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Mass and Energy. W = work if the work done to increase kinetic energy then W = ΔEk = Ek 2 - Ek 1 = 0.5mv 2 2 - 0.5mv 1 2 = 0.5m(v 2 2 - v 1 2 ). Note: For classical mechanics we assume that mass is constant and that all energy would be transferred as speed.
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W = work if the work done to increase kinetic energy then W = ΔEk = Ek2 - Ek1 = 0.5mv22 - 0.5mv12 = 0.5m(v22 - v12)
Note: For classical mechanics we assume that mass is constant and that all energy would be transferred as speed. • (classical mechanics can be used if v is less than 0.1c) • This is not true as speeds become relativistic, close to the speed of light, v at or greater than 0.1c.
Einstein suggested that the total relativistic energy with a rest mass of m, moving at a speed of v, relative to an inertial frame is: Etotal = mc2/(1- v2/c2) 0.5 where Etotal = total mass energy (in J) m = rest mass (in kg) v = speed of an object (in m/s)
If at rest in at inertial frame then v = 0 Therefore Etotal=mc2/(1- (0)2/c2)0.5 = mc2/(1- 0)0.5 = mc2/(1)0.5 = mc2/1 = mc2 Thus Erest = mc2 Where Erest = rest mass energy (in J)
Einstein proposed: 1. rest mass is a form of energy which all objects with mass have. 2. there might be forces or interactions in nature that transform mass energy into other types of energy
Energy Mass Equivalence • Also implies that as you acquire energy, you are also acquiring mass • The faster you move, the heavier you are • This is why we need relativistic momentum • According to this equivalence, • Light has mass because it has energy • But light has zero rest mass
In classical mechanics; mass and energy are conserved separately. • Conservation of Mass-Energy: the principle that rest mass and energy are equivalent. Etotal = Erest + Ek Ek = Etotal - Erest = mc2/(1- v2/c2)0.5 - mc2 = mc2[1/(1- v2/c2)0.5 -1]
Sample Problem # 1 A 4.0 kg of coal is burned. The thermal energy released from the combustion of coal is about 3.3 X 107 J/kg. What is the % efficiency of the burning of the coal?
Solution Etotal = mc2 Ein = mc2 = (4.0 kg)(3.00 X 108 m/s)2 = 3.6 X 1017 J Eout = (4.0 kg)(3.3 X 107 J/kg) = 1.32 X 108 J
% eff = Eout X 100% Ein = 1.32 X 108 J X 100% 3.6 X 1017 J = 3.7 X 10-8 % The % efficiency of coal is 3.7 X 10-8 %. (Coal is not very efficient!!)
Example # 2: Find the rest mass energy of a 1.0 kg object
Solution Erest= mc2 = (1.0 kg)(3.00 X 108m/s)2 = 9.0 X 1016 J The rest mass energy of a 1.0 kg object is 9.0 X 1016 J.
Example # 3: An proton is moving at about 0.9c. Knowing 1 eV = 1.602 X 10-19 J, calculate the protons's: (a) rest energy in MeV. (b) total energy in MeV. (c ) kinetic energy in MeV. Mproton = 1.67x10-27kg
Solution (a) Erest = mc2 =(1.67X10-27kg)(3.00X108m/s)2 =8.199X10-14JX(1eV/1.602X10-19J) = 5.12 X 105 eV = 0.512 MeV The rest energy is 0.512 MeV.
(b) Etotal = mc2/(1- v2/c2) 0.5 = (9.11X10-31kg)(3.00X108m/s)2 [1-(0.90c)2/c2] 0.5 =1.88097X10-13J X(1eV/1.602 X10-19J) = 1.17 X 106 eV = 1.17 MeV The total energy is 1.17 MeV.
(c ) Etotal = Erest + Ek Ek = Etotal - Erest = 1.17 MeV – 0.512 MeV = 1.11 MeV The kinetic energy of the electron is 1.11 MeV.
"In a nuclear process, you convert something like one part in 1,000 of your rest mass into energy, whereas if you fall into a black hole, you can convert something like 20, 30, 40 percent," Hogg says. "So from the point of view of the energetics of the universe, these black holes are important, because they are big converters of rest mass into energy."
11.3 Practice Questions • Page 583 Questions 1-6 • Page 584 Question 3
Chapter 11 Review Questions • Page 588 Questions 1-14, 16-19, 22 • Page 590 Questions 4-13, 27
Also not a cartoon, Einstein spent the last of his days trying to find a theory that unifies all types of fields. The String Theory is the most commonly accepted unifying theory, but it is far from complete.
Incompetent Slug Assassins ALSO NOT EINSTEIN CARTOONS May I be excused my brain is full.
