AP Physics C: Mechanics 2003 Free-Response Questions

Transcription

1 AP Physics C: Mechanics 3 Fee-Response Questions The mateials inclue in these files ae intene fo use by AP teaches fo couse an eam pepaation; pemission fo any othe use must be sought fom the Avance Placement Pogam. Teaches may epouce them, in whole o in pat, in limite quantities fo noncommecial, face-to-face teaching puposes. This pemission oes not apply to any thi-paty copyights containe heein. This mateial may not be mass istibute, electonically o othewise. These mateials an any copies mae of them may not be esol, an the copyight notices must be etaine as they appea hee. These mateials wee pouce by Eucational Testing Sevice (ETS ), which evelops an aministes the eaminations of the Avance Placement Pogam fo the College Boa. The College Boa an Eucational Testing Sevice (ETS) ae eicate to the pinciple of equal oppotunity, an thei pogams, sevices, an employment policies ae guie by that pinciple. The College Boa is a national nonpofit membeship association whose mission is to pepae, inspie, an connect stuents to college an oppotunity. Foune in 9, the association is compose of moe than 4,3 schools, colleges, univesities, an othe eucational oganizations. Each yea, the College Boa seves ove thee million stuents an thei paents,, high schools, an 3,5 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 equity an ecellence, an that commitment is emboie in all of its pogams, sevices, activities, an concens. Fo futhe infomation, visit Copyight 3 College Entance Eamination Boa. All ights eseve. College Boa, Avance Placement Pogam, AP, AP Vetical Teams, APCD, Pacesette, Pe-AP, SAT, Stuent Seach Sevice, an the acon logo ae egistee taemaks of the College Entance Eamination Boa. AP Cental is a taemak owne by the College Entance Eamination Boa. PSAT/NMSQT is a egistee taemak jointly owne by the College Entance Eamination Boa an the National Meit Scholaship Copoation. Eucational Testing Sevice an ETS ae egistee taemaks of Eucational Testing Sevice. Othe poucts an sevices may be taemaks of thei espective ownes. Fo the College Boa s online home fo AP pofessionals, visit AP Cental at apcental.collegeboa.com.

2 TABLE OF INFORMATION FOR 3 CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u = kg = 93 MeV/ c Poton mass, m p = kg Neuton mass, m n = kg Electon mass, m e = 9. 3 kg Magnitue of the electon chage, e = 6. 9 C Avogao s numbe, N = 3 6. mol Univesal gas constant, R = 83. J/ ( mol ¼ K ) Boltzmann s constant, k B = J/K Spee of light, c = 3. 8 ms / Planck s constant, h 34 = 663. Js = ev s 5 hc = 99. J m 3 = 4. ev nm Vacuum pemittivity, = 885. C / N m 9 Coulomb s law constant, k = / 4π = 9. Nm / C Vacuum pemeability, 7 µ = 4π ( Tm) / A Magnetic constant, k = µ / 4π = 7 ( T m) / A Univesal gavitational constant, G = m 3 / kg ¼s Acceleation ue to gavity at the Eath s suface, g = 98. m/s atmosphee pessue, atm 5 =. N / m 5 =. Pa electon volt, ev = 6. 9 J UNITS Name Symbol mete kilogam secon ampee kelvin mole hetz newton pascal joule watt coulomb volt ohm heny faa tesla egee Celsius electonvolt m kg s A K mol Hz N Pa J W C V Ω H F T o C ev PREFIXES Facto Pefi Symbol 9 giga G 6 mega M 3 kilo k centi c 3 milli m 6 mico µ nano n pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES θ sin θ cos θ tan θ o 3 o / 3 / 33 / 37 o 3/5 4/5 3/4 45 o / / 53 o 4/5 3/5 4/3 6 o 3 / / 3 9 o 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. IV. Fo mechanics an themoynamics equations, W epesents the wok one on a system.

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 3 MECHANICS ELECTRICITY AND MAGNETISM u = u + at a = acceleation qq A = aea F = foce F = 4p B = magnetic fiel = + ut + at f = fequency h = height u = u + a - 5 E = F C = capacitance = istance I = otational inetia q E = electic fiel Ê F = Fnet = ma J = impulse Q e = emf p K = kinetic enegy E A= F = foce F = t k = sping constant I = cuent l = length V L = inuctance J = I F t = Dp E = L = angula momentum l = length p = mv m = mass q n = numbe of loops of wie pe i Ffic ˆ mn N = nomal foce V = unit length P = powe 4p i i P = powe W = I F œ p = momentum qq Q = chage K = m = aius o istance UE = qv = u 4p q = point chage = position vecto W P = T = peio C Q R = esistance = = istance t t = time V t = time P = F v U = potential enegy k A U = potential o stoe enegy DUg = mgh u = velocity o spee C = V = electic potential W = wok one on a system υ = velocity o spee u ac = = w = position Cp = Ci = esistivity i m = coefficient of fiction f t = F q = angle m = magnetic flu = k = ielectic constant Ê t = tnet = Ia t = toque Cs i Ci w I = I m = Ê m = angula spee Q a = angula acceleation I = cm = Ê m Ê m t u = w Uc = QV = CV L = p = Iw l K = Iw R = A w = w + at V = IR q = q + wt + at R = R s i i Fs =-k = Us = k R i R p i p P= IV T = = w f FM = qv B m Ts = p B ø = m I k Tp = l F= I Iø B p g Bs = mni Gmm FG =- $ f m = I B A fm Gmm e = UG =- t e =L I t UL = LI 3

