Physcs 0, Lecture 4 Conseraton Laws n Physcs q Physcal states, process, and state quanttes: Today s Topcs Partcle Syste n state Process Partcle Syste n state q Lnear Moentu And Collsons (Chapter 9.-9.4) n Moentu and Ipulse n Collsons Inelastc Elastc Exaple: D Collson u Hope you hae preewed. Intal State Physcal Quanttes Energy(E ), Moentu (P ) etc. q Conseraton Prncples: Under certan condton, one can assert E E and/or P P, etc. ndependent o process detals E.g. Mechanc Energy: E KU ½ gh ½ kx Fnal State E, P,... Ø I W non-conserte 0, E E Ø Usng conserate laws can greatly sply proble solng (Lnear) Moentu q Lnear oentu P or a partcle (Unt: kg /s) Ø Moentu s a ector P has the sae drecton as Coponents o P: P x x, P y y, P z z q Consder a syste o two.0 kg balls as shown.0 /s.0 /s A B q For ult-partcle syste: p p p p 3... p j * Note: Lnear Moentu (P ) s oten sply called Moentu. what s total oentu?.0kg/s, 4.0 kg/s, 0.0 p A M A A.0x.0.0 kg/s, p B M B B.0x(-.0)-.0 kg/s pp A p B.0 (-.0) 0 what s total knetc energy? KE A ½ M A A ½.0x.0.0 J, KE B ½ M B B.0 J also KEKE A KE B.0.0 4.0 J Is t possble or a syste o two objects to hae zero total oentu whle hang a non-zero total knetc energy!
When and Why Moentu s Consered q For a sngle partcle, when the net orce on t s zero, then p why? ery sple! F net 0 a0 ( ) p ( ) q Mult-partcle syste Consder two class o orces: F EXT_ Internal orces: F, F 3, F,... F F 3 3 F EXT_3 3 External orces: F EXT _,,3 q Newton s nd F Law on each partcle: F 3 F F EXT_ F F 3 Δ /Δt 3 F F EXT_ F F 3 Δ /Δt F EXT_ F EXT_3 F 3 F 3 3 Δ 3 /Δt q Su oer all equatons or the syste: (Note: F -F etc. ) F EXT_ F F 3 F EXT_ F F 3 F EXT_3 F 3 F 3 Δ( 3 3 )/Δt è F EXT Σ F EXT_ Δ ( 3 3 )/Δt ΔP /Δt (dp/dt) I F EXT 0, ΔP0 P P! Equalently: F EXT 0 Δ( 3 3 ) 0 workout detals ater class Moentu Conseraton p Su oer all objects Ø Moentu s a ector: P P P x P x, P y P y, P z P z Ø Explct expresson: 3 3 3 3 Ø I a net external orce does exst: p, F ext 0 F ext (t)dt I (pulse) (Ipulse-Moentu Theore) Ipulse and Aerage Ipact Force q Recall: Ipulse oentu theore (preous slde) p I F ext (t)dt F ext _ aerage Δt q Two dentcal balls are dropped ro the sae heght onto the loor. In case the ball bounces back up, and n case the ball stcks to the loor wthout bouncng. In whch case s the pulse gen to the ball by the loor the larger? è F ag I /Δt P -P /Δt (render: bold ace denotes ectors) q Exercse/Exaple: Typcal contact te between gol club head and the ball s about 0.5 s ( 5x0-4 s), ater beng ht, a 45g gol ball les at a speed o 40 /s. Estate the aerage httng orce. Ø Answer: P 0, P 0.045 kg x 40 /s.8 kg/s ΔP.8 kg/s I F ag I / Δt.8 / 5x0-4 3600 N ( ~ 360 kg o orce) q Answer: See nuercal exaple (take: kg) Ball : Beore.0 /s down, ater.0 /s up p -.0x-.0,.0x.0 Δp 4.0 kg/s Ball : Beore.0 /s down, ater 0 p -.0x-.0, 0 Δp.0 kg/s
Deo: Bouncng Ball pulse Force * Δt - p q Two dentcal balls are dropped ro the sae heght onto the loor. In case the ball bounces back up, and n case the ball stcks to the loor wthout bouncng. In whch case s the pulse gen to the ball by the loor the bggest? te q Answer: See nuercal exaple (take: kg) Ball : Beore.0 /s down, ater.0 /s up p -.0x-.0,.0x.0 Δp 4.0 kg/s Ball : Beore.0 /s down, ater 0 p -.0x-.0, 0 Δp.0 kg/s p Also: See Ipact Force s. Te on Pasco Collsons Elastc and Inelastc Collsons q Beore and ater collson, the total oentu s always consered (Ipulse approxaton) q Howeer, total knetc energy o the syste ay or ay not be consered. q Collson: An eent n whch two partcles coe close and nteract wth each other by orce. Collson occurs n a ery short perod Ipulse s nte, but colldng orce s large. Ipulse approxaton: external orces gnored. P P Collson occurs locally: do not consder change o gratatonal potental energy o the syste. In collson probles, only two colldng partcles are consdered. In general, beore and ater collson, knetc energy o the syste ay not be consered. Collsons that DO consere knetc energy are called elastc collsons Collsons that do NOT consere knetc energy are called nelastc collsons Ø In act, practcally ost o collsons are nelastc collsons Ø In an extree case, ater collson, the two objects are stck together. Ths s called copletely nelastc collson. Can proe, the syste s total knetc energy s lost to the axu n a copletely nelastc collson. 3
4 Elastc and Perectly Inelastc Collsons Elastc Collson: Knetc Energy Consered Perectly nelastc Collson: Two partcle stck together Two Extree Cases -Dentonal Elastc Collson q Moentu n x drecton P P : q Knetc energy: KE KE : ½ ½ ½ ½ q Algebra (practce ater class) Deo: Newton s Cradles Take 0: I << : -, 0 (thnk o a tenns ball httng ground) I >> :, I : 0, (Next slde) Newton s Cradles: Equal Mass : 0,
-Dentonal Perectly Inelastc Collson q Perectly nelastc collson: Ater collson, two partcles hae sae elocty. q Moentu n x drecton: P P à ( )/ ( ) q Queston: Is knetc energy the sae beore and ater? Beore: KE ½ ½ Ater: KE ½ ½ à KE -KE - ½ /( ) ( - ) <0!!! Quzzes: What s the work done n collson? Where s the lost energy? 5