is Energy
What Energy
From Merriam Webster:
From Merriam Webster:
Energy: The capacity for doing work (or to produce heat
Energy: The capacity for doing work (or to produce heat))
What are some forms/types of energy?
What are some forms/types of energy?
1. Energy of motion (kinetic energy)
1. Energy of motion (kinetic energy)
2. Heat
2. Heat
3. Electricity
3. Electricity
4. Electromagnetic waves like visible light, x-rays, UV rays,
4. Electromagnetic waves --like visible light, x-rays, UV rays,
microwaves, etc
microwaves, etc
5. Mass
5. Mass
Huh, what do you mean mass is form of energy?
Huh, what do you mean mass is aaform of energy?
Well get to this later.
Well get to this later.
The thing about energy is that it annot be created or
The thing about energy is that it ccannotbe created or
destroyed it can only be ransformed from one form into another
destroyed,,it can only be ttransformedfrom one form into another
Energy Conservation
Like momentum, energy is a conserved quantity.
This provides powerful constraints on what can and cannot happen
in nature.
This is an extremely important concept, and we will come back to
this over and over throughout the remainder of the course.
Kinetic Energy Energy of Motion
Kinetic energy KE) refers to the energy associated with the motion
Kinetic energy ((KE)refers to the energy associated with the motion
o an object The kinetic energy is simply:
offan object.. The kinetic energy is simply:
KE= ()mv22
KE = ()mv
where
where
m = mass in [kg],
m = mass in [kg],
v = velocity of object in [m/sec]
v = velocity of object in [m/sec]
aand
nd
What are the units of KE?
What are the units of KE?
2
22
[[KE]= [mass] [velocity]2 = [[kg*m /s2]]== [Joule] or just, [J]
KE] = [mass] [velocity] = kg*m2 /s == [Joule] or just, [J]
A Joule is a substantial amount of energy!
A Joule is a substantial amount of energy!
Energy
The unit, Joules] applies to all forms of energy not just KE.
The unit, [[Joules]applies to all forms of energy,,not just KE.
A well see later, here are sometimes more convenient units
Asswell see later, tthereare sometimes more convenient units
ttouse for energy..
o use for energy
You have probably heard of the unit Watt. For example,
You have probably heard of the unit Watt. For example,
a 100 Watt light bulb?
a 100 Watt light bulb?
A Watt [W] is simply nergy usage per unit time or [J/s].
A Watt [W] is simply eenergyusage per unit time,,or [J/s].
So, 100 [W] means the bulb uses 100 [J] per second!
So, 100 [W] means the bulb uses 100 [J] per second!
How many [J] are used by a 100 [W] bulb in 2 minute?
How many [J] are used by a 100 [W] bulb in 2 minute?
A 200 [J]
B) 1200 [J] C) 12000 [J]
C) 12000 [J]
D) 2000 [J]
A))200 [J]
B) 1200 [J]
D) 2000 [J]
Kinetic Energy Examples
What is the kinetic energy of a 1 [kg] mass moving at 4 [m/sec] ?
1 kg
A) 4 [J]
4 m/sec
B) 0.25 [J]
C) 2 [J]
D) 8 [J]
KE = (1)(4)2 = 8 [J]
What if the mass was going in the opposite direction
(v = - 4 [m/sec])?
1 kg
-4 m/sec
A) 4 [J]
B) 0.25 [J]
C) 2 [J]
D) 8 [J]
KE = (1)(- 4)2= 8 [J]
KE Examples (cont)
An electron has a mass of 9.1x10-31 [kg]. If it is moving at one-tenth
of the speed of light, what is its kinetic energy? The speed of light
is 3x108 [m/sec].
The electrons velocity is v = (1/10)*(3x108) = 3x107 [m/sec]
So, KE = (9.1x10-31 )(3x107 )2 = 8.2x10-16 [J]
How does this compare to the 1 [kg] block moving at 4 [m/sec] ?
KE(electron) / KE(block) = 8.2x10-16/8 = 2.6x10-17 [J]
(Wow, this is a small number. Well come back to this fact in a bit)
Electricity
Electricity generally refers to the flow of
charges.
In most cases, electrons are the charges which
are actually moving.
The units of charge is a Coulomb or simply [C].