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 3 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Tiangle A = bh Cicle A = p C = p Paallelepipe V = lwh Cyline V = p l S = pl + p Sphee 4 3 V = p 3 S = 4p Right Tiangle a + b = c a sin q = c b cos q = c a tan q = b A = aea C = cicumfeence V = volume S = suface aea b = base h = height l = length w = with = aius q c b 9 a CALCULUS f = n e n 7 7 f u u = n = e n - ( ) = ( sin ) = cos ( cos ) =-sin n n + I = n + e= e I = n I cos = sin I sin =-cos, n ž- 4

5 3 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C Section II, MECHANICS Time 45 minutes 3 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.. The kg bo shown above is being pulle along the -ais by a stuent. The bo slies acoss a ough suface, 3 an its position vaies with time t accoing to the equation = 5. t + t, whee is in metes an t is in secons. (a) Detemine the spee of the bo at time t =. (b) Detemine the following as functions of time t. i. The kinetic enegy of the bo ii. The net foce acting on the bo iii. The powe being elivee to the bo (c) Calculate the net wok one on the bo in the inteval t = to t = s. () Inicate below whethe the wok one on the bo by the stuent in the inteval t = to t = s woul be geate than, less than, o equal to the answe in pat (c). Geate than Less than Equal to Justify you answe. Copyight 3 by College Entance Eamination Boa. All ights eseve. Available to AP pofessionals at apcental.collegeboa.com an to stuents an paents at 5 GO ON TO THE NEXT PAGE.

6 3 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech.. An ieal sping is hung fom the ceiling an a pan of mass M is suspene fom the en of the sping, stetching it a istance D as shown above. A piece of clay, also of mass M, is then oppe fom a height H onto the pan an sticks to it. Epess all algebaic answes in tems of the given quantities an funamental constants. (a) Detemine the spee of the clay at the instant it hits the pan. (b) Detemine the spee of the pan just afte the clay stikes it. (c) Detemine the peio of the simple hamonic motion that ensues. () Detemine the istance the sping is stetche (fom its initial unstetche length) at the moment the spee of the pan is a maimum. Justify you answe. (e) The clay is now emove fom the pan an the pan is etune to equilibium at the en of the sping. A ubbe ball, also of mass M, is oppe fom the same height H onto the pan, an afte the collision is caught in miai befoe hitting anything else. Inicate below whethe the peio of the esulting simple hamonic motion of the pan is geate than, less than, o the same as it was in pat (c). Geate than Less than The same as Justify you answe. Copyight 3 by College Entance Eamination Boa. All ights eseve. Available to AP pofessionals at apcental.collegeboa.com an to stuents an paents at 6 GO ON TO THE NEXT PAGE.

7 3 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. Some physics stuents buil a catapult, as shown above. The suppoting platfom is fie fimly to the goun. The pojectile, of mass kg, is place in cup A at one en of the otating am. A counteweight bucket B that is to be loae with vaious masses geate than kg is locate at the othe en of the am. The am is elease fom the hoizontal position, shown in Figue, an begins otating. Thee is a mechanism (not shown) that stops the am in the vetical position, allowing the pojectile to be launche with a hoizontal velocity as shown in Figue. (a) The stuents loa five iffeent masses in the counteweight bucket, elease the catapult, an measue the esulting istance tavele by the kg pojectile, ecoing the following ata. Mass (kg) (m) i. The ata ae plotte on the aes below. Sketch a best-fit cuve fo these ata points. ii. Using you best-fit cuve, etemine the istance tavele by the pojectile if 5 kg is place in the counteweight bucket. Copyight 3 by College Entance Eamination Boa. All ights eseve. Available to AP pofessionals at apcental.collegeboa.com an to stuents an paents at 7 GO ON TO THE NEXT PAGE.

8 3 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS (b) The stuents assume that the mass of the otating am, the cup, an the counteweight bucket can be neglecte. With this assumption, they evelop a theoetical moel fo as a function of the counteweight mass using the elationship = u t, whee u is the hoizontal velocity of the pojectile as it leaves the cup an t is the time afte launch. i. How many secons afte leaving the cup will the pojectile stike the goun? ii. Deive the equation that escibes the gavitational potential enegy of the system elative to the goun when in the position shown in Figue, assuming the mass in the counteweight bucket is M. iii. Deive the equation fo the velocity of the pojectile as it leaves the cup, as shown in Figue. (c) i. Complete the theoetical moel by witing the elationship fo as a function of the counteweight mass using the esults fom (b)i an (b)iii. ii. Compae the epeimental an theoetical values of fo a counteweight bucket mass of 3 kg. Offe a eason fo any iffeence. END OF SECTION II, MECHANICS Copyight 3 by College Entance Eamination Boa. All ights eseve. Available to AP pofessionals at apcental.collegeboa.com an to stuents an paents at 8