Energy and Energy Conservation
A Physics MOSAIC
MIT 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).
W  F  d  F// d  Fd cos 
What Work ?
In each of the following cases, determine whether the work done is
positive, negative, or zero.
Photo by SKMay
Photo of Gullfoss, Iceland by SKMay
Water falls. What work
does gravity do? Air
resistance?
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 noncommercial 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
Area = Work
Area = ½ base * height
Work = ½ Fmaxd
d
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.
1 2
KE  mv
2
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.
PE  Wagent
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:
PEg  mgh
Photo by SKMay
Grendel has more potential
energy than Kea, but both cats
have approximately the same
mass. Which cat is which?
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:
1 2
PEe  kx
2
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:
GMm
PE  
r
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):
kQq
PE 
r
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:
3
3
KEtot  Nk BT  nRT
2
2
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).
Q  mCT 
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:
2
EA
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:
E  hf
(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:
MEi  ME f  mCT 
Wikipedia, Image by Cody Hough, a
photographer and student in the Michigan area,
Creative Commons
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.