10/24/2013. PHY 113 C General Physics I 11 AM 12:15 PM TR Olin 101. Plan for Lecture 17: Review of Chapters 913, 1516


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1 0/4/03 PHY 3 C General Physcs I AM :5 PM T Oln 0 Plan or Lecture 7: evew o Chapters 93, 56. Comment on exam and advce or preparaton. evew 3. Example problems 0/4/03 PHY 3 C Fall Lecture 7 0/4/03 PHY 3 C Fall Lecture 7 Webassgn questons Assgnment #5 Consder the snusodal wave o the gure below wth the wave uncton y = 0.50 cos(5.7x 50.3t) where x and y are n meters and t s n seconds. At a certan nstant, let pont A be at the orgn and pont B be the closest pont to A along the x axs where the wave s 43.0 out o phase wth A. What s the coordnate o B? o x o 80 0/4/03 PHY 3 C Fall Lecture 7 3
2 0/4/03 Webassgn questons Assgnment #5 A transverse wave on a strng s descrbed by the ollowng wave uncton. y = 0.5 sn ((π/9)x + 5πt) where x and y are n meters and t s n seconds. (a) Determne the transverse speed at t = 0.50 s or an element o the strng located at x =.50 m. y( x, t) 0.5 cos x 5t t 9 9 (b) Determne the transverse acceleraton at t = 0.50 s or an element o the strng located at x =.50 m. y( x, t) 0.5 sn x 5t t 9 9 0/4/03 PHY 3 C Fall Lecture 7 4 Webassgn questons Assgnment #5 A snusodal wave n a rope s descrbed by the wave uncton y = 0.0 sn (0.69πx + 0πt) y0 snkx t where x and y are n meters and t s n seconds. The rope has a lnear mass densty o 0.30 kg/m. The tenson n the rope s provded by an arrangement lke the one llustrated n the gure below. What s the mass o the suspended object? T c k T mg mg 0/4/03 PHY 3 C Fall Lecture 7 5 Comment about exam on Tuesday 0/9/03 0/4/03 PHY 3 C Fall Lecture 7 6
3 0/4/03 clcker queston What s the purpose o exams? A. Pure pan and suerng or all nvolved. B. To measure what has been learned. C. To help students learn the materal. D. Other. 0/4/03 PHY 3 C Fall Lecture 7 7 Advce on how to prepare or the exam evew lecture notes and text chapters 93,56 Prepare equaton sheet Work practce problems Topcs covered Lnear momentum otatonal moton and angular momentum Gravtatonal orce and crcular orbts Statc equlbrum Smple harmonc moton Wave moton 0/4/03 PHY 3 C Fall Lecture 7 8 What to brng to exam: Clear head Calculator Equaton sheet Pencl or pen 0/4/03 PHY 3 C Fall Lecture 7 9 3
4 0/4/03 clcker queston: Have you looked at last year s exams? A. Yes B. No 0/4/03 PHY 3 C Fall Lecture 7 0 Lnear momentum What s t? When s t conserved? Conservaton o momentum n analyss o collsons Noton o center o mass Dene "lnear momentum": mv p Unts o lnear momentum : kg m/s N s dv dmv dp F ma m F dp Impulse: I F dp p p 3 0/4/03 PHY C Fall Lecture 7 Lnear momentum  contnued Physcs o composte systems Newton' s second law : dv F ma m Note that d 0/4/03 PHY 3 C Fall Lecture 7 F 0, then : p 0 p (constant) p ntal p nal d m v d p 4
5 0/4/03 Example completely nelastc collson; balls movng n one dmenson on a rctonless surace m v m v v For p ntal v p 0/4/03 PHY 3 C Fall Lecture 7 3 mv mv m m m 0.3kg, m 0.5kg v m / sˆ, v m / sˆ nal m m 0.3 ˆ 0.5 ˆ m/s ˆ v m / s Examples o twodmensonal collson; balls movng on a rctonless surace p ntal p nal mv mv cos mv cos 0 mv sn mv sn Knowns : m, m, v Unknowns : v, v,, Need more equatons   0/4/03 PHY 3 C Fall Lecture 7 4 The noton o the center o mass and the physcs o composte systems Newton' s second law : Dene : F F F m a r total M d r M d r m m r M d m r m 0/4/03 PHY 3 C Fall Lecture 7 5 5
6 0/4/03 Fndng the center o mass r m r M M m In ths example : m m kg; m3 kg m ˆ ˆ ˆ x mx m3 y3j r m m m3 ()(m )ˆ m ˆ mˆ j r mˆ.00mˆj 0/4/03 PHY 3 C Fall Lecture 7 6 otatonal moton and angular momentum Angular varables Newton s law or angular moton otatonal energy Moment o nerta Angular momentum d d 0/4/03 PHY 3 C Fall Lecture 7 7 evew o rotatonal energy assocated wth a rgd body otatonal energy : K rot m v m r where I m r m r I 0/4/03 PHY 3 C Fall Lecture 7 8 6
