First Name:Key. Physics 101 Fall2006: Test1 Free Response #1 - Solution

Transcription

1 Las Name: Key Firs Name:Key Physics 101 Fall2006: Tes1 Free Response #1 - Soluion 1. (20 ps) A person is running a a maximum velociy of 10 f/s o cach a rain. When he person is a disance d from he neares enry of he rain, he rain sars from res wih a consan acceleraion of 1 f/s 2 away from he person. If he person jus caches he rain (a) plo a graph of posiion vs ime for he rain and person on a common graph. x (f) x T x P (s) (b) how long will i ake he person o cach he rain? IF he person jus caches he rain, he rain mus have he same speed as he person a ha insan in ime. From he x-versus ime graph, he slope of he rain a he ime he wo mee is he same as he slope of he line governing he person s posiion versus ime. v person = v rain (1) v 0 = a (2) = v0 a (c) wha is he disance d? For he wo objecs o mee, we mus equae he final x posiions: = 10 s (3) x fperson = x frain (4) v 0 = d a2 (5) d = 1 2 v 2 0 a = 50 f (6)

2 Las Name: Key Firs Name:Key Physics 101 Fall 2006: Tes 1 Free Response #2 - Soluion 2. (25 ps) Three idenical boxes of mass 10 kg are sacked verically inside an elevaor as shown in Fig.1 below. The elevaor is pulled up he elevaor shaf wih a consan acceleraion of 2.5 m/s 2. (a) Draw and label a free-body-diagram for each box inside he elevaor. Label he boom-mos box as B1, he middle box as B2, and he op-mos box as B3. NFloor N1,2 N2,3 10 kg B1 B2 B3 10 kg N2,1 N3,2 10 kg W W W Figure 1: Problem 1 (b) Apply Newon s 2 nd law o each box. B1 B2 B3 (c) Find he ne resulan force on each box. F y = N floor N 2,1 W = m 1 a (1) F y = N 1,2 N 3,2 W = m 2 a (2) F y = N 2,3 W = m 3 a (3) F neb1 = m 1 a = 25 N. (4) F neb2 = m 2 a = 25 N. (5) F neb3 = m 3 a = 25 N. (6) (d) If he elevaor cable breaks and i descends in free-fall, wha are now he forces acing on he individual boxes? IF he cable breaks, hen everyhing is in free fall. The only force acing on he individual boxes is he force of graviy (i.e., he weigh).

3 Ocober 3, 2006 PHYS101 Tes1 - Free Response Secion Page 3 Physics 101 Fall 2006: Tes 1 Free Response #3 - Soluion 3. (25 ps) Darh Vader of he Empire (oherwise known as he Dark Side ) is esing he personnel of a new defense saion on Earh. A es aircraf raveling horizonally a few fee above sea-level is cruising a a consan speed of 200 m/s. The aircraf passes direcly over he cannon of he new defense saion. The surprised operaor of he cannon akes 5 seconds o reac o he overfligh of he es aircraf a which poin she fires a cannonball a 30 wih respec o he horizonal. To her surprise, she his he es aircraf. Assuming ha he es aircraf coninues o fly in a sraigh line and remains a he same aliude (a) Wha was he iniial speed of he cannonball? Afer 5 s have elapsed, he es plane has moved a horizonal disance of (200 m/s) 5s = 1000 m. In order for he cannon ball o hi he es plane, we require ha x fplane = x fcball and y fplane = y fcball. We know ha he iniial y value of he plane is he same as he iniial y value of he cannon passes direcly over he cannon. x fplane = x fcball (1) x 0plane + v 0xplane = x 0cball + v 0xc (2) = 0 + (v c cos 30 ) (3) y fplane = y fcball (4) y 0plane + v 0yplane = y 0cball + v 0yc 1 2 g 2 (5) 0 = v c sin g 2 (6) = 2 vc sin 30 g (7) = vc g (8) v 2 c 3 2 g v c 200 g 1000 = 0 (9) (b) How long was he cannonball in he air? v c = m/s 273 m/s (10) = vc g s (11)

