Name (print neatly): Section #: Physics 111 Exam 1. First, write your name on this sheet and on the Scantron Card.

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1 Name (prnt neatly): Secton #: Physcs 111 Exam 1 Frst, wrte your name on ths sheet and on the Scantron Card. The Physcs faculty would lke to help you do well: 1. Budget your tme: 80 mnutes/14 questons=4.4 mn each.. Questons vary n dffculty. Look for ones you can do frst. 3. If you get stuck on a queston, move on. 4. All answers are n standard unts of m, s, kg and J. 5. If you show your work on the exam sheet, you wll do better and the work wll mprove your ablty to study the exam afterward. 6. If any queston s unclear, ask a tutor to clarfy t mmedately. 7. Use a calculator. 8. Answers are approxmate. Select the closest one. Snce the NJIT Student Councl asks for scrupulous farness n exams, we remnd you that you have pledged to comply wth the provsons of the NJIT Academc Honor Code. The tutors wll help by allowng no devces wth nternet access. Sgnature: 1

2 1. A student s drvng a car at 60.0 mles/hr. What s ts speed n m/s? There are 3.8 feet n a meter and 580 feet n a mle. a..4 b. 7 c. 134 d. 45 e. 3. How many mllon gallons of blood does a human heart pump n an average lfetme? The average number of beats n a lfetme s about 3000 mllon and the volume pumped wth each beat s about 50 cm 3. A gallon s 3800 cm 3. a. 39 b. 8,000 c. 150,000 d e Car A starts 10 meters ahead of car B. Car A moves at v A =( j) m/s and Car B moves forward at v B =( j) m/s. How many seconds does t take car B to catch up? a..5 b. 3.3 c. 1.4 d. 10 e. 7

3 4. An arplane accelerates wth ( j) m/s from an ntal velocty ( j) m/s for a dstance of ( j)km. What s the fnal velocty n m/s? a. ( j) b. ( j) c. ( j ) d. ( j) e. ( j) 5. A car drves carryng a flag of wdth w=0.5m. When the flag goes through a photogate, t blocks and unblocks a lght. If the average speed of the car s 0m/s, what s the photogate tme nterval n seconds? a. 40 b. 4 c. 0.5 d e A jet test plot can accelerate at 5g (5x9.8 m/s ). At that acceleraton she wll black out n 5 s. She plans to start from rest and to speed up to Mach 3 (3x331m/s). How long (n s) would ths part of her planned flght take, f she can do t? a. 0 b. 15 c. 00 d. 4 e. 1 3

4 7. A mltary jet frst fles n one drecton, turns sharply and then fles n another, as descrbed by the vectors: A=+4j; B=5-3j. Take the x-axs as east and fnd the angle n degrees of the sum of these motons relatve to east. a. 4 b. 8 c. 10 d. 8 e A car slows down because of traffc and has an acceleraton of -1.0 m/s. After movng for 6.0 m, t has a velocty of 4.0 m/s. What was ts ntal velocty? a. b. 16 c. 5.3 d. 15 e A car drves off a clff next to a rver at a speed of 30 m/s and lands on the bank on the other sde. The road above the clff s horzontal and 8.3 m above the other shore where the car lands. The tres on the car all ht at once and the ar resstance s nsgnfcant. How long s the car n the ar? a. 1.3 b. 0.9 c d e.. 4

5 10. The launch angle of a projectle s 30 degrees and ts velocty n the x drecton s 1.7 m/s after s. Neglectng frcton, what s the ntal magntude of the projectle s velocty along ts frng drecton? a. 0 b. 1.7 c. 0.6 d. e A rocket-launchng vehcle s movng forward at a constant velocty of 5 m/s. A cannon on the vehcle shoots a shell straght up wth a velocty of 0 m/s. The shell moves wthout frcton, (no ar resstance). How hgh does the shell go, n m? a. 1 b. 10 c. 40 d..0 e A second launchng vehcle s movng forward at 5m/s and ts cannon shoots a shell straght up. The shell moves through the ar wthout frcton for s. How far, n m, n front of the cannon does the shell land? a. 10. b. 40. c d. 0 e. 0. 5

