1. Mass and Energy

2. W = work
if the work done to increase kinetic energy then
W = ΔEk
= Ek2 - Ek1
= 0.5mv mv12
= 0.5m(v22 - v12)

3. 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.

4. 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)

5. 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)

6. 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

7. 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

8. 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]

9. 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?

10. 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

11. % eff = Eout X 100% Ein = 1. 32 X 108 J X 100% 3. 6 X 1017 J = 3
% 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!!)

12. Example # 2: Find the rest mass energy of a 1.0 kg object

13. Solution Erest= mc2 = (1. 0 kg)(3. 00 X 108m/s)2 = 9
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.

14. Example # 3: An proton is moving at about 0. 9c. Knowing 1 eV = 1
Example # 3: An proton is moving at about 0.9c. Knowing 1 eV = X J, calculate the protons's: (a) rest energy in MeV. (b) total energy in MeV. (c ) kinetic energy in MeV. Mproton = 1.67x10-27kg

15. Solution (a) Erest = mc2 =(1. 67X10-27kg)(3. 00X108m/s)2 =8
Solution (a) Erest = mc2 =(1.67X10-27kg)(3.00X108m/s)2 =8.199X10-14JX(1eV/1.602X10-19J) = 5.12 X 105 eV = MeV The rest energy is MeV.

16. (b) Etotal = mc2/(1- v2/c2) 0.5 = (9.11X10-31kg)(3.00X108m/s)2 [1-(0.90c)2/c2] 0.5 = X10-13J X(1eV/1.602 X10-19J) = 1.17 X 106 eV = 1.17 MeV The total energy is 1.17 MeV.

17. (c ) Etotal = Erest + Ek Ek = Etotal - Erest = 1. 17 MeV – 0
(c ) Etotal = Erest + Ek Ek = Etotal - Erest = 1.17 MeV – MeV = 1.11 MeV The kinetic energy of the electron is 1.11 MeV.

19. "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."

20. 11.3 Practice Questions
Page 583 Questions 1-6
Page 584 Question 3

21. Chapter 11 Review Questions
Page 588 Questions 1-14,
16-19, 22
Page 590 Questions 4-13, 27

22. Einstein cartoons

25. Ok, so this is not a cartoon.

26. 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.

27. ALSO NOT EINSTEIN CARTOONS
Incompetent Slug Assassins
May I be excused my brain is full.

28. ALSO NOT EINSTEIN CARTOONS

29. ALSO NOT EINSTEIN CARTOONS

30. ALSO NOT EINSTEIN CARTOONS

31. ALSO NOT EINSTEIN CARTOONS