Chapter 8 Moentu Ipulse and Collsons Analyss o oton: key deas Newton s laws o oton Conseraton o Energy
Newton s Laws st Law: An object at rest or traelng n unor oton wll rean at rest or traelng n unor oton unless and untl an external orce s appled r r F net a nd Law: F a, F a F a net, x x net, y y, net, z z 3 rd Law: For eery Acton, there s an equal but opposte Reacton 3 Conseraton o Mechancal Energy The echancal energy o a syste s the su o ts potental energy U and the knetc energy K o the objects wthn t E K + U ech In an solated syste where only conserate orces cause energy change, the knetc energy and potental energy can change, but ther su, the echancal energy o the syste cannot change K + U K + U 4
Conseraton o Energy The total energy o a syste can change only by aounts o energy that are transerred to or ro that syste ΔE ΔK + ΔU + ΔE theral + ΔE nternal The total energy o an solated syste cannot change ΔK + ΔU + ΔE theral + ΔEnternal 0 5 Conseraton o Mechancal Energy (cont.) Exaples: 6 3
Probles wth two (or ore) objects Exaple Three (or ore) body proble s one o the ost dcult n physcs 7 Part Moentu and Ipulse 8 4
Lnear Moentu The lnear oentu o a partcle s a ector dened as p s the ass o the partcle s the elocty o the partcle Newton s nd Law s now r r d F a dt d( ) dt r dp dt NOTE: Newton s orgnal stateent was n ters o lnear oentu 9 Ipulse 0 5
Ipulse (cont) J p p F dt t t F ae Δt aerage orce F ae p Δt p exaple: What the use o an ar bag n a car? exaple A car has abrupt stop by drng nto a stone ebankent: ass o the car s 800 kg, ass o a drer s 60 kg, speed 7.8 /s, (00 k/h), pact occurred oer te nteral 0 s. Estate aerage sze o orce exerted on the drer: F 60.0 kg * 7.8 /s/0.0s.67*0 5 N coparng to weght o the drer W 60 kg * 9.8 /s Stoppng orce s approxately 80 tes weght 6
Checkpont F ae p Δt p A student's le was saed n an autooble accdent because an arbag expanded n ront o hs head. I the car had not been equpped wth an arbag, the wndsheld would hae stopped the oton o hs head n a uch shorter te. Copared to the wndsheld, the arbag: A) causes a uch saller change n oentu B) exerts a uch saller pulse C) causes a uch saller change n knetc energy D) exerts a uch saller orce E) does uch ore work 3 Part Conseraton o Moentu 4 7
Conseraton o oentu 5 Syste o N partcles 6 8
Moentu conseraton or a syste o partcles 7 The law o conseraton o lnear oentu F net I no net external orce acts on a syste o partcles, the total oentu o the syste can not change d P dt 0 or closed, solated syste P const. P total lnear oentu total lnear oentu at soe ntal te t at soe later te t P oentu o a sngle partcle s not necessarly consered, only oentu o a closed syste 8 9
Checkpont A an, standng at rest on a horzontal rctonless loor, ght get hsel ong by: A) walkng B) rollng C) exhalng ertcally D) crawlng slowly E) throwng a shoe horzontally 9 Two asses on rctonless surace exaple 0 0
Part 3 Syste o partcles Moton o syste as a whole
The center-o-ass 3 Coordnates o the center-o-ass 4
The center o ass (exaple) + x CM d x + x x CM + r CM r + r +... + +... M n r 5 exaple Syste o three pont partcles n -D 6 3
CM or Contnuous Mass Dstrbutons 7 Mass dstrbuted oer a olue 8 4
Mass dstrbuted oer a surace 9 Mass dstrbuted oer a cure 30 5
Constant lnear densty 3 CM s n the ddle pont 3 6
Constant surace densty 33 CM at center - agan! 34 7
CM o hal-dsk 35 CM s Independent o Orgn 36 8
Iportance o CM 37 Exaple 38 9
Newton s Second Law or a syste o partcles Net orce on a syste o partcles F net F F + +... Denton or the center o ass M rcm r r + +... Derentatng twce wth respect to te M M a CM CM + a + a +... +... F M net acm 39 Practcal applcatons: F net M acm I the net orce on a syste o partcles s zero F net F F +... + 0 then acm 0, CM const and CM 0, rcm const 40 0
exaple What s the change n elocty o the car the an runs so that hs speed relate to the car s rel? P 0 + MV V rel 0 ( V rel ) + MV V rel M + 4 exaple The cat To, o ass 5 kg, and the ouse Jerry (see the cartoon "To and Jerry") are n kg canoe. When the canoe s at rest n the placd water, they exchange seats, whch are.0 apart and syetrcally located wth respect to the canoe's center. The canoe oes.5 relate to the shore durng the exchange. What s Jerry's ass? 4
Fshng exaple Ge a an a sh and he wll eat or a day. Teach h how to sh, and he wll st n a boat and drnk beer all day. 43 Part 4 Collsons 44
Collsons A collson s an solated eent n whch two or ore bodes exert orces on each others or a relately short te orce between bodes can be: conserate (total energy consered) > elastc collson dsspate (energy lost to theral oton etc.) > nelastc collson Ether way, total oentu s consered (as long as no external orce s present) 45 Collsons 46 3
Types o collsons (agan) 47 Perectly nelastc collsons 48 4
One o the bodes s at rest 49 Partcular cases 50 5
One-densonal collsons 5 Change n total knetc energy 5 6
Inelastc collson n one denson P P + + Because the oton s one denson we can drop arrows or ector Exaples: trac accdents 53 P Copletely Inelastc collson n one denson P ) V ( + V + Ater the collson two bodes oe together 54 7
Exaple: ballstc pendulu V + M ( + M ) V ( + M ) gh + M gh 55 exaple Two cars slde on an cy road as they attept to stop at a trac lght. The ass o A s 00 kg, and the ass o B s 400 kg. The coecent o knetc rcton between the locked wheels o ether car and the road s 0.3. Car A succeeds n stoppng at the lght, but car B cannot stop and rear-end car A. Ater the collson, A stops 8. ahead o ts poston at pact, and B 6. ahead. Both drers had ther brakes locked through the ncdent. Fro the dstance each car oed ater the collson, nd the speed o cars A and B edately ater the pact. Use conseraton o lnear oentu to nd speed at whch car B struck car A 56 8
exaple There are two eents n ths proble:. the collson o ong car B wth statonary car A. stoppng due to rctonal orces on cars 57 exaple collson : b 0 a a + b b stoppng : aa μkagda a μk gda bb μkbgdb b μk gdb ro the last two equatons we ay nd then usng the rst equaton we ay nd a 0 and b 58 9
Perectly elastc collsons 59 One-densonal collsons 60 30
One-densonal collsons 6 Equal asses 6 3
Heay body at rest 63 Lght body at rest 64 3
33 65 Elastc collson n one denson + E E P P + + + Specal stuatons Equal asses A asse target A asse projectle 66 Mong target + + + + + + + + + +
Relate elocty 67 Two-densonal elastc collsons 68 34
Two bllard balls 69 Algebrac proo 70 35
Veloctes o balls 7 36