BEST Pathway Session: Energy in K–12 Physics

Arthur Eisenkraft

March 30, 2012

Energy Savings

• Who will save more gasoline?

– Adam who switches from a gas-guzzler of 12 mpg to a slightly less voracious guzzler that runs at 14 mpg.

– The environmentally virtuous Beth switches from a 30 mpg car to one that runs at 40 mpg.

– Both travel equal distances over the year.

The MPG Illusion

• Intuition – Beth’s action is more significant

• She reduced by 10 mpg rather than by 2 mpg

– Calculation • Adam: 10,000 miles will go from 833 gal to 714 gal

– A savings of 119 gallons

• Beth: 10,000 miles will go from 333 gal to 250 gal – A savings of 83 gallons

• Larrick and Soll showed that mpg is not as good as gallons/(100 miles) for these decisions – Study done in 2008 – Policy change expected in 2013 (in small print)

Energy in Physics

• Energy in the new Framework for K-12 – Energy as a “disciplinary core idea”

– Energy as a crosscutting concept

• How do we present energy?

• Can we bring our presentations more in line with the 3-dimensions of the Framework – Scientific and Engineering Practices

– Crosscutting Concepts

– Disciplinary Core Ideas

Types of Energy

• Please assist

Types of Energy

• GPE • KE • SPE • Electrostatic PE • Heat • Light • Nuclear • Sound • Binding energy • Activation energy • Solar energy • Magnetic • Electrical

Equations for energy

Types of Energy

• GPE mgh or –GMm/R • KE 1/2mv^2 • SPE ½ kx^2 • Electrostatic PE -kqq/R • Heat mc<delta>T • Light hf • Nuclear mc^2 • Sound • Binding energy • Activation energy • Solar energy • Magnetic • Electrical VIt

Types of Energy Equation what we measure

• GPE mgh or –GMm/R • KE 1/2mv^2 • SPE ½ kx^2 • Electrostatic PE -kqq/R • Heat mc<delta>T • Light hf • Nuclear mc^2 • Sound • Binding energy • Activation energy • Solar energy • Magnetic • Electrical VIt

Issues mentioned in the Framework

• The idea that there are different forms of energy, such as thermal energy, mechanical energy, and chemical energy, is misleading, as it implies that the nature of the energy in each of these manifestations is distinct when in fact they all are ultimately some mixture of kinetic energy, stored energy, and radiation.

Issues mentioned in the Framework

• Furthermore, what is meant by the first three terms above is seldom precisely defined. It is likewise misleading to call sound or light a form of energy; they are phenomena that, among their other properties, transfer energy from place to place and between objects.

Feynman’s 28 Blocks

• Day 1- 28 blocks; Day 2 – 28 blocks; etc.

• 27 (but one is under the couch)

• 25 (but box is heavier) – We can write an equation:

• (# of blocks seen) + (wt of box – 150 g)/20g = 28

• 26 (but water level in pail is higher) – We can write a new equation

• (# seen) + (weight…) + (ht of water – 2cm)/0.5 cm) = 28

• How else could blocks be hidden?

Feynman’s 28 blocks

• 28 blocks

• One day – 30 blocks!!!!

Energy Analogy

• First – a new level of abstraction – there are NO blocks

– Take away the first term in the equations

(# seen) + (weight…) + (ht of water – 2cm)/0.5 cm) = 28

• Second – Calculate energy (we don’t measure energy)

• Third – use the same units (Joules, calories, BTU, gallons of gas, eV….)

• Fourth – in a closed system – the sum is constant

Conservation of Energy

• A closed system

• Different forms – each form has an equation – GPE, KE, elastic energy, heat energy, chemical

energy, radiant energy, nuclear energy

• The total of all of these numbers is constant.

• WE HAVE NO KNOWLEDGE OF WHAT ENERGY IS. We only know how to calculate energy and the total always remains the same.

Our Faith in Energy Conservation

• Beta decay problems

– Energy was not conserved

• Wolfgang Pauli solution in 1931

– There must be a neutral particle unseen (neutron?)

