1. Instructor: Dr. Alexey Belyanin http://faculty.physics.tamu.edu/belyanin/ Office: MIST 426 Office Phone: (979) 845-7785 Email: belyanin@tamu.edu Office Hours: MWF 1:40-2:40 pm or by appointment

2. Momentum For N particles: Why bother introducing one more definition? Most general form of the Newton’s law: Valid when mass is changing Valid in relativistic physics Total momentum is conserved if the sum of external forces equals to zero!

4. 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!!

5. 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

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

7. 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!

8. 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:

9. Center of Mass

10. Motion of the Center of Mass

11. 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

12. Momentum is a vector! Vector equation!

13. If

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

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

17. True in X and Y directions separately! If onlythen