6 13. A quarterback throws a football at a speed of 3.1 m/s at an angle 41. degrees. What horzontal dstance n m can he throw t down feld s f wnd and ar resstance are nsgnfcant? a. 5 b. 104 c d. 4. e A plane n level flght at 98 m/s at an alttude of 935 m drops a package. Fnd the speed n m/s wth whch the package lands. a. 940 b. 167 c. 336 d. 98 e A bean flls a volume of 3.0 mm 3. To compare the sze of a bean wth a large contaner, what s the volume of the bean n unts of m 3? a m 3 b m 3 c. 3 x 10-6 m 3 d. 3 x 10-9 m 3 e. 3 x 10 9 m 3 6

7 16. A speedng car movng at constant speed of 60 m/s passes a polceman who mmedately starts hs motorcycle (from rest) and accelerates at m/s. How long, n seconds, wll t take the polceman to catch up wth the car? a. 0 b. 30 c. 60 d. 80 e Another car movng at a constant speed of 60m/s passes a polceman who starts hs motorcycle (from rest) n 10 seconds and then accelerates at m/s. How far, n meters, from the orgnal pont wll t catch up wth the car? a b. 700 c d e A drone s n level flght at a speed of 01 m/s and an alttude of 80 m. At what horzontal dstance, n m, from the target should the remote plot drop an ad package so t lands on target? a. 57 b. 375 c. 890 d e

8 Constants: 1 nch =.54 cm; 1 m =1.61 km; 1 cm=10 - m; 1 mm= 10-3 m; 1 gram=10-3 kg; g = 9.8 m/s 11 ; G = N m /kg 4 6 ; M Earth = kg ; R Earth = m 1D and D moton: x=x+vt (constant v); 1 1 x = x + vt + at ; v = v + at ; v = v + ax ( x) ; r = r + vt + at ; v = v + at Crcular moton: T = π R/ v ; T = π / ω ; a c = v / R Force: F = ma ; F1 = F1 ; Frcton: ff ss μμ ss NN ; ff kk = μμ kk NN Energes: KK = 1 mmvv ; UU gg = mmmmmm ; UU ss = 1 kkxx ; WW = FF ddrr = FF rr Etotal = K + Ug + US ; Emech = K+ Ug + Us = fd P = dw / dt = F v s K = W ; ; Momentum and Impulse: p = mv ; I = Fdt = p Center of mass: r mr / m ; v mv / m = cm = cm Collsons: p = const and E const (nelastc) or p = const and E= const (elastc) Rotatonal moton: ω = π /T ; ω = dθ / dt ; α = dω/ dt ; vt = rω ; at = rα ac = ar = vt / r = ω r ; atot = ar + a ; t vcm = rω (rollng, no slppng) ; acm = rα ω = ωo + αt ; θ = θ + ω t+ α f o t / ; ωf = ω + αθ ( f θ) = MR ; I MR I = MR /5; I pont hoop = ; I = MR /; dsk sphere I shell = MR /3; I rod ( center ) = ML / 1 Irod ( end ) = ML /3 ; I = mr ; I = Icm + Mh ; τ = r F ; τ = Iα ; L = r p ; L = Iω Energy: K rot = Iω / ; K = Krot + Kcm ; K + U = 0 ; W = τ θ ; Pnst = τω Flud: ρρ = MM ; PP = PP VV oo + ρρρρh ; AA 1 vv 1 = AA vv ; PP 1 + ρρρρyy ρρvv 1 = PP + ρρρρyy + 1 ρρvv ; BB = ρρ ffffffffff VV oooooooooooo gg Gm1m Gravtaton: F ˆ g = r 1 ; g() r = GM / r ; 1 r U = Gm m / r ; 4π 3 T = a GM 3 Math: 360 = π rad = 1 rev; Arc: s = rθ ; = 4 π R /3 ; = 4π R ; A = π R Vsphere Asphere b ± b 4ac quadratc formula to solve ax + bx + c = 0 : x = a Vectors: A= Aˆ ˆ x + Ay j ; Ax = A cos( θ ) ; Ay = A A y sn( θ ) ; A = Ax + Ay ; tanθ = Ax C = A+ B => Cx = Ax + Bx ; Cy = Ay + B ; y AA BB = AA BB cos θθ = AA xx BB xx + AA yy BB yy + AA zz BB zz ; ıı ıı = ȷȷ ȷȷ = kk kk = 1 ; ıı ȷȷ = ıı kk = ȷȷ kk = 0 A B= ABsnθ ; A B= ˆ( AB ) ˆ( ) ˆ y z AB z y + j AB z x AB x z + k( AB x y AB y x) ˆ ˆ= ˆj ˆj = kˆ kˆ= 0 ˆ ˆ ˆ ; j = k ˆ ˆ ˆ ; j k = ˆ ˆ ˆ ; k = j crcle 8

