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Energy What is Energy Energy Conservation Kinetic Energy Energy of Motion Energy Kinetic Energy Examples KE Examples (cont) Electricity Electrical Current ... – PowerPoint PPT presentation

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Title: Energy

What is Energy
  • From Merriam Webster
  • Energy The capacity for doing work (or to
    produce heat)What are some forms/types of
  • 1. Energy of motion (kinetic energy) ?
  • 2. Heat
  • 3. Electricity ?
  • 4. Electromagnetic waves - like visible light,
    x-rays, UV rays, microwaves, etc ?
  • 5. Mass ?
  • Huh, what do you mean mass is a form of energy?
  • Well get to this later.
  • The thing about energy is that it cannot be
    created or destroyed, it can only be transformed
    from one form into another

Energy Conservation
Like momentum, energy is a conserved
quantity.This provides powerful constraints on
what can and cannot happenin nature.This is an
extremely important concept, and we will come
back tothis 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 of an object. The
    kinetic energy is simply
  • KE (½)mv2 where
  • m mass in kg, and
  • v velocity of object in m/sec
  • What are the units of KE?
  • KE mass velocity2 kgm2/s2
    Joule or just, J
  • A Joule is a substantial amount of energy!

  • The unit, Joules applies to all forms of
    energy, not just KE.
  • As well see later, there are sometimes more
    convenient units to use for energy.
  • You have probably heard of the unit Watt. For
    example,a 100 Watt light bulb? A Watt W is
    simply energy usage per unit time, or J/s.
  • So, 100 W means the bulb uses 100 J per
  • How many J are used by a 100 W bulb in 2
    minute? A) 200 J B) 1200 J
    C) 12000 J D) 2000 J

Kinetic Energy Examples
What is the kinetic energy of a 1 kg mass
moving at 4 m/sec ?
A) 4 J B) 0.25 J C)
2 J D) 8 J
KE ½ (1)(4)2 8 J
KE ½ (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 ½ (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 generally refers to the flow of
  • 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 Current
  • Electrical current is the rate of flow of
    charges, that is C/sec
  • The units of current are Amperes, or just Amps
  • 1 A 1 C/sec
  • 1 A 6.25x1018 charges/sec
  • Lightening bolts can contain several thousand
    amps of current !

Electrical Energy and the Electron-Volt
  • How much energy does an electron gain as it is
    accelerated across a voltage? (Length of arrow
    is proportional to velocity)

1000 V
-1000 V
  • Its energy is the product of the charge times
    the voltage. That is,
  • E q(DV) Charge q is in C
    (1.6x10-19)(2000) Voltage DV is in
    Volts (V) 3.2x10-16 J Energy E
    is in Joules (J).
  • Because 1 electron is only a tiny fraction of a
    Coulomb, the energyis also tiny ! This is a
    pain, but .

The Electron-Volt (eV)
  • How much energy does an electron gain as it
    crosses 1 volt.
  • Energy q(DV) (1.6x10-19 C) (1
    Volt) 1.6x10-19 J
  • Since this amount of energy is so small, we
    define a more convenient unit of evergy, called
    the Electron-Volt Define the
    electron-Volt 1 eV 1.6x10-19 J
  • An electron-volt is defined as the amount of
    energy an electron would gain as it accelerates
    across 1 Volt.
  • In most cases, we will use the eV as our unit
    of energy. To convert back to J, you need only
    multiply by 1.6x10-19.

An electron is accelerated across a gap which has
a voltage of 5000 Vacross 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 Vacross 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
  • In the classical picture, they are just
    transverse waves...

The speed of EM waves in vacuum is alwaysc
3 x 108 m/sec
The wavelength (l) is the distance from
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 mm 1 m
Longest wavelengths (Least energetic)
Consider two waves moving to the right at the
speed c, and count the number of waves which
pass a line per second
  • 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, n (nu) n 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, l, and the frequency

Example I
What is the frequency of a gamma-ray with l10-6
nm ? I want to use c ln, but we need l in
m So, first convert nm to meters
n c / l (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 l0.5
km ? First, convert km to m
n c / l (3x108) / (5x102) 6 x 105
hz 0.6 Mhz This is AM Radio! FM
Radio waves are typically around 80 Mhz. Show
thatthis is the case
Mass Energy
According to Einsteins Theory of Special
Relativity, Mass is a form of Energy, and they
are related by the simple and well-known formula
E mc2
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
  • 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)
  • 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 of this 1 kg
    block if it were moving at 200 m/sec (about
    430 mi/hr) ?
  • KE ½ (1 kg) (200 m/sec)2 2x104 J
  • What fraction of the rest mass energy is this ?
  • Fraction (2x104 J ) / (9x1016 J )
    2.2x10-13 ( or 0.000000000022)
  • ? That is, the KE is only a tiny fraction of
    the rest mass energy. Alternately, it
    gives you a flavor for how much energy is
    bottled up in the rest mass !!!

Example III
  • What is the rest mass energy of a neutron, which
    has a massof 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.

9.4x108 eV 940 MeV
Example IV
An electron and positron (a positively-charged
electron) each having10 keV collide and
annihilate into pure energy. How much energyis
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
  • There are many forms of energy,
    including Energy of motion Electrical
    energy Electromagnetic energy (EM waves) Mass
  • Energy of motion is given by KE(1/2)mv2
  • One of the most important forms of energy which
    well deal withis mass energy.
  • Mass IS a form of energy.
  • Mass can be converted into energy. If you
    convert all of themass of some object with mass
    M to energy, the correspondingenergy will be