4 Las Name: Firs Name: Physics 101 Fall 2006: Tes 1 Muliple-Choice Quesions Refer o he figure below for quesions 1 and 2. A cyclis follows he rack shown below. While moving beween he saring poin and poin P, he cyclis acquires a maximum speed v which she mainains consan around he circular pah defined by poins P and Q. Q r sar 1. Which vecor bes represens he average velociy beween poins P and Q? P (a) (b) (c) (d) (e) 0 2. Which vecor bes represens he average acceleraion beween poins P and Q? (a) (b) (c) (d) (e) 0

5 Ocober 3, 2006 PHYS101 Tes1 - Muliple-Choice Secion Page 5 Refer o he figure below for quesions 3 and 4. Three rajecories labeled A, B, and C are shown below. 3. For which rajecory is he verical velociy componen a launch he greaes. a. A. b. B. c. C. d. All hree rajecories have he same iniial verical velociy componen a launch. e. More informaion is needed o answer he quesion. 4. For which rajecory is he horizonal velociy componen a launch he greaes. a. A. b. B. c. C. d. All hree rajecories have he same iniial horizonal velociy componen a launch. e. More informaion is needed o answer he quesion. 5. You are sanding on a spring scale inside of an elevaor. Of he following scenarios, he scale shows he highes reading when he elevaor: (a) moves downward wih increasing speed. (b) moves downward wih decreasing speed. (c) remains saionary. (d) moves upward wih decreasing speed. (e) moves upward wih consan speed.

6 Ocober 3, 2006 PHYS101 Tes1 - Muliple-Choice Secion Page 6 6. A lamp of mass m is suspended from he ceiling by wo cords as indicaed below. Which of he following relaionships beween he y-componens of ensions T 2 and T 3(i.e., T 2y and T 3y) is correc? (a) T 2y = T 3y. (b) T 2y = 2T 3y. (c) T 2y = 3 3 T3y. (d) T 2y = 3 2 T3y. (e) T 2y = 3T 3y. T2 60 o 30 o T3 T1 7. Two objecs are raveling around differen circular orbis wih consan speed. They boh have he same acceleraion, bu objec A is raveling wice as fas as objec B. The orbi radius for objec A is (a) one-fourh he orbi for objec B. (b) one-half he orbi for objec B. (c) he same as he orbi for objec B. (d) wice he orbi for objec B. (e) four imes he orbi for objec B. 8. Idenical guns fire idenical bulles horizonally a he same speed from he same heigh above level planes, one on he Earh and one on he Moon. Which of he following saemen(s) is (are) rue? Noe: he acceleraion due o graviy on he Moon is subsanially less han ha on Earh. I. The horizonal disance raveled by he bulle is greaer on he Moon. II. The fligh ime is less for he bulle on he Earh. III. The fligh ime is less for he bulle on he Moon. IV. The speed of he bulles a impac are he same. (a) I only. (b) II only. (c) I and IV only. (d) I and II only. (e) I, II and III only.

7 Ocober 3, 2006 PHYS101 Tes1 - Muliple-Choice Secion Page 7 9. Consider he following five graphs (noe he axes carefully). Which of hese represen(s) one-dimensional moion a consan speed? (a) I only. x v x a x (b) I, II and III only. (c) I and II only. (d) I and IV only. (e) IV only. I. II. III. v x a x IV. V. 10. An elevaor is moving upward wih consan acceleraion. The dashed curve shows he posiion y of he ceiling of he elevaor as a funcion of ime. A he insan indicaed by he do, a bol breaks loose and drops from he ceiling. Which curve labeled A hru D bes represens he posiion of he bol as funcion of ime? Y A B E D C (a) A. (b) B. (c) C. (d) D. (e) E.

8 Las Name:Key Firs Name: Key Physics 101 Fall 2006: Tes 1 Muliple-Choice Answers A B C D E 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X