Energy and Energy Conservation

A Physics MOSAICMIT Haystack Observatory RET 2010

Background image by SKMay

What is Energy?• Energy is the ability for an object to do work.• Energy comes in many forms.

Image from Wikipedia, Fanny Schertzer, Creative Commons

Wayne National Forest Solar Panel Construction, found on Flickr, Creative Commons

Thomasbrightbill, from flickr, Creative Commons

What is Work?• In physics, work has a specific meaning.– Work is done if a force is applied over a distance.– Work increases with

• Greater force.• Greater displacement.• Angle between force and displacement close to zero.

– Work can be positive, negative, or zero.• Work is positive if force and displacement are same direction.• Work is negative if force and displacement are opposite directions.• Work is zero if force and displacement are perpendicular.

– Units of work are Newtons * meters (N·m) = Joules (J).cos// FddFdFW

What Work ?In each of the following cases, determine whether the work done is

positive, negative, or zero.

Photo of Gullfoss, Iceland by SKMay

Water falls. What work does gravity do? Air resistance?

Photo by SKMay

Marlene and Bob climb Camel’s Hump.What work do they do on their backpacks? What work does gravity do on them?

Image from Briar Press, free for non-commercial use

A waiter carries a tray across a level room. What work does gravity do? The waiter?

More on Work

• If the force is not constant over the distance, work is equal to the area under the force-displacement curve.

F

d

Area = WorkArea = ½ base * heightWork = ½ Fmaxd

Types of Energy• Every force or interaction can be thought of having energy

associated with it.• Sometimes it is useful to think of energy in categories, as

below.– Mechanical Energy

• Kinetic Energy• Gravitational Potential Energy• Elastic Potential Energy

– Electrostatic Energy• Electrostatic Potential Energy

– Nuclear Energy• Nuclear Binding Energy

– Energy from Waves– Thermal Energy

• Kinetic Energy of small particles in motion

Kinetic Energy• Kinetic Energy is the energy of

motion.• Moving objects have the ability to

do work when they come to rest.• The amount of energy contained in

a moving object is– Proportional to the mass of the

object.– Proportional the square of the

object’s speed.• Because speed is always measured

relative to some reference frame, the kinetic energy of any object is arbitrary based on the choice of reference.

2

2

1mvKE

Potential Energy

• Potential Energy is stored energy, associated with the state or position of an object.

• Potential Energy can only be calculated relative to a chosen reference level.– This reference level is arbitrary and should be chosen

for maximum convenience and/or consistency.• Potential Energy is equal to the amount of work

done by an external agent bringing an object to its state or position from the reference level.

agentWPE

Positive and Negative Potential Energy

• Positive Potential Energy relative to “zero” indicates that an agent would have to do work on the system to bring it from the reference level to its current state.– Objects with positive potential energy have the ability to

release energy (and do work) in returning to the reference level.

– These objects may spontaneously return to the reference level (releasing energy) if they are allowed to do so.

• Negative Potential Energy relative to “zero” indicates that an agent would have to do work on the system to bring it from its current state to the reference level. – This is sometimes called a “bound” state, since it will generally

not spontaneously end up at the reference level.

Gravitational Potential Energy (Near Earth)

• In order to lift something near Earth, you must apply a force equal to the weight of the object.

• That is, Fapp = mg.• The work done lifting an object to

a height h, is Wagent = Fapp·d = mgh.• And, since the work done

bringing the object to this height is equal to the potential energy of the object, we find that:

mghPEg

Grendel has more potential energy than Kea, but both cats have approximately the same mass. Which cat is which?

Photo by SKMay

Elastic Potential Energy

• Just as with gravitation, the force necessary to extend an elastic material (such a spring or rubber band) changes as the material extends.

• Specifically, Hooke’s Law describes that many materials have a region of linearity, when the force is proportional to the displacement.

• Thus, the work done extending an elastic material (characterized by a spring constant, k) from its equilibrium position (where we choose PE = 0) to an extension or compression x is:

2

2

1kxPEe

Gravitational Potential Energy (Not Necessarily Near Earth)

• The force of gravity depends on the distance between the two objects being attracted.

• Specifically, the force of attraction due to gravity between two masses is proportional to 1/d2.

• It is conventional to choose our reference level where PE = 0 when the two masses are infinitely far apart.

• With that choice, we could (with some calculus) prove that at any distance apart, the potential energy of a pair of masses is:

r

GMmPE

G = 6.67 x 10-11 N m / kg2

Electrostatic Potential Energy• The electrostatic force between two charges is very similar

in form to the force of gravity between two masses, except– The electrostatic force can be attractive or repulsive, while

gravity is always attractive (so far).– Charges come in two flavors, while mass only comes in one (so

far).• It is again customary to choose our reference level for PE =

0 when two charges are infinitely far apart, which gives (with some calculus):

r

kQqPE k = 9.0 x 109 N m / C2

Nuclear Potential Energy• The nucleus of an atom is

held together by the strong nuclear force (one of the fundamental forces of nature).

• This force acts on the quarks that comprise protons and neutrons.