– Chadwick discovers neutron in 1932 but is too massive for solution

Our Faith in Energy Conservation

• Enrico Fermi in 1934 –theory of weak interactions – Neutrino with no charge, no mass

– But energy will be conserved

– Rejected by Nature ("it contained speculations too remote from reality to be of interest to the reader”)

• 1956 – the neutrino is experimentally discovered – Clyde Cowan and Fred Reines (Nobel Prize 1995) (Pauli

loses case of champagne in bet that it would never be detected)

• 1962 – not all neutrinos are identical

How do we present energy?

• The Pole Vault

– The world’s record is 6.14 m (19.8 feet)

– Why not use a 7 meter pole and beat the record?

– How would you teach this?

Energy in the Pole Vault

• Explore

– Investigate shooting

the penny in the air.

– Investigate bending

the flexible ruler.

Energy in the Pole Vault

• Explain

– Speed of moving ball determines ruler bend

– Ruler bend determines height of penny

• Elaborate

ΔKE ΔEPE ΔGPE

• Pole length does not determine height

Analysis of a Jump

Analysis of a Jump

Elastic

Potential

Energy

Gravitational

Potential

Energy

Kinetic

Energy

ready position maximum 0 0

launch position 0 some maximum

peak position 0 maximum 0Po

siti

on

Energy

Qualitative treatment

Analysis of a Jump

Elastic

Potential

Energy

Gravitational

Potential

Energy

Kinetic

Energy

ready position 410 J 0 0

launch position 0 150 J 260 J

peak position 0 410 J 0

Energy

Po

siti

on

Quantitative treatment

Analysis of a Jump

Elastic

Potential

Energy

Gravitational

Potential

Energy

Kinetic

Energy

ready position 600 J 0 0

launch position 0 150 J 450 J

peak position 0 600 J 0Po

siti

on

Energy

Analysis of a Jump on the Moon

Elastic

Potential

Energy

Gravitational

Potential

Energy

Kinetic

Energy

ready position 600 J 0 0

launch position 0 150 J 450 J

peak position 0 600 J 0Po

siti

on

Energy

Which values change?

Analysis of a Jump on the Moon

Which values change?

Energy

Elastic Potential Energy Gravitational Potential

Energy Kinetic Energy

Po

siti

on

ready position 600 J 0 0

launch position 0 25 J 575 J

peak position 0 600 J 0

Since g is 1/6th on the moon, the corresponding height will be 6 x

0.8 m 0.2 m

5.0 m 0.8 m 0.2 m

Sports on the Moon

Popping Toy

Popping Toy

0

100

200

300

400

500

600

700

beforepopping

just afterleaving the

table

halfway up at the top

Ene

rgy

(J)

Energy at different locations

Elastic Potential Energy (J)

Gravitational PotentialEnergy (J)

Kinetic Energy (J)

Popping Toy

0

100

200

300

400

500

600

700

beforepopping

just afterleaving

the table

halfwayup

at the top

Ene

rgy

(J)

Energy at different locations

Elastic Potential Energy (J)

Gravitational PotentialEnergy (J)

Kinetic Energy (J)

0

100

200

300

400

500

600

700

beforepopping

just afterleaving the

table

halfway up at the top

Ene

rgy

(J)

Energy at different locations

Kinetic Energy (J)

Gravitational PotentialEnergy (J)

Elastic Potential Energy (J)

Thermal Energy

• What is the final temperature when

– 100 g of water at 10° C is mixed with

– 100 g of water at 50°C ?

• Student “incorrect” response is often 40° C

– How do they get this?

Thermal Energy

• What is the final temperature when

– 100 g of water at 10° C is mixed with

– 100 g of iron at 50°C ?

0 10 20 30 40 50 60 70 80

Thermal Energy

• What is the final temperature when

– 100 g of water at 10° C is mixed with

– 100 g of iron at 50°C ?

• Experimental answer = 22°C

• How can our students explain?

Thermal Energy

• What is the final temperature when

– 100 g of water at 10° C is mixed with

– 100 g of water at 50°C ?

