans = ½ m v2

Baseball

WorkKEKE

SpeedSpeed

WorkWorkWorkWork

€

E total = ΔE1 + ΔE 2 + ΔE 3 + ... = Q + WRemember this equation for an open system?

You have worked a lot with Q, Heat. Now we introduce Work:

Work: A transfer of energy that takes place from a physical system to another physical system due to an interaction that involves a Force.

KEKESpeedSpeed

Baseball

Work

1) The pitcher’s hand “pushed” the baseball.2) The pitcher’s hand exerted force on the baseball.3) As a result, the baseball started moving (its KE increased).

May the Force Be With You!May the Force Be With You!

"an energy field, created by all living things, that surrounds us, penetrates us, and binds the galaxy together."

ForceForceForceForceTo be more precise, we need the concept of

“Force” : “Push” or “Pull”

An overall push (or pull!) in the direction the object is travelling

has the effect of speeding it up.

1) Block is already moving, you push in same direction:

direction of travel

direction of Force

KEKESpeedSpeed

Work

Consider a block being pushed by you on a level surface with no friction:

ForceForceForceForceTo be more precise, we need the concept of

“Force” : “Push” or “Pull”

Consider a block being pushed by you on a level surface with no friction:

2) Block is already moving, you push in opposite direction:

direction of travel

direction of Force

KEKESpeedSpeed

Work

An overall push (or pull!) in against the direction the object

is travelling has the effect of slowing it down.

Work Work Work Work

What’s force got to do with work?

WorkWork Transfer of energy into or out of a physical system by a force exerted by another physical system.

The change in energy results from an interaction in which an object moves through a distance parallel to the force exerted on it.

Work = Fparallel ∆x = F|| ∆x

[Joule] = [Newton] [m]=[Nm]

Work Example Work Example Work Example Work Example How much energy was transferred to the KE system

of the baseball in form of Work?

KEKESpeedSpeedBaseb

all

Work

(290 J, assume v=100mph=44m/s, m=0.3kg)

1. Conservation of Energy says…

∆KE = Work

∆KE = KEfinal - KEinitial =1/2(m)(vf2) - 0

2. What about force?

Work = F|| ∆ x= F|| (1m)

F|| = 290 N

Properties of ForcesProperties of ForcesProperties of ForcesProperties of Forces

Force is a vector quantityi.e. Forces have both magnitude and direction

Force is the agent of interaction of TWO objectse.g. The pitcher’s hand and the baseball

The two forces involved in an interaction are opposite and equal

(Newton’s Third Law)

Fhand on the baseball = - Fbaseball on the hand

Properties of ForcesProperties of ForcesProperties of ForcesProperties of Forces

Force is a vector quantityi.e. Forces have both magnitude and direction

Force is the agent of interaction of TWO objectse.g. The pitcher’s hand and the baseball

The two forces involved in an interaction are opposite and equal

(Newton’s Third Law)

Contact force v. non contact force:

Fgravitational

Conservation of Energy says…

∆PEgrav = Work

= Fyou on mass ∆height= mg(hfinal - hinitial)

mm

mm vf=0

Pull

vi=0

Work was done on the mass:Work = F||∆x

Where did the energy go??

∆x PEgrav

HeightWork

What is the indicator of the object change?

Temperature? Phase? Speed?

Potential Energy System (PE)Potential Energy System (PE)Potential Energy System (PE)Potential Energy System (PE)

• Potential energy due to gravity: Eheight. (There are other

types of PE, such as PE in a spring, or chemical PE.)

• For gravitational PE, the indicator is height; a higher object (with respect to something else) has more PEgravity. Can we show this?

• The quantitative relationship between PE and height:

(g~10 m/s2 is the acceleration due to gravity on Earth.)

PEgravity = mghPEgravity = mgh

PEgrav

Height

Gravitational Potential EnergyGravitational Potential EnergyGravitational Potential EnergyGravitational Potential Energy

PEgravity = mghPEgravity = mgh

• Gravitational potential energy-system exists for each pair of objects interacting by the gravitational force

• ∆PEgravity depends on two quantities: the change in vertical distance that the object moved, and the mass of the object.

• Usually, we focus on the gravitational potential energy due to the interaction between an object and the Earth.

Crumpled PaperKE

SpeedNote: we are neglecting the friction

KE KE PE PEgravitygravityKE KE PE PEgravitygravity

1) You throw a ball to the height of the first floor window.2) Now you want to throw a ball to the height of the 4th floor.

Question: How much faster do you need to throw it?

a) 2 times as fastb) Twice as fast• Thrice as fast• 4 times as fast• 16 times as fast

Bowling BallBowling BallBowling BallBowling Ball

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

(a) Same

(b) Higher

(c) Lower


(a) Starting point

(b) When rope is vertical

(c) After reaches point c.

When is the speed of the bowling ball maximum?

ab

c


(a) Starting point

(b) When rope is vertical

(c) After reaches point c.

When is the PEgravity of the bowling ball maximum?

ab

c

Conservation of EnergyConservation of EnergyConservation of EnergyConservation of Energy

PEgravity = KEtranslational

mgh = ½ m v2

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

• At the bottom of the motion, the object is moving quickly, and h=0. Etrans = ½ m v2

Conservation of Energy dictates that:

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

Work Work Kinetic Energy Only? Kinetic Energy Only?Work Work Kinetic Energy Only? Kinetic Energy Only?

mm

mm v=0

Pull

v=0

Mass is pulled part way up a well (like in FNT).

This time work is done but there is no change in KE when v=0.

Work entering or leaving does NOT automatically mean KE is increasing or decreasing.

Similar to how heat entering or leaving does NOT automatically mean the temperature is changing.


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: SpringsPotential 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 (rest) state.

• 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 = ½ kx2PEspring = ½ kx2

x

Mass-Spring SystemsMass-Spring SystemsMass-Spring SystemsMass-Spring Systems

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

PEvertical spring = ½ ky2 +CPEvertical spring = ½ ky2 +C

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Mass-Spring SystemsMass-Spring SystemsMass-Spring SystemsMass-Spring Systems

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Is the KE (kinetic energy) of a mass-spring system a function of position?

a) No, in this case the potential energy is a function of position.

b) The kinetic energy can be treated as a function of position provided the system is closed.

c) The kinetic energy can always be treated as a function of position in a mass-spring system.

d) The kinetic energy can be treated as a function of position provided the system is open.

e) Not enough information is given.

Kinetic EnergyKinetic EnergyKinetic EnergyKinetic Energy

• In any situation, KE is:

• Sometimes from the conservation of energy:

we can express KE in terms of position (h, y, etc).

• KE can never be negative!

PEgravity = KEtranslational

mgh = ½ m v2

KEtrans = ½ m v2 KEtrans = ½ m v2

Next Time: Potentials, and Particle Models of

Matter

Next Time: Potentials, and Particle Models of

Matter

Physics 7A -- Lecture 3 Winter 2008 Prof. Robin D. Erbacher 343 Phy/Geo Bldg...

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