• The nucleus is also affected by the electrostatic repulsion of like charges (protons).

• The result is binding energy that varies with size of nucleus, as shown

Wikipedia, Public Domain

Thermal Kinetic Energy• The kinetic theory of matter tells us that

– Matter is made of small particles.– Those particles are in constant, random motion.

• We know those “small particles” are really atoms and molecules, and that the “constant, random motion” gives the object an internal thermal energy.

• We measure the average kinetic energy of the particles (due to constant, random motion) that make up an object as temperature. – The faster those particles move, the more thermal energy the object will

have. – The more particles that are present, the more thermal energy the object

will have.• For an ideal gas, the total kinetic energy contained in the gas is related to

temperature by:

nRTTNkKE Btot 2

3

2

3

Heat• Heat is the exchange of thermal energy due to a difference

in temperature. – If two objects at different temperatures are brought into

thermal contact, energy spontaneously flows from the hot object to the colder object.

– The process will continue until the objects become the same temperature, provided enough time is provided.

• The amount of energy (heat, Q) gained or lost during a change of temperature depends on– The mass of the objects. – The temperature difference.– The objects’ specific heat capacities (C). TmCQ

Specific Heat of Water• The specific heat of water is one of the highest for

any common substance (only ammonia is higher).– Oceans rarely freeze.– December isn’t the coldest month, and June isn’t the

hottest.– The Southern hemisphere has a milder climate than the

Northern hemisphere.• Specific Heat of water is 4186 J/kg.• Definition of Calorie– Amount of energy necessary to raise 1 kg of water 1 °C.– 1 Calorie = 4186 J.

Energy in Mechanical Waves

• Mechanical waves transport energy by sending oscillations through a medium.– Sound, water waves, waves on strings, and stadium waves

are all mechanical waves.• Because the particles in the medium act like

individual oscillators, the energy is similar to that of a mass on a spring, or ½ kx2, where x is the displacement of the particle from equilibrium.

• Thus, the total energy transferred in a mechanical wave is proportional to the amplitude of the wave squared, or: 2AE

Energy in Electromagnetic Waves• Unlike mechanical waves, electromagnetic waves

(light, radio, microwave, x-rays, etc) can travel in a vacuum.

• It was discovered in the early 1900’s (by Einstein, and others) that the energy of an electromagnetic wave is not dependent on amplitude as for mechanical waves, but is instead proportional to frequency.

• Energy in these waves is quantized (comes in discrete packets), and is equal to:hfE

(h = 6.626 x 10-34 Js)

Energy Conservation• Like mass, momentum, charge, and angular momentum,

energy is a physical quantity with an associated conversation law.

• Energy conservation means that while energy can change forms, the total amount of energy in a system stays constant.

• Like all conserved quantities, energy often provides a powerful and efficient means for problem solving and analysis.– Energy is a scalar (no direction associated with it).– The total amount of energy is constant; if you can calculate

what you start with, you know what you end with.

Energy Conservation: Mechanical

• If no friction or air resistance are present, the mechanical energy of a system will remain constant.

• That is, Ei = Ef, with the initial and final energies equal to the total energy, coming from both kinetic and potential (gravitational and/or elastic).

From Wikipedia, user Stevage, Creative Commons,

Energy Conservation:Mechanical and Thermal

• If friction and air resistance are present, some mechanical energy may be converted to thermal energy of the surroundings.

• This will result in an increase in the temperature of the surroundings.

• If the surrounds are well-defined in material and mass, you may be able to compute the change in temperature:

Wikipedia, Image by Cody Hough, a photographer and student in the Michigan area, Creative Commons

TmCMEME fi

Energy Conservation:Electrostatic and Light

• When an electron gains or loses electrostatic potential energy by moving closer or further from the nucleus it orbits, energy is emitted or absorbed in the form of a photon.

• The energy of the photon will exactly equal the difference in the energy levels of the electron.

• Like photon energies, the energy levels of electrons are quantized.

• This forms the basis for spectroscopy.From Wikipedia, GNU Free Documentation

Light and Thermal Energy

• As an object becomes warmer, it emits energy in the form of light.

• This type of radiation is often called blackbody radiation, since the model used to theorize it is that of a perfect absorber (a blackbody).

• The wavelength of electromagnetic radiation emitted gets shorter as the temperature gets higher.– Humans (average healthy temp = 37 °C = 98.6 °F) emit most of their

thermal radiation in the infrared.– The sun and other stars emit most of the their radiation in the visible.

• By studying the blackbody radiation of an object, it’s temperature can be determined.

MOSAIC’s Photons• The MOSAIC

spectrometer receives photons emitted by ozone in Earth’s mesosphere.

• These photons arise due to a transition of the ozone molecule from one (quantized) rotational kinetic energy to another.

Antenna Temperature

• Radio astronomers often report the intensity of their source in terms of antenna temperature.– Antenna temperature is the

temperature a blackbody would have to be in order to emit the detected radiation at the frequency being observed.

– Most radio astronomy targets, including mesospheric ozone, are not blackbodies.