unj fmipa-fisika

1. Sesion #25-28 MekanikaKlasik Riser Fahdiran, M.Si Umiatin, M.Si JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam

2. Outline Center of Mass Conservation of Linear Momentum Conservation of Angular Momentum Conservation of Energy Elastic Collision and Conservation Law Elastic Collision 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2

3. System of Particles 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3

5. Understanding of conservations law are required to explore those motion

6. Two approach are used :

7. Newton’s Law

9. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 6

13. Or :

16. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 13 Conservation of Linear Momentum : “the rate of change of total linear momentum is equal to the total external applied force” or In the term of center of mass coordinate system :

18. 3. Conservation of Angular Momentum 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 15 The angular momentum of a single particle is defined in terms of a cross product as : For N particles :

20. The first term on the right vanishes because :

22. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 18 Conservation of Angular Momentum : “For an isolated—one on which no net external forces act—the total torque τwill be zero; hence the angular momentum remains constant both in magnitude and direction”

23. 4. Conservation of Energy 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19 In many situations, the total force acting on any particle in a system of particles is a function of the positions of the particles in the system : If the force Fksatisfies the condition that :

24. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20 There exists a potential function : Such that : The motion of kth particle is described by :

27. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 24 Collisions may be divided into : elastic collisions inelastic collisions

28. 6. Elastic Collision 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25

32. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 31