Energy

What is EnergyFrom 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. Heat3. 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?We’ll 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] [velocity]2 = [kg*m2/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 we’ll 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 ExamplesWhat is the kinetic energy of a 1 [kg] mass moving at 4 [m/sec] ?

1 kg 4 m/sec

KE = ½ (1)(4)2 = 8 [J]

KE = ½ (1)(- 4)2= 8 [J]

A) 4 [J] B) 0.25 [J] C) 2 [J] D) 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 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 it’s kinetic energy? The speed of light is 3x108 [m/sec].

How does this compare to the 1 [kg] block moving at 4 [m/sec] ?

The electron’s velocity is v = (1/10)*(3x108) = 3x107 [m/sec]

So, KE = ½ (9.1x10-31 )(3x107 )2 = 8.2x10-16 [J]

KE(electron) / KE(block) = 8.2x10-16/8 = 2.6x10-17 [J]

(Wow, this is a small number. We’ll 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

It’s energy is the product of the charge times the voltage. That is,

E = q(V) Charge: q is in [C] = (1.6x10-19)(2000) Voltage: V 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 ….

e e e e e

The Electron-Volt (eV)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]

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 [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 don’t 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)

Longest wavelengths(Least energetic)

Recall 109 [nm] = 1 [m]

106 [m] = 1 [m]

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

Consider two waves moving to the right at the speed c, and count the number of waves which pass a line per second

7 waves

14 waves

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 …

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]

10-6 [nm] * ( [ m ] )

( [nm] )

Example IWhat is the frequency of a gamma-ray with =10-6 [nm] ?

I want to use c = , but we need in [m]…

So, first convert [nm] to [meters]

109

1

= c / = (3x108) / (1x10-15)

= 3 x 1023 [hz]

= 300,000,000,000,000,000,000,000 waves/sec !

That’s A LOT of waves!

= 10-15 [m]

Example IIWhat is the frequency of a gamma-ray with =0.5 [km] ?

First, convert [km] to [m]…

= c / = (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…

0.5 [km] * ( [ m ] )

( [km] )1

103

= 5x102 [m]

Mass Energy

According to Einstein’s 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]

E=mc2

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 !!!

1.5x10-10 [J] * ( [ eV ] )

( [J] )

Example IIIWhat 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]1.6x10-19

1

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 energyElectromagnetic energy (EM waves)Mass energy

Energy of motion is given by KE=(1/2)mv2

One of the most important forms of energy which we’ll 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 E=Mc2.