1 [C] = 6.25x1018 charges (such as electrons or protons)
Alternately, 1 electron = (1 / 6.25x1018) [C] = 1.6x10-19 [C]
Charges are made to flow by applying a voltage
Batteries
Power Supplies
Electrical generators
Electrical
Electrical
Current
Current
Electrical current is the rate of flow of charges, that is [C/sec]
Electrical current is the rate of flow of charges, that is [C/sec]
The units of current are Amperes or just Amps == A]
The units of current are Amperes,,or just Amps == [[A]
1 A] = 1 [C/sec]
1 [[A]= 1 [C/sec]
1 A] = 6.25x1018 harges/sec
1 [[A]= 6.25x1018 ccharges/sec
Lightening bolts can contain everal thousand amps o current
Lightening bolts can contain sseveralthousand amps offcurrent !!
Electrical Energy and the Electron-Volt
How much energy does an electron gain as it is accelerated
How much energy does an electron gain as it is accelerated
aacrossaavoltage? ((Lengthof arrow is proportional to velocity)
cross voltage? Length of arrow is proportional to velocity)
-1000 [V]
e
e
e
e
e
e
+1000 [V]
ts energy is the product of the charge times the voltage. That is,
IItsenergy is the product of the charge times the voltage. That is,
E = q( V)
E = q( V)
=((1.6x10-19)(2000)
= 1.6x10-19)(2000)
= 3.2x10-16 J]
= 3.2x10-16 [[J]
Charge q is in [C]
Charge:: q is in [C]
Voltage V is in [Volts] ([V])
Voltage:: V is in [Volts] ([V])
Energy E is in [Joules] ([J]).
Energy:: E is in [Joules] ([J]).
Because 1 electron is only tiny fraction of Coulomb, the energy
Because 1 electron is only aatiny fraction of aaCoulomb, the energy
is also tiny This is pain, but .
is also tiny !!This is aapain, but .
The Electron-Volt (eV)
How much energy does an electron gain as it crosses 1 volt
How much energy does an electron gain as it crosses 1 volt..
Energy= q*( V) = (1.6x10-19 [[C])* (1 [Volt]) = 1.6x10-19 [[J]
= q*( V) = (1.6x10-19 C]) * (1 [Volt]) = 1.6x10-19 J]
Energy
Since this amount of energy is so small, we define more
Since this amount of energy is so small, we define aamore
cconvenientunit of evergy, called the Electron-Volt
onvenient unit of evergy, called the Electron-Volt
Define the electron-Volt:
Define the electron-Volt:
1 [[eV]= 1.6x10-19 [[J]
= 1.6x10-19 J]
1 eV]
An lectron-volt s as defined the amount of energy n electron
An eelectron-voltiisdefined as the amount of energy aanelectron
would gain as it accelerates across 1 Volt
would gain as it accelerates across 1 Volt..
n most cases, we will use the [eV] as our unit of energy. To
IInmost cases, we will use the [eV] as our unit of energy. To
-19
cconvertback to [J], you need only multiply by 1.6x10-19..
onvert back to [J], you need only multiply by 1.6x10
Examples
An electron is accelerated across a gap which has a voltage of 5000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 electron)(5000 V) = 5000 [eV]
A proton is accelerated across a gap which has a voltage of 10,000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 proton)(10000 V) = 10,000 [eV]
(we dont refer to them as proton-volts !)
Electromagnetic Waves
Electromagnetic (EM) waves are
another form of energy.
In the classical picture, they are
just transverse waves...
The speed of EM waves
in vacuum is always
c = 3 x 108 [m/sec]
The wavelength ( ) is the
distance from crest-to-crest
In vacuum
c = 3x108 [m/sec] for
all wavelengths !
(~3x108 [m/sec] in air too)
The Electromagnetic Spectrum (EM)
Shortest wavelengths
(Most energetic)
Recall
109 [nm] = 1 [m]
106 [m] = 1 [m]
Longest wavelengths
(Least energetic)
Frequency
Consider two waves moving to the right at the
speed c, and count the number of waves which
pass a line per second
1, 2, 3, 4,
5, 6, 7, 8,
9, 10
14 waves
7 waves
Since all EM waves move at the same speed, they would measure
twice as many waves for the top wave as the bottom wave.
We call the number of waves that pass a given point per second the
frequency
Frequency (cont)
The frequency is usually symbolized by the greek letter, (nu)
== frequency
Frequency has units of [number/sec], or just [1/sec],
or [hertz] == [hz]
A MegaHertz [Mhz] is 1 million hertz, or 1 million waves/second!
There is a simple relation between the speed of light, c, the
wavelength, , and the frequency .
c =
c = 3x108 [m/sec]
Example I
What is the frequency of a gamma-ray with =10-6 nm] ?
