AP Physics C: Mechanics 2007 Free-Response Questions

Transcription

1 AP Physics C: Mechanics 7 Fee-Response Questions The College Boa: Connecting Stuents to College Success The College Boa is a not-fo-pofit membeship association whose mission is to connect stuents to college success an oppotunity. Foune in 9, the association is compose of moe than 5, schools, colleges, univesities, an othe eucational oganizations. Each yea, the College Boa seves seven million stuents an thei paents,, high schools, an,5 colleges though majo pogams an sevices in college amissions, guiance, assessment, financial ai, enollment, an teaching an leaning. Among its best-known pogams ae the SAT, the PSAT/NMSQT, an the Avance Placement Pogam (AP ). The College Boa is committe to the pinciples of ecellence an equity, an that commitment is emboie in all of its pogams, sevices, activities, an concens. 7 The College Boa. All ights eseve. College Boa, Avance Placement Pogam, AP, AP Cental, SAT, an the acon logo ae egistee taemaks of the College Boa. PSAT/NMSQT is a egistee taemak of the College Boa an National Meit Scholaship Copoation. Pemission to use copyighte College Boa mateials may be equeste online at: Visit the College Boa on the Web: AP Cental is the official online home fo the AP Pogam: apcental.collegeboa.com.

2 TABLE OF INFORMATION FOR 6 an 7 CONSTANTS AND CONVERSION FACTORS UNITS unifie atomic mass unit, -7 u.66 kg Name Symbol 9 MeV c mete m -7 Poton mass, m p.67 kg kilogam kg -7 Neuton mass, m n.67 kg secon s - Electon mass, m e 9. kg ampee A -9 Electon chage magnitue, e.6 C Avogao s numbe, - kelvin N 6. mol K Univesal gas constant, R 8. J (moli K) mole mol Boltzmann s constant, - k B.8 J/K hetz Hz Spee of light, 8 c. m s newton N Planck s constant, -4 h 6.6 Jis pascal Pa evis -5 joule J hc.99 Jim watt W.4 evinm Vacuum pemittivity, C i m N coulomb C Coulomb s law constant, k 4p 9 9. Nm i C volt V -7 Vacuum pemeability, m 4p (Tim) A ohm W Magnetic constant, k -7 m /4p (T m) A heny H Univesal gavitational constant, - G 6.67 m kgi s faa F Acceleation ue to gavity tesla T at Eath s suface, g 9.8 m s egee atmosphee pessue, 5 atm. N m Celsius C 5. Pa electon- -9 volt electon volt, ev.6 J ev PREFIXES Facto Pefi Symbol 9 giga G 6 mega M kilo k - centi c - milli m 6 - mico m 9 - nano n - pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q sin q cos q tan q / / / 7 /5 4/5 /4 45 / / 5 4/5 /5 4/ 6 / / 9 The following conventions ae use in this eamination. I. Unless othewise state, the fame of efeence of any poblem is assume to be inetial. II. The iection of any electic cuent is the iection of flow of positive chage (conventional cuent). III. Fo any isolate electic chage, the electic potential is efine as zeo at an infinite istance fom the chage. --

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 6 an 7 u u + at + ut + at u ( ) u + a -  F Fnet ma F p t J Ft Dp p mv Ffic W K mn F P mu W t P Fv D Ug mgh ac t u w F  t tnet Ia I m  m cm Âm Âm u w L p Iw K Iw w w + at q q + wt + at MECHANICS a acceleation F foce f fequency h height I otational inetia J impulse K kinetic enegy k sping constant length L angula momentum m mass N nomal foce P powe p momentum aius o istance position vecto T peio t time U potential enegy u velocity o spee W wok one on a system position m coefficient of fiction q angle t toque w angula spee a angula acceleation F s Us -k k p T w f T s p T p p F U G G m k g Gm m - Gm m - ˆ qq F 4p E F q E A V E - ELECTRICITY AND MAGNETISM Q i qi V 4p  U C C E Cp qq qv 4p Q V k A  Ci i  Cs i Ci I Q t Uc QV CV R A E J I Neu A V R s IR  Ri i  R p i Ri P IV F qv B M i A aea B magnetic fiel C capacitance istance E electic fiel e emf F foce I cuent J cuent ensity L inuctance length n numbe of loops of wie pe unit length N numbe of chage caies pe unit volume P powe Q chage q point chage R esistance istance t time U potential o stoe enegy V electic potential u velocity o spee esistivity f m magnetic flu k ielectic constant B m m B 4p I I F I B Bs f m m ni B A f e - t m I e - L t UL LI --