7 0/4/03 Moment o nerta: I m r I Ma I Ma mb 0/4/03 PHY 3 C Fall Lecture 7 9 Total knetc energy o rollng object : K total K rollng K I Mv Note that : d ds d v K total K rollng K I Mv I M v 0/4/03 PHY 3 C Fall Lecture 7 0 clcker exercse: Three round balls, each havng a mass M and radus, start rom rest at the top o the nclne. Ater they are released, they roll wthout slppng down the nclne. Whch ball wll reach the bottom rst? I A M B C I B M 0.5M A I C M 0.4M 5 K U K U I 0 Mgh M M gh v I / M 0/4/03 PHY 3 C Fall Lecture 7 v 0 7
8 0/4/03 How can you make objects rotate? Dene torque: t = r x F t = rf sn F ma r F τ r ma Iα r sn r F Newton's law or rotatonal moton : τ Iα 0/4/03 PHY 3 C Fall Lecture 7 Example orm Webassgn # X t 3 clcker exercse When the pvot pont s O, whch torque s zero? A. t? B. t? C. t 3? t t 0/4/03 PHY 3 C Fall Lecture 7 3 Vector cross product; rght hand rule C AB C A B sn ˆ ˆ ˆj ˆj kˆ kˆ 0 ˆ ˆj ˆj ˆ kˆ ˆj kˆ kˆ ˆj ˆ kˆ ˆ ˆ kˆ ˆj 0/4/03 PHY 3 C Fall Lecture 7 4 8
9 0/4/03 From Newton s second law contnued conservaton o angular momentum: d r F τ r p Dene : L r p dl I τ 0 0 L (constant) 0/4/03 PHY 3 C Fall Lecture 7 5 Example o conservaton o angular momentum L L b b wheel L L wheel b L L b 0 L L L wheel wheel wheel 0/4/03 PHY 3 C Fall Lecture 7 6 Summary conservaton laws we have studed so ar Conserved quantty Necessary conon Lnear momentum p F net = 0 Angular momentum L t net = 0 Mechancal energy E No dsspatve orces 0/4/03 PHY 3 C Fall Lecture 7 7 9
10 0/4/03 Fundamental gravtatonal orce law and planetary moton Newton s gravtatonal orce law Gravty at Earth s surace Crcular orbts o gravtatonal bodes Energy assocated wth gravtaton and orbtal moton 0/4/03 PHY 3 C Fall Lecture 7 8 Unversal law o gravtaton Newton (wth help rom Galleo, Kepler, etc.) 687 Gm m rˆ F r G N m kg 0/4/03 PHY 3 C Fall Lecture 7 9 Gravtatonal orce o the Earth E m GM m F E E GM g E E (6.370 ) 4 m/s 9.8m/s Note: Earth s gravty acts as a pont mass located at the Earth s center. 0/4/03 PHY 3 C Fall Lecture
11 0/4/03 Stable crcular orbt o two gravtatonally attracted objects (such as the moon and the Earth) EM F a v Newton's law or Moon due to Earth : F M a M v a EM v ω M EM M GM T π GM π T 3 EM E EM E EM 8 3 (3.840 ) π s 7.4 days 0/4/03 PHY 3 C Fall Lecture 7 3 Crcular orbtal moton about center o mass m v Note that v m T T G m m m then v m Gmm m m T T 3 3 m Gm v m m T m m T 3 G m m v 0/4/03 PHY 3 C Fall Lecture 7 3 dl τ 0 L (const) v m L =m v L =m v L = L + L m v L L Note: More generally, stable orbts can be ellptcal. 0/4/03 PHY 3 C Fall Lecture 7 33
12 0/4/03 Gravtatonal potental energy Example: U U gravty gravty ( r) ( r) r r rre F dr Gmm r' Gmm dr' r Gmmrˆ F r U gravty GM EmS ( r E h) h E 0/4/03 PHY 3 C Fall Lecture 7 34 Analyss o statc equlbrum Meanwhle back on the surace o the Earth: Conons or stable equlbrum Balance o orce : Balance o torque : F 0 τ 0 0/4/03 PHY 3 C Fall Lecture 7 35 Torques : F (m ) mg ( ) g 0 0/4/03 PHY 3 C Fall Lecture 7 36
13 0/4/03 t 0 T mgx Mg T sn 0 mgx / Mg / T sn For 53 mg 600 N T 33 N o 8m x m Mg 00 N * *X x mg / Mg 0/4/03 PHY 3 C Fall Lecture 7 37 Some practce problems 0/4/03 PHY 3 C Fall Lecture /4/03 PHY 3 C Fall Lecture
14 0/4/03 From webassgn: A 00kg merrygoround n the shape o a unorm, sold, horzontal dsk o radus.50 m s set n moton by wrappng a rope about the rm o the dsk and pullng on the rope. What constant orce would have to be exerted on the rope to brng the merrygoround rom rest to an angular speed o rev/s n.00 s? (State the magntude o the orce.) vew rom top: F τ r F Iα I M 0/4/03 PHY 3 C Fall Lecture 7 40 From webassgn: A 0.3kg monkey clmbs a unorm ladder wth weght w =.4 0 N and length L = 3.35 m as shown n the gure below. The ladder rests aganst the wall and makes an angle o θ = 60.0 wth the ground. The upper and lower ends o the ladder rest on rctonless suraces. The lower end s connected to the wall by a horzontal rope that s rayed and can support a maxmum tenson o only 80.0 N. 0/4/03 PHY 3 C Fall Lecture 7 4 4
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