Collisions! Short, Sharp Shocks
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1 d b n, b d,, -4 Introducng Collsons Quz 9 L9 Mult-artcle Systes 6-8 Scatterng 9- Collson Colcatons L Collsons 5, Derent Reerence Fraes ranslatonal ngular Moentu Quz RE a RE b RE c EP9 RE a; HW: Pr s 3*,, 3, 39 Collsons! Short, Shar Shocks
2 Collson: Oeratonal denton: quck enough/strong enough nteracton that all others are neglgble Short, Shar Exale Syste = ball Sack! F F E F E Can gnore Earth s ull durng sack Say an 5 kg ball s n contact s n contact wth the bat or 5 s Durng that te, t swtches ro gong orward at h = 447 /s to gong 8 h backward = 358 /s F net t 358 / s 5kg 447 / s 5kg 5s O that, the Earth s ull accounts or only 5kg98 / s 4 N F b E g 9 8,5N
3 Exale Syste = carts & F rcton ntally -D Collson F rcton t nally F rcton Pow! F rcton Oten know ntal oton, want to redct nal oton wo unknowns: and Generally need two equatons to sole or the
4 d Exale Syste = carts & ntally syste dt F rcton -D Collson One o the Equatons: Moentu Prncle F net ext syste Fnet extt F rcton t nally F rcton syste F ( F systenet ext Pow! t rcton F rcton F ) t rcton I we look rght beore and rght ater collson
5 Syste = carts & F rcton ntally -D Collson One o the Equatons: Moentu Prncle F rcton t nally F rcton Pow! F ' s rcton c
6 sace satellte o ass 5 kg has elocty <,, 8 > /s just beore beng struck by a rock o ass 3 kg wth elocty < 3,, 9 > /s ter the collson the rock s elocty s < 7,, 3 > /s Now what s the elocty o the sace satellte? a < 5,, 4 > /s b <,, 8 > /s c <,, 8 > /s d < 3688,, 9 > /s e < 3688,, 9 > /s
7 -D Collson One o the Equatons: Moentu Prncle Syste = carts & Secal Case: Maxally Inelastc ht & stck F rcton ntally F rcton t nally F rcton Pow! Other Equatons: or Maxally Inelastc F ' s rcton c
8 squshy clay ball colldes n dar wth a baseball, and stcks to the baseball, whch kees gong Intal oenta: and _CLY _ LL Whch equaton correctly descrbes ths collson? ) ) 3) _ CLY _ CLY _ CLY _ LL _ LL _ LL Fnal oentu o clay+ball :
9 Maxally Inelastc Intal M? nal bullet o ass traelng horzontally at a ery hgh seed ebeds tsel n a block o ass M that s sttng at rest on a nearly rctonless surace What s the seed o the block just ater the bullet ebeds tsel n the block? () (4) () (5) (3) M M M M
10 -D Collson Secal Case: Maxally Inelastc ht & stck Mult-ste Exale: 6kg kd s on a swng, say she s gotten hersel gong so that at her hghest her center o ass s 4 aboe the ground and when she swoos down her center o ass s just 5 aboe the ground On her down-swee, she reaches down and cks u her 3kg backack that s sttng on the ground (aybe her cell hone started rngng) How hgh wll she get on her uswng wth the ack n her la? k = 6kg 4 b = 3kg C D Y = Y C = 5 Y D =?
11 Second Equatons: Energy Prncle Syste = carts & ntally -D Collson E & t nally Pow! E & K E nt K E nt U &
12 Intal Maxally Inelastc M nal? Whch s an accurate energy equaton or ths collson or the syste o bullet + block? () () (3) (4) (5) ( M ) M ( M ) E Enternal ( M ) nternal E nternal
13 squshy clay ball colldes n dar wth a baseball, and stcks to the baseball, whch kees gong Intal knetc energes: K clay, K baseball Fnal knetc energy o clay+ball : Whch equaton correctly descrbes ths collson? nal ntal ) K clay+ball = K clay + K baseball ) K clay+ball > K clay + K baseball 3) K clay+ball < K clay + K baseball
14 Second Equatons: Energy Prncle Syste = carts & ntally -D Collson E & t Pow! nally E & K E nt K E nt U & Secal Case: Perectly Elastc (all nternal changes bounce back ) ' s c E & K E nt K E nt U &
15 Whch o the ollowng s a roerty o all elastc collsons? () he colldng objects nteract through srngs () he knetc energy o one o the objects doesn t change (3) he total knetc energy s constant at all tes -- beore, durng, and ater the collson (4) he total knetc energy ater the collson s equal to the total knetc energy beore the collson (5) he elastc srng energy ater the collson s greater than the elastc srng energy beore the collson
16 Exale -D Collson Syste = carts & F rcton ntally F rcton nally F rcton Pow! F rcton rue or all collsons Oten know ntal oton, want to redct nal oton wo unknowns: and Generally need two equatons to sole or the E & E E U & K Ent & K Ent
17 Pow! Syste = carts & ntally nally c s ' -D Collson U E K E K E & nt nt & ecal Case: Perectly Elastc (all nternal changes bounce back ) Equaton Equaton
18 Derng relaton or Fnal Seed -D Collson ecal Case: Perectly Elastc (all nternal changes bounce back ) Equaton Equaton For o c b a Soled by a ac b b 4 ck!
19 Extra secal case: Say s ntally statonary -D Collson ecal Case: Perectly Elastc (all nternal changes bounce back ) Pow! Syste = carts & ntally nally
20 Extra secal case: Say s ntally statonary -D Collson ecal Case: Perectly Elastc (all nternal changes bounce back ) Pow! Syste = carts & ntally nally
21 -D Collson ecal Case: Perectly Elastc (all nternal changes bounce back ) Extra secal case: Say s ntally statonary Syste = carts & ntally nally Pow! Intally Statonary
22 d b n, b d,, -4 Introducng Collsons Quz 9 L9 Mult-artcle Systes 6-8 Scatterng 9- Collson Colcatons L Collsons 5, Derent Reerence Fraes ranslatonal ngular Moentu Quz RE a RE b RE c EP9 RE a; HW: Pr s 3*,, 3, 39 Collsons! Short, Shar Shocks
23
24 Fast (~c) Collson P P
25 P,, P, sn, cos, sn, cos Conseraton o Moentu Fast (~c) Collson sn sn : ˆ cos cos : ˆ y x
26 P,, P, sn, cos, sn, cos Conseraton o Moentu where c Fast (~c) Collson sn sn : ˆ cos cos : ˆ y x
27 Fast (~c) Collson cos, sn, P,, P Conseraton o Moentu xˆ : yˆ : where cos sn cos sn c cos, sn, Conseraton o Energy E E E E where E c c
28 Fast (~c) Collson cos, sn, P,, P Conseraton o Moentu xˆ : yˆ : where cos sn c Conseraton o Energy sn cos E E E E where E c c CW: show E y luggng that nto t and recoerng that cos, sn c c,
29
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