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Energy

What is Energy

- From Merriam Webster
- Energy The capacity for doing work (or to

produce heat)What are some forms/types of

energy? - 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!

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

second! - 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

- 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 Current

- Electrical current is the rate of flow of

charges, that is C/sec - The units of current are Amperes, or just Amps

A - 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

e

- 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.

Examples

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

energy. - 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

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 mm 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

- 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

n.

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

Emc2

- 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 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

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 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

EMc2.