9 Name (prnt neatly): Secton #: Physcs 111 Exam Frst, wrte your name on ths sheet and on the Scantron Card. The Physcs faculty would lke to help you do well: 1. Budget your tme: 80 mnutes/0 questons=4 mn each.. Questons vary n dffculty. Look for ones you can do frst. 3. If you get stuck on a queston, move on. 4. All answers are n standard unts of m, s, kg and J. 5. If you show your work on the exam sheet you wll do better and the work wll mprove your ablty to study the exam afterward. 6. If any queston s unclear, ask a tutor to clarfy t mmedately. 7. Use a calculator. 8. Answers are approxmate. Select the closest one. Snce the NJIT Student Councl asks for scrupulous farness n exams, we remnd you that you have pledged to comply wth the provsons of the NJIT Academc Honor Code. The tutors wll help by allowng no devces wth nternet access. Sgnature: 1

10 1. Two blocks are on a horzontal, frctonless table. A force of.0 N pulls a block that has m=3.0 kg. The block s connected to a second block, M=4.0 kg, by a wre. What s the tenson, n N, n the wre? a. 1.1 b c. 0.9 d..0 e A beam s tlted up by 0.0 m at one end, and t s 1m long. Frcton s nsgnfcant. Mass of the glder s 1 kg. What s the magntude of the component of net force, n N, actng on the glder along the beam. a. 100 b. c. 5 d. 0.0 e An elevator of mass 1000 kg pulls down on one sde of a cable that goes over a pulley that has no frcton. A counter weght of 900 kg pulls on the other sde. The elevator starts to fall wth no frcton. What s the net force on the system, n N? Take the elevator s drecton of moton as postve. a. 50 b. 980 c. 100 d. 460 e. 0

11 4. On a Force table, forces are appled to a small rng near the center. If the forces are F1= j and F= j, what s the magntude, n N, of a thrd force whch wll keep the rng n equlbrum wthout touchng the pn at the center? a. 1. b. 1.6 c. 1.4 d. 0.9 e A crate of weght 100-N s sttng on a ramp wth a 30 degree slope, as shown. The playful man lets go and the crate sldes down wth no frcton and an acceleraton a1. He then places another crate of half the weght on the ramp. Agan, he lets go and the second crate sldes down wth acceleraton a. What are values of a1 and a n m/s? a. 9.8, 4.9 b. 4.9,.5 c. 9.8, 9.8 d. 4.9, 9.8 e. 4.9, The man lets go of the rope attached to the 100-N crate. It starts from rest and sldes down the 30-degree slope wth no frcton. The crate s velocty ncreases to 9.8 m/s at a tme t. What s t n s? a. 9.8 b c. 0.3 d..0 e

12 7. Two masses M 1 = kg and M = 4 kg are attached by a strng as shown. They start from rest and move wth no frcton untl they reach a velocty of 6.5 m/s. When do they reach that speed, n s? a b. 4.3 c..0 d. 1.4 e A lght fxture of mass 3.55 kg hangs by two wres (arranged lke a Y ), each of whch makes an angle of 10 degrees wth the celng. What s the tenson, n N, n one of the wres? a. 00 b. 100 c. 5 d. 0 e A lght fxture s suspended from a wall and a celng by wres, as shown. The tenson, T1 n wre 1 s 3.5 N. What s the mass, M, n kg? a. 3.4; b..0 c. 1.7 d e

13 10. A block sts on a horzontal surface wth a coeffcent of statc frcton of 0. between them. A horzontal force of 14 N s just able to move the block parallel to the surface. What s the mass, n kg, of the block? a. 7.1 b. 14 c. 70 d. 1.4 e Two masses are attached by a strng as shown. The mass, M, s 4 kg and the coeffcent of frcton s 0.5. What s the maxmum mass M 1, n kg, that allows the system to stay at rest? a. 0.3 b. c. 4 d. 0.5 e The block s at rest. Then, the ramp s gradually tlted. At at an angle of 14 degrees, the block begns to slde. What s the coeffcent of statc frcton between the block of unknown mass, m, and the ramp? a. Can t tell; need m b c d e

