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
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 (KE) refers to the energy associated with the motion of an object. The kinetic energy is simply:
KE = (½)mv2where
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!
What if the mass was going in the opposite direction (v = - 4 [m/sec])?
A) 4 [J] B) 0.25 [J] C) 2 [J] D) 8 [J]
-4 m/secKinetic 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]
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…)
eElectrical Energy and the Electron-Volt
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]).
Energy = q*(DV) = (1.6x10-19 [C]) * (1 [Volt]) = 1.6x10-19 [J]
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” !)
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 vacuumc = 3x108 [m/sec] for all wavelengths !(~3x108 [m/sec] in air too)
Recall 109 [nm] = 1 [m]
106 [mm] = 1 [m]
Consider two waves moving to the right at the speed c, and count the number of waves which pass a line per second
c = ln
c = 3x108 [m/sec]Frequency (cont)
10-6 [nm] * ( [ m ] )
( [nm] )
= 10-15 [m]
What is the frequency of a gamma-ray with l=10-6 [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 !
That’s A LOT of waves!
= 5x102 [m]
0.5 [km] * ( [ m ] )
( [km] )
What is the frequency of a gamma-ray with l=0.5 [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…
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 = (1 [kg])(3x108 [m/sec])2 = 9x1016 [J] . This is a HUGE amount of energy stored in the rest mass!
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…
KE = ½ (1 [kg]) (200 [m/sec])2 = 2x104 [J]
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 III
E = mc2 = (1.68x10-27 [kg])(3x108 [m/sec])2 = 1.5x10-10 [J]
= 9.4x108 [eV]
= 940 [MeV]
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