Conservation of EnergyConservation of Energy

Mr. Finn

Honors Physics

December, 2011

Key QuestionsKey Questions

1. What does “conservation” mean?

2. What is “energy?”

3. Is this law the result of “circular reasoning?”

4.4. ““Misconceptions” about energy.

ConservationConservation

• Use sparingly or carefully– Avoid waste, economize– Saving for future use

• Preservation from loss, damage, neglect– Protection of natural resources

• Maintenance of a physical quantity during a change

Scientific usage of the term!Scientific usage of the term!Scientific usage of the term!Scientific usage of the term!

Conservation LawsConservation Laws

As a systemsystem (collection of physical objects interacting with each other) undergoes a change of statestate (configuration or arrangement of the objects), a physical quantity remains constant. Or the initial value of the quantity is the same as the final value of the quantity:

Qi = Qf

Classical Conservation LawsClassical Conservation Laws

• Linear/Translational Momentum• Angular/Rotational Momentum• Energy

– Mechanical energy

• Mass – quantity that determines gravitationalgravitational forces

• Electric Charge– quantity that determines electromagneticelectromagnetic forces

Recall - Noether Theorem and SymmetryRecall - Noether Theorem and SymmetryRecall - Noether Theorem and SymmetryRecall - Noether Theorem and Symmetry

EnergyEnergy

• What ISIS energy?– Is this a scientifically valid question?

– Science is concerned with observable, measurable behavior of objects in the natural world.

– It is a conserved quantity that measures how objects interact or their ability to do “work” on each other and change their states of motion.

• It partially replaces Newton’s idea of a force.

• It is a scalar quantity measured in the units of a J (N m)

AnalogyAnalogy

• Dennis the Menace– Older version of Bart Simpson

• Messy Playroom – 18 wooden blocks

• Mother believes there should always be 18 blocks in the room– Every day she counts them

Richard Feynman

Missing Blocks?Missing Blocks?

• One day – only 14 blocks?– 4 blocks appear to be missing

• Mother notices a box– Mass of box increased by mass of missing 4

blocks

• What remains constant:

m

MMnN o−+=

More Missing Blocks?More Missing Blocks?

• Next day – only 6 blocks?– 8 more blocks appear to be missing

• Mother notices the bath tub– Level of water increased by amount equivalent

to volume of 8 blocks

• What remains constant:

3a

VhA

m

MMnN oo −

+−

+=

All Blocks Gone?All Blocks Gone?

• Next day – no blocks?– Last 6 blocks appear to be missing

• Mother notices a bag hanging in the closet– Length of cord increased proportional to

weight of missing blocks

• What remains constant:

( )mg

Lxk

a

VhA

m

MMN ooo −

+−

+−

=3

Forget the blocks!Forget the blocks!

• Mother notices the following expression remains constant:

A M + B h + C x = constant

– Original reference to blocks is irrelevant– Energy discovered in much the same way!

M = mass of boxM = mass of boxh = water level in tubh = water level in tubx = length of cordx = length of cordA, B, C = constantsA, B, C = constants

M = mass of boxM = mass of boxh = water level in tubh = water level in tubx = length of cordx = length of cordA, B, C = constantsA, B, C = constants

Energy found the Energy found the SAMESAME way! way!

Galileo:– ball roll down ramp: height = speed at bottom

• regardless of angle of ramp

– ball rolls up 2nd ramp to same height• regardless of angle of ramps

• ball “remembers” its initial height

GPE KE GPEGPE KE GPE

Galileo

More Data … More Data …

Huygens– balls colliding on a level, horizontal table,

quantity v2 remains constant

Christiaan Huygens

KE KEKE KE

Yet More Data …Yet More Data …

Joule:– object falling a certain height produces a

corresponding change in temperature of a certain mass of water

James Joule

GPE TEGPE TE

Put it together …Put it together …

• Combination of quantities remains constant:

• Or a system of objects in one state has the same “energy” as in another state: Ei = Ef

€

E = 12 mv 2 + mgh + 1

2 kx 2 + cmΔT +L = constant

WorkWork

W = F∆x

NoResistance W = ∆KE

€

KE = 12 mv 2

Resistance(Fnet = 0)

Gravity

Elastic

Friction

W = ∆GPE

W = ∆EPE

W = heat

€

GPE = mgy

€

EPE = 12 kx 2

Circular ReasoningCircular Reasoning

• Have we simply defined a concept whose total remains constant by definition?– Is this science or not?

• Question:– Can we find/define a set of “state functions”

whose sum is alwaysalways constant for closed, isolated systems?

This condition avoids circularity - repeated tests against new experimental conditions.This condition avoids circularity - repeated tests against new experimental conditions.

MisconceptionsMisconceptions

• On a piece of paper, indicate whether the following statements are TRUE or FALSE.

• Briefly justify your answer.• Do so QUIETLY! Do not blurt out any

answers.• There is NO need to ask any clarifying

questions. The statements are fully self-explanatory.

True - False?True - False?

1. Energy is a force.

2. Potential energy can be stored in an object, but is not really energy until it has been released.

3. Some energy is consumed or lost when converted from one form to another - so we need to “conserve” it.

4. Objects that are not moving do not have energy unless they are alive.