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 6 an 7 GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Tiangle A bh Cicle A p C p Paallelepipe V wh Cyline V p S p + p Sphee 4 V p S 4p Right Tiangle a + b c A aea C cicumfeence V volume S suface aea b base h height length w with aius f f u u n n- ( ) n ( ) e e ( n ) ( sin ) ( cos ) cos - sin n n+, n π - n + e e ln cos sin sin -cos sinq cosq a c b c q c b 9 a tanq a b -4-

5 7 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C: MECHANICS SECTION II Time 45 minutes Questions Diections: Answe all thee questions. The suggeste time is about 5 minutes fo answeing each of the questions, which ae woth 5 points each. The pats within a question may not have equal weight. Show all you wok in the pink booklet in the spaces povie afte each pat, NOT in this geen inset. Mech.. A block of mass m is pulle along a ough hoizontal suface by a constant applie foce of magnitue F that acts at an angle q to the hoizontal, as inicate above. The acceleation of the block is a. Epess all algebaic answes in tems of m, F, q, a, an funamental constants. (a) On the figue below, aw an label a fee-boy iagam showing all the foces on the block. (b) Deive an epession fo the nomal foce eete by the suface on the block. (c) Deive an epession fo the coefficient of kinetic fiction m between the block an the suface. () On the aes below, sketch gaphs of the spee u an isplacement of the block as functions of time t if the block state fom est at an t. (e) If the applie foce is lage enough, the block will lose contact with the suface. Deive an epession fo the magnitue of the geatest acceleation a ma that the block can have an still maintain contact with the goun. 7 The College Boa. All ights eseve. Visit apcental.collegeboa.com (fo AP pofessionals) an (fo stuents an paents). -5- GO ON TO THE NEXT PAGE.

6 7 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech.. In Mach 999 the Mas Global Suveyo (GS) entee its final obit about Mas, sening ata back to Eath. Assume a cicula obit with a peio of.8 minutes 7.8 s an obital spee of.4 m s. 6 The mass of the GS is 9 kg an the aius of Mas is.4 m. (a) Calculate the aius of the GS obit. (b) Calculate the mass of Mas. (c) Calculate the total mechanical enegy of the GS in this obit. () If the GS was to be place in a lowe cicula obit (close to the suface of Mas), woul the new obital peio of the GS be geate than o less than the given peio? Geate than Less than Justify you answe. (e) In fact, the obit the GS entee was slightly elliptical with its closest appoach to Mas at above the suface an its futhest istance at closest appoach is.4 m s, calculate the spee at the futhest point of the obit. 5.7 m m above the suface. If the spee of the GS at 7 The College Boa. All ights eseve. Visit apcental.collegeboa.com (fo AP pofessionals) an (fo stuents an paents). -6- GO ON TO THE NEXT PAGE.

7 7 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech.. The appaatus above is use to stuy consevation of mechanical enegy. A sping of foce constant 4 N/m is hel hoizontal ove a hoizontal ai tack, with one en attache to the ai tack. A light sting is attache to the othe en of the sping an connects it to a glie of mass m. The glie is pulle to stetch the sping an amount fom equilibium an then elease. Befoe eaching the photogate, the glie attains its maimum spee an the sting becomes slack. The photogate measues the time t that it takes the small block on top of the glie to pass though. Infomation about the istance an the spee u of the glie as it passes though the photogate ae given below. Tial # Etension of the Sping (m) Spee of Glie u (m/s) Etension Squae ( m ) Spee Squae u ( m s ) (a) Assuming no enegy is lost, wite the equation fo consevation of mechanical enegy that woul apply to this situation. (b) On the gi below, plot u vesus. Label the aes, incluing units an scale. 7 The College Boa. All ights eseve. Visit apcental.collegeboa.com (fo AP pofessionals) an (fo stuents an paents). -7- GO ON TO THE NEXT PAGE.

8 7 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS (c) i. Daw a best-fit staight line though the ata. ii. Use the best-fit line to obtain the mass m of the glie. () The tack is now tilte at an angle q as shown below. When the sping is unstetche, the cente of the glie is a height h above the photogate. The epeiment is epeate with a vaiety of values of. i. Assuming no enegy is lost, wite the new equation fo consevation of mechanical enegy that woul apply to this situation. ii. Will the gaph of u vesus fo this new epeiment be a staight line? Yes No Justify you answe. END OF EXAM 7 The College Boa. All ights eseve. Visit apcental.collegeboa.com (fo AP pofessionals) an (fo stuents an paents). -8-