What is the frequency of a gamma-ray with =10-6 [[nm]?
want to use = but we need n [m]
IIwant to use cc= ,,but we need iin[m]
So, first onvert [nm] to [meters]
So, first cconvert[nm] to [meters]
10-6 [nm] * (
1 [m])
(
109 [nm] )
= 10-15 [m]
= c / = (3x108) / (1x10-15)
= 3 x 1023 [hz]
= 300,000,000,000,000,000,000,000 waves/sec !
Thats A LOT of waves!
Example II
What is the frequency of a gamma-ray with =0.5 [km] ?
What is the frequency of a gamma-ray with =0.5 [km] ?
First, onvert [km] to [m]
First, cconvert[km] to [m]
0.5 [km] * ( 103 [ m ] )
(
1
[km] )
= 5x102 [m]
= = 3x1088 (5x102
= cc// = ((3x10 ))//(5x102))
= 6 x 105 hz]
= 6 x 105 [[hz]
= 0.6 [Mhz]
= 0.6 [Mhz]
This is AM Radio! FM Radio waves are typically around 0 Mhz Show that
This is AM Radio! FM Radio waves are typically around 880Mhz. .Show that
this is the case
this is the case
Mass Energy
According to Einsteins Theory of Special Relativity,
According to Einsteins Theory of Special Relativity,
Mass is a form of Energy
Mass is a form of Energy,,
aandthey are related by the simple and well-known formula:
nd they are related by the simple and well-known formula:
E = m c2
The units of energy, E can be expressed in [J], as before, but it is
more convenient to use the electron-volt [eV].
Recall that
1 [eV] = 1.6x10-19 [J]
E=mc22
E=m c
The important point here is that energy and mass are really
equivalent, and are related to one another by simply the speed of
light (c) squared!
This equation implies that even if a particle is at rest, it in fact
does have a rest-mass energy given by this formula.
Example I
What is the rest-mass energy of a 1 [kg] block in [J].
E = mc2 = (1 [kg])(3x108 [m/sec])2 = 9x1016 [J] .
This is a HUGE amount of energy stored in the rest mass!
Really, how much energy is this?
To put it in context, you could power a 100 [Watt] light bulb for 29
million years if you could convert all of this rest mass to energy !!!!
Unfortunately, this is not possible at this point
Example II
What would be the kinetic energy o this 1 [kg] block if it were
What would be the kinetic energy offthis 1 [kg] block if it were
moving at 200 [m/sec] (about 430 [mi/hr])
moving at 200 [m/sec] (about 430 [mi/hr]) ??
KE = (1 [kg]) (200 [m/sec])2 = 2x104 J]
KE = (1 [kg]) (200 [m/sec])2 = 2x104 [[J]
What fraction of the rest mass energy is this
What fraction of the rest mass energy is this ??
16
-13
Fraction = (2x104 J]
Fraction = (2x104 [[J]))//((9x10 [[J]))= 2.2x10-13
9x1016 J] = 2.2x10
o 0.000000000022%)
((orr0.000000000022%)
That is, the KE is only iny fraction of the rest mass energy.
That is, the KE is only aattinyfraction of the rest mass energy.
Alternately, it gives you flavor for how much nergy is
Alternately, it gives you aaflavor for how much eenergyis
bottled up in the rest mass !!
bottled up in the rest mass !!!!
Example III
What is the rest mass energy of a neutron, which has a mass
of 1.68x10-27 [kg]? Express the result in [eV].
E = mc2 = (1.68x10-27 [kg])(3x108 [m/sec])2 = 1.5x10-10 [J]
Now convert to [eV].
1.5x10-10 [J] * (
1 [ eV ] )
( 1.6x10-19 [J] )
= 9.4x108 [eV]
= 940 [MeV]
Example IV
An electron and positron (a positively-charged electron) each having
10 [keV] collide and annihilate into pure energy. How much energy
is carried away after the collision?
Total energy is conserved, so it must be the same as
before the collision.
10 keV + 10 keV = 20 keV
Summary
There are many forms of energy, including:
Energy of motion
Electrical energy
Electromagnetic energy (EM waves)
Mass energy
Energy of motion is given by KE=(1/2)mv2
One of the most important forms of energy which well deal with
is mass energy.
Mass IS a form of energy.
Mass can be converted into energy. If you convert all of the
mass of some object with mass M to energy, the corresponding
energy will be E=Mc2.