1. Center of Mass

2. Motion of the Center of Mass

3. The center of mass of a system moves as if all of the mass of the system were concentrated at that point and as if all of the forces were acting at that point For internal forces Only external forces affect the motion of the center of mass

4. Momentum is a vector! Vector equation!

5. If

6. Conservation of Momentum If there is no external force acting on a system, then the total momentum of the system is a constant

7. True in X and Y directions separately!

8. Problem Solving For Conservation of Momentum problems: 1.BEFORE and AFTER 2.Do X and Y Separately

9. Inelastic collision A collision in which the total kinetic energy after the collision is less than that before the collision is an inelastic collision. A B BEFORE AFTER A B V after ?

10. Perfectly elastic collision A collision in which the total kinetic energy after the collision is the same than that before the collision is called an elastic collision. A B

11. Nuclear reactions Fission: decay of heavy nuclei into lighter fragments Fusion: synthesis of light nuclei into a heavier nucleus Energy released per proton is ~10-20 MeV!!

12. Energy is released in fission reaction if the mass of an initial nucleus is larger that the sum of masses of all final fragments M U > M Rb + M Cs + 3 m n Rubidium and Cesium are more tightly bound, or have larger binding energy than Uranium. It is energetically favorable for Uranium to split. When is the energy released in fission reactions?  M = M U – (M Rb + M Cs + 3 m n ) Energy released E =  M c 2

13. Proton-proton cycle: four hydrogen nuclei fuse to form one helium nucleus Hydrogen Fusion

14. There are no heavy elements on the stars |U b |

15. Einstein’s relation: E = mc 2 Energy released in one reaction: (Binding energy) Hans Bethe 1939 0.007, or 0.7% of the rest energy of protons (4m p c 2 ) is released This is 10 7 times more efficient than chemical reactions!

16. 600 million tons of hydrogen are fused every second on the Sun! How much hydrogen should be fused per second to provide the Sun’s luminosity? Nuclear fusion efficiency: 0.7% of the hydrogen mass is converted into radiation in the p-p cycle Matter-antimatter annihilation has even higher efficiency: 100% !!

17. There is more than enough nuclear fuel for 10 10 years! Does nuclear fusion provide enough energy to power the Sun? Assume 10 56 protons in the core:

18. 10,000 years Neutrino have very small mass, no electric charge, and they almost do not interact with matter How do we know? Neutrino!!

19. Neutrino image of the Sun