Chapter 10: Collisions

Transcription

1 PHYS 172: odern echanics Sring 2010 EXA 2 Please check your ultile choice art a.s.a.. (on CHIP). The aer eas will be discarded in one week fro now. Lecture 18 Collisions Read PHYS 172: odern echanics Sring 2010 Chater 10: Collisions htt://

2 Elastic and inelastic collision ELASTIC COLLISION: the internal energy of the objects in the syste does not change: E int =0 INELASTIC COLLISION: the internal energy of the objects in the syste changes: E int = 0 AXIALLY INELASTIC COLLISION: Objects stick together aiu energy dissiation 3 oentu and iulse 1 2 d dt = F d = Fdt = F t 1 2on1 = F t 2 1on2 P Clicker: sys = Ptot = ( ) = 0 The changes in the oenta of orange and green balls are: A)Equal in agnitude and direction Conservation of oentu B)Equal in agnitude, oosite in direction = 0 C)Larger in agnitude for the lighter sall ball D)Saller in agnitude for the lighter sall ball 4

3 Collisions: conservation of oentu syste Collision with contact sys During collision t is sall: P = + = F t ( ) 1 2 eternal Collision without contact 5 A head-on collision Ping-ong ball 2 = 0 1 Tennis ball 4 3 oentu conservation: Ptot = ( + ) = + = = + 4 Two unknowns Energy conservation: tot ( ) E = K + U + E = No interaction =0 before/after collision Elastic collision: =0 ( K ) = int ernal 0

4 A head-on collision: elastic Ping-ong ball 2 = 0 1 Tennis ball 4 3 oentu conservation: Energy conservation: = Two equations Two unknown ± = + + no interaction - interaction 7 Head-on collision: equal asses 1 = ± = + 2 = = 0 = 4 8

5 Heavy rojectile, light target 1 = ± = + 1 After collision: =0 Case > = > 0 The rojectile will continue otion in the sae direction 9 Very heavy rojectile, very light target Case >> = =0 After collision: 3 4 Projectile continues otion with aroiately the sae seed in the sae direction + + = = v4 v1 = 2 4 v 2v 4 The sae result: chose reference frae that oves with 10

6 Elastic scattering: Collisions in 2D and 3D 1 θ 3 y 2 =0 1 = searate for and y coonents: 1 = 3 cosθ + 4 cosφ 0 = 3 sinθ 4 sinφ φ (ositive angle) Three equations Four unknowns: 3, 4, θ, φ 11 Elastic scattering: equal asses one initially at rest 1 = = + = cos A ( ) cos A cos A = 0 A = ± π / 2 or: 3 4 =0 =0 A = ± π / 2 12

7 Elastic scattering: equal asses 1 A = ± π / 2 2 CLICKER: Can you ocket both balls in one shot? (Ignore sin) A) No B) Yes, if you use ball 1 as a cue ball C) Yes, if you use ball 2 as a cue ball D) Yes, you can do it using any ball as a cue ball 13 Iact araeter -the distance between the centers erendicular to the incoing velocity Too far for interaction 14

8 15 Discovery of the nucleus: early odels 1903, Kelvin: electrons are ebedded in a shere of unifor ositive charge 1906, Thoson: lu udding odel Ernst Rutherford, forer student of Thoson, tested lu udding odel in

9 What s inside? Suose you have a Christas resent and you would like to find out what is inside it without oening it The contents of a Christas resent could be robed by firing a rifle into it and noting how bullets are scattered by the contents. 17 Rutherford: discovery of the nucleus (undergrad Ernest arsden) 1910 He nucleus (2 rotons + 2 neutrons) Alha articles are too heavy to be scattered by electrons The ass ust be concentrated in sall areas - nuclei Plu udding odel is incorrect Nucleus is ~10-15 in diaeter Electrons roa ety sace ~10-10 across (1 Å) htt://galileo.hys.virginia.edu/classes/252/rutherford_scattering/rutherford_scattering.htl 18

10 Rutherford: discovery of the nucleus Rutherford (in one of the later lectures): (Geiger counter) "I had observed the scattering of alha-articles, and Dr. Geiger in y laboratory had eained it in detail. He found, in thin ieces of heavy etal, that the scattering was usually sall, of the order of one degree. One day Geiger cae to e and said, "Don't you think that young arsden, who I a training in radioactive ethods, ought to begin a sall research?" Now I had thought that, too, so I said, " Why not let hi see if any alha-articles can be scattered through a large angle?" I ay tell you in confidence that I did not believe that they would be, since we knew the alha-article was a very fast, assive article with a great deal of energy, and you could show that if the scattering was due to the accuulated effect of a nuber of sall scatterings, the chance of an alhaarticle's being scattered backward was very sall. Then I reeber two or three days later Geiger coing to e in great eciteent and saying "We have been able to get soe of the alha-articles coing backward " It was quite the ost incredible event that ever haened to e in y life. It was alost as incredible as if you fired a 15-inch shell at a iece of tissue aer and it cae back and hit you." htt://galileo.hys.virginia.edu/classes/252/rutherford_scattering/rutherford_scattering.htl 19