Consider two masses m 1 at x = x 1 and m 2 at x 2.

Transcription

1 Chapte 09 Syste of Patcles Cete of ass: The cete of ass of a body o a syste of bodes s the pot that oes as f all of the ass ae cocetated thee ad all exteal foces ae appled thee. Note that HRW uses co but I wll use because s oe stadad otato fo the cete of ass. Chapte 09 Syste of Patcles Cosde two asses at x x ad at x. x x + x +

2 Cete of ass fo a syste of patcles:.. c x x.. c.. c y y kˆ ĵ y î x. c... c c s just the total ass of the syste Theefoe: Usg ectos, we hae:

3 Fo a sold body, we ca teat t as a cotuous dstbuto of atte d x x d If the object has ufo desty, d (/V)dV x x dv y y y d y dv d V V V If a object has a pot, a le o a plae of syety, the cete of ass of such a object the les at that pot, o that le o that plae. dv Saple 9-: the fgue shows a ufo etal plate P of adus R fo whch a dsk of adus R has bee staped out (eoed). Usg the x-y coodate syste show, locate the cete of ass of the plate.

4 Newto s d law fo a syste of patcles We kow take deate wth espect to te take deate wth espect to te aga a a a + a a F + F F F Σ et F Newto s secod law fo a syste of patcles et,x a,x F a et F et,y a,y F et, a F et s the et foce of all exteal foces that act o the syste. s the total ass of the syste. a s the acceleato of the cete of the ass,

5 Lea oetu The lea oetu of a patcle s a ecto defed as p Newto s secod law tes of oetu dp d d d () + a F et dt dt dt dt F et dp dt ost of the te the ass does t chage, so ths te s eo. Exceptos ae ockets The fgue ges the lea oetu esus te fo a patcle og alog a axs. A foce dected alog the axs acts o the patcle. (a) Rak the fou egos dcated accodg to the agtude of the foce, geatest fst (b) I whch ego s the patcle slowg?

6 Lea oetu of a syste of patcles P p P c.. Newto s d law fo a syste of patcles dp d a Fet dt dt dp F et dt Coseato of Lea oetu Fo a syste of patcles, f t s both solated (the et exteal foce actg o the syste s eo) ad closed ( o patcles leae o ete the syste ). If Σ F 0 the d P 0 Theefoe the the total lea oetu of the syste caot chage. Law of coseato of lea oetu dt P costat o P Pf

7 Coseato of lea oetu alog a specfc decto: If Σ F x 0 The P, x P f, x If Σ F y 0 The P, y P f, y If the copoet of the et exteal foce o a closed syste s eo alog a axs, the the copoet of the lea oetu of the syste alog that axs caot chage. Check pot 9-4: A tally statoay dece lyg o a fctoless floo explodes to two peces, whch the slde acoss the floo. Oe pece sldes the poste decto of the x axs. (a) What s the su of the oetu of the two peces afte the exploso? (b) Ca the secod pece oe at a agle to the x axs? c) What s the decto of the oetu of the secod pece?

8 Textbook Poble 9-7. A 9 kg a stadg o a fctoless suface shoes a 68g stoe away fo h, gg t a speed of 4.0/s. What elocty does the a acque as a esult? Textbook Poble A 4.0 kg ess kt sldg o a fctoless suface explodes to two.0 kg pats, oe og at 3.0/s, due oth, ad the othe at 5.0 /s 30 o oth of east. What s the ogal speed of the ess kt? N E S

9 Exteal foces ad teal eegy chages Fo the skate syste, o eegy tasfeed to ad fo the syste E ec + E t 0 E ec Fdcosφ So, E t E ec Fdcosφ Tasfe of the teal bochecal eegy of the skate to he echacal eegy a foce F Tasfe of the teal eegy stoed the fuel to the ketc eegy of the ca a fcto foce