• Conservation of Energy

– Energy gain of the cold water = Energy loss of the hot water

– Energy change of the cold water + energy change of the hot water = 0

– Total energy remains constant

Thermal Energy

• What is the final temperature when

– 100 g of water at 10° C is mixed with

– 100 g of iron at 50°C ?

• Experimental answer = 22°C

• Conservation of Energy

– Energy gain of the cold water = Energy loss of the iron OR Total energy remains constant

• Water requires more energy to change its temperature definition of specific heat

Energy as a Crosscutting Concept

Traditional Lesson with Disciplinary Core Ideas in Foreground

Revised Lesson with Crosscutting Concepts in Foreground

Place hot iron in cold water and heat up water Place hot iron in cold water and heat up water

Research Question: Find the specific heat of the iron.

Research Question: Is energy conserved?

Measure the temperature gain of the water. Calculate the energy gain of the water.

Measure the temperature gain of the water. Calculate the energy gain of the water.

Assume that energy is conserved Calculate the energy loss of the iron using the Handbook value.

Determine the specific heat of the iron. Determine if energy is conserved

Compare the calculated specific heat of the iron with the “correct” value in the Handbook .

Account for the loss of energy (the energy loss of the iron is greater than the energy gain of the water.)

Calculate the percent error. Account for this percent error.

Energy as a Crosscutting Concept

• We pulled off the internet the first 23 sets of lab instructions for this lesson. In only 7 of these lesson descriptions and handouts did we find any mention of either “energy conservation (1 lab),” “conservation of energy (3 labs),” “law of conservation of energy (1 lab),” or “energy loss = energy gain (2 labs).”

• No other explicit phrases for conservation of energy (e.g. total energy remains constant) were found. In the remaining 16 sets of instruction, the conservation of energy is implied and used but never stated.

Relevance of Thermal Energy

• What way to heat water uses least energy?

Relevance of Thermal Energy

• What is the best way to cook a hot dog? – Fry, boil, microwave, grill

• Define “best” – Fastest

– Cheapest

– Least cleanup

– Best taste

– Best appearance

• Engineering Design

Energy in Physics

• Energy in the new Framework for K-12 – Energy as a “disciplinary core idea”

– Energy as a crosscutting concept

• How do we present energy?

• Can we bring our presentations more in line with the 3-dimensions of the Framework – Scientific and Engineering Practices

– Crosscutting Concepts

– Disciplinary Core Ideas

Energy in Physics

• Energy in the new Framework for K-12 – Energy as a “disciplinary core idea” – Energy as only one crosscutting concept

1. Patterns

2. Cause and effect: Mechanism and explanation

3. Scale, proportion, and quantity

4. Systems and system models

5. Energy and matter: Flows, cycles, and conservation

6. Structure and function

7. Stability and change

Conservation of Energy

• A closed system

• Different forms – each form has an equation – GPE, KE, elastic energy, heat energy, chemical

energy, radiant energy, nuclear energy

• The total of all of these numbers is constant.

• WE HAVE NO KNOWLEDGE OF WHAT ENERGY IS. We only know how to calculate energy and the total always remains the same.

• Please check out our website: www.umb.edu/cosmic

for a copy of the power point.

Or email with questions: arthur.eisenkraft@umb.edu

A Falling Object

• How do we determine it’s path – Kinematics equations

• vf = at + vi • • vf

2= 2ad + vi2

• • vf = aΔt + vi • • y= ½ at2 + vit • • Δy = vΔt

Least Action

• Calculate the Lagrangian, L = T - V, at several instants (t), and draw a graph of L against t. The area under the curve is the action. Any different path between the initial and final positions leads to a larger action than that chosen by nature. Nature chooses the smallest action - this is the Principle of Least Action.

• Total energy = T + V • • 6.2 The principle of stationary action • Consider the quantity, • S ´ • Z t2 • t1 • L(x; x_ ; t) dt: (6.14) • S is called the action. It is a quantity with the dimensions of (Energy)£(Time). S depends • on L, and L in turn depends on the function x(t) via eq. (6.1).4 Given any function x(t), • we can produce the quantity S. We'll just deal with one coordinate, x, for now. • • • • •