Energy and Energy Conservation. A Physics MOSAIC MIT Haystack Observatory RET 2010. Background image by SKMay. Energy is the ability for an object to do work. Energy comes in many forms. What is Energy?. Image from Wikipedia, Fanny Schertzer , Creative Commons.
A Physics MOSAIC
MIT Haystack Observatory RET 2010
Background image by SKMay
Work is done if a force is applied over a distance.
Work increases with
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).What is Work?
Photo by SKMay
Image from Briar Press, free for non-commercial use
Marlene and Bob climb Camel’s Hump.
What work do they do on their backpacks? What work does gravity do on them?
A waiter carries a tray across a level room. What work does gravity do? The waiter?
Photo of Gullfoss, Iceland by SKMay
Water falls. What work does gravity do? Air resistance?
Area = Work
Area = ½ base * height
Work = ½ Fmaxd
Sometimes it is useful to think of energy in categories, as below.
Gravitational Potential Energy
Elastic Potential Energy
Electrostatic Potential Energy
Nuclear Binding Energy
Energy from Waves
Kinetic Energy of small particles in motionTypes of Energy
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.Kinetic Energy
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.Potential Energy
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.Positive and Negative Potential Energy
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:Gravitational Potential Energy (Near Earth)
Photo by SKMay
Grendel has more potential energy than Kea, but both cats have approximately the same mass. Which cat is which?
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 xis:Elastic Potential Energy
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:Gravitational Potential Energy (Not Necessarily Near Earth)
G = 6.67 x 10-11 N m / kg2
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):Electrostatic Potential Energy
k = 9.0 x 109 N m / C2
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 shownNuclear Potential Energy
Wikipedia, Public Domain
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:Thermal Kinetic Energy
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).Heat
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.Specific Heat of Water
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:Energy in Mechanical Waves
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:Energy in Electromagnetic Waves
(h = 6.626 x 10-34 Js)
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
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).Energy Conservation: Mechanical
From Wikipedia, user Stevage, Creative Commons,
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:Energy Conservation:Mechanical and Thermal
Wikipedia, Image by Cody Hough, a photographer and student in the Michigan area, Creative Commons
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.Energy Conservation:Electrostatic and Light
From Wikipedia, GNU Free Documentation
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.Light and Thermal Energy
These photons arise due to a transition of the ozone molecule from one (quantized) rotational kinetic energy to another.MOSAIC’s Photons
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.Antenna Temperature