10/15/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101

Transcription

1 10/15/01 PHY 11 C Geneal Physcs I 11 AM-1:15 PM MWF Oln 101 Plan fo Lectue 14: Chapte 1 Statc equlbu 1. Balancng foces and toques; stablty. Cente of gavty. Wll dscuss elastcty n Lectue 15 (Chapte 15) 10/14/01 PHY 11 C Fall Lectue /14/01 PHY 11 C Fall Lectue 14 Suay of gavty: Newton s law of gavtaton: Eath s gavty: GM F g E E GM g E E (6.710 ) G ˆ F Stable ccula obts of gavtatonal attacted objects: E /s 9.8/s GM M F E sat ES M sat v ES ES F a v M sat 10/14/01 PHY 11 C Fall Lectue 14 1

2 10/15/01 Fo Webassgn Assgnent #1: When a fallng eteood s at a dstance above the Eath's suface of.40 tes the Eath's adus, what s ts acceleaton due to the Eath's gavtaton? /s towads eath GME a GME GME a 4.4E =4.4 E 10/14/01 PHY 11 C Fall Lectue 14 4 Fo Webassgn Assgnent #1: An atfcal satellte ccles the Eath n a ccula obt at a locaton whee the acceleaton due to gavty s 6.79 /s. Detene the obtal peod of the satellte. GME v a v / T T 1/ 4 GME T a a T /14/01 PHY 11 C Fall Lectue s 5 1/ 4 4 Fo Webassgn Assgnent #1: How uch wok s done by the Moon's gavtatonal feld as a 1090 kg eteo coes n fo oute space and pacts on the Moon's suface? M W M GMM GMM d GMM M clcke queston A. W>0 B. W<0 M 10/14/01 PHY 11 C Fall Lectue 14 6

3 10/15/01 Fo Webassgn Assgnent #1: A space pobe s fed as a pojectle fo the Eath's suface wth an ntal speed of /s. What wll ts speed be when t s vey fa fo the Eath? Ignoe atosphec fcton and the otaton of the Eath. K U K U 1 GM 1 v v E v f E f f 10/14/01 PHY 11 C Fall Lectue 14 7 Fo Webassgn Assgnent #1: Plaskett's bnay syste conssts of two stas that evolve n a ccula obt about a cente of ass dway between the. Ths stateent ples that the asses of the two stas ae equal (see fgue below). Assue the obtal speed of each sta s v = 190 k/s and the obtal peod of each s 10.7 days. Fnd the ass M of each sta. (Fo copason, the ass of ou Sun s kg.) v GM M Know v, T; want to know M vt v T Afte soe algeba : 4Tv M 10/14/01 PHY 11 C Fall Lectue 14 G 8 Fo Webassgn Assgnent #1: Plaskett's bnay syste conssts of two stas that evolve n a ccula obt about a cente of ass dway between the. Ths stateent ples that the asses of the two stas ae equal (see fgue below). Assue the obtal speed of each sta s v = 190 k/s and the obtal peod of each s 10.7 days. Fnd the ass M of each sta. (Fo copason, the ass of ou Sun s kg.) clcke execse: Who ght pose a queston lke ths? A. A ean pofesso. B. A puzzle aste. C. An obsevatonal astonoe. 10/14/01 PHY 11 C Fall Lectue 14 9

4 10/15/01 Meanwhle back on the suface of the Eath: Condtons fo stable equlbu Balance of foce : Balance of toque : F 0 τ 0 10/14/01 PHY 11 C Fall Lectue Stablty of gd bodes N g 10/14/01 PHY 11 C Fall Lectue Cente-of-ass CM Toque on an extended object due to gavty (nea suface of the eath) s the sae as the toque on a pont ass M located at the cente of ass. τ g j CM Mg j CM 10/14/01 PHY 11 C Fall Lectue

5 10/15/01 Noton of equlbu: F τ 0 Noton of stablty: 0 q T F=a t=i a T- g cos q 0 g sn q a q g sn q = a a q g(-j) Exaple of stable equlbu fo q 0 10/14/01 PHY 11 C Fall Lectue 14 1 Unstable equlbu: Suppot above CM: Suppot below CM: q T g(-j) 10/14/01 PHY 11 C Fall Lectue Nk Wallenda walkng on hgh we acoss Gand Canyon 10/14/01 PHY 11 C Fall Lectue

6 10/15/01 Analyss of stablty: F τ /14/01 PHY 11 C Fall Lectue X Foces Toques : : n M M D D g c g (1 ) g c P g gx /14/01 PHY 11 C Fall Lectue /14/01 PHY 11 C Fall Lectue

7 10/15/01 CM F g1 X g Toques : F 1 ( ) g ( ) g CM 0 10/14/01 PHY 11 C Fall Lectue clcke queston: F 1 F L/ L Mg g Consde the above dawng of the two suppots fo a unfo plank whch has a total weght Mg and has a weght g at ts end. What can you say about F 1 and F? (a) F 1 and F ae both up as shown. (b) F 1 s up but F s down. (c) F 1 s down but F s up. 10/14/01 PHY 11 C Fall Lectue 14 0 F F 1 X L/ Foces Toques : : F 1 L F F Mg Mg L Mg g g 0 L gl 1 F Mg g F1 Mg g 0 10/14/01 PHY 11 C Fall Lectue

8 10/15/01 clcke queston: The fact that we found F 1 <0 eans: A. We set up the poble ncoectly B. The analyss s coect, but the decton of F 1 s opposte to the aow C. Physcs akes no sense clcke queston: What would happen f we analyzed ths poble by placng the pvot pont at F 1?: A. The answe would be the sae. B. The answe would be dffeent. C. Physcs akes no sense 10/14/01 PHY 11 C Fall Lectue 14 t 0 T gx Mg T sn 0 gx / Mg / T sn Fo 5 g 600 N T 1 N o 8 x Mg 00 N X x g / Mg 10/14/01 PHY 11 C Fall Lectue 14 d X t 0 gd F g h 10/14/01 PHY 11 C Fall Lectue 14 4 gd F h 0 h h 8

9 10/15/01 Mg = 10 N g = 98 N F wall T < 110 N N X T g Mg T F N g Mg 0 MgL gxl cos q cos q F L sn q 0 T wall 0 wall gx Mg / cos q sn q 10/14/01 PHY 11 C Fall Lectue 14 5 F wall f q X x A ladde of weght Mg and of length L s suppoted by the gound wth statc fcton foce f and by a fctonless wall as shown. The fefghte has weght g and s half-way up the ladde. Fnd the foce that the ladde exets on the wall. F wall f 0 a 1 Fwall h Mg x g a 0 L ax a Fwall f Mg g Lh h 10/14/01 PHY 11 C Fall Lectue