14 13. A woman pulls a block along a horzontal surface at a constant speed wth a 15-N force actng 0 above the horzontal. She does 85 J of work. How many meters does the block move? a. 5.6 b. 90 c. 6.0 d e A person does 00 J work lftng an object from the bottom of a well at a constant speed of.0 m/s n a tme of 5.1 s. What s the object s mass? (Neglect frcton.) a. 0 b..0 c. 6. d..1 e A woman throws a.0-kg ball from the orgn to a pont at (0 + 3 j + h k) meters, where k s the upward unt vector. The work done by the gravtatonal force on the ball s -90J. What s the heght, h? a. 19 b. 15 c. 39 d. 7 e

15 16. Suddenly, the drver of a fast car travellng 50 m/s sees a deer and slams on the brakes. The car travels for 10 s before t stops. What s the coeffcent of knetc frcton between the tres and the road? a b. 0.6 c. 0.3 d e An object falls vertcally downward n water at a constant speed. The vscosty of the water does work of -0 J as the object falls 0.80 m. What s the mass, n kg, of the object? a..0 b. 0 c. 3.7 d..6 e A constant force of ( -15 j + k) N acts on a partcle as t moves from the orgn to a pont (4 + 3 j + 5 k) m. How much work, n J, does the force do durng ths dsplacement? a. +30 b. 7 c. +45 d. 45 e

16 19. A CONSTANT force acts on an object and ncreases ts knetc energy, by 4 J. The object moves from (7-8 j +4 k)m to ( 11 5 j + 4 k) m. The net force actng on the object s equal to (Fx + 4 j + 5 k) N. What s Fx, n N. a. 1 b. -4 c. 4 d. 3 e As shown n the fgure, a block s pushed up aganst a vertcal wall by a force 0 N. The force s at an angle of 40 degrees from horzontal. The coeffcent of statc frcton between the block and the wall s Fnd the maxmum mass, n kg, that the force can prevent from sldng down. a. Infnte b. 0.9 c..1 d. 0.5 e. 10 8

17 Constants: 1 nch =.54 cm; 1 m =1.61 km; 1 cm=10 - m; 1 mm= 10-3 m; 1 gram=10-3 kg; g = 9.8 m/s 11 ; G = N m /kg 4 6 ; M Earth = kg ; R Earth = m 1D and D moton: x=x+vt (constant v); 1 1 x = x + vt + at ; v = v + at ; v = v + ax ( x) ; r = r + vt + at ; v = v + at Crcular moton: T = π R/ v ; T = π / ω ; a c = v / R Force: F = ma ; F1 = F1 ; Frcton: ff ss μμ ss NN ; ff kk = μμ kk NN Energes: KK = 1 mmvv ; UU gg = mmmmmm ; UU ss = 1 kkxx ; WW = FF ddrr = FF rr Etotal = K + Ug + US ; Emech = K+ Ug + Us = fd P = dw / dt = F v s K = W ; ; Momentum and Impulse: p = mv ; I = Fdt = p Center of mass: r mr / m ; v mv / m = cm = cm Collsons: p = const and E const (nelastc) or p = const and E= const (elastc) Rotatonal moton: ω = π /T ; ω = dθ / dt ; α = dω/ dt ; vt = rω ; at = rα ac = ar = vt / r = ω r ; atot = ar + a ; t vcm = rω (rollng, no slppng) ; acm = rα ω = ωo + αt ; θ = θ + ω t+ α f o t / ; ωf = ω + αθ ( f θ) = MR ; I MR I = MR /5; I pont hoop = ; I = MR /; dsk sphere I shell = MR /3; I rod ( center ) = ML / 1 Irod ( end ) = ML /3 ; I = mr ; I = Icm + Mh ; τ = r F ; τ = Iα ; L = r p ; L = Iω Energy: K rot = Iω / ; K = Krot + Kcm ; K + U = 0 ; W = τ θ ; Pnst = τω Flud: ρρ = MM ; PP = PP VV oo + ρρρρh ; AA 1 vv 1 = AA vv ; PP 1 + ρρρρyy ρρvv 1 = PP + ρρρρyy + 1 ρρvv ; BB = ρρ ffffffffff VV oooooooooooo gg Gm1m Gravtaton: F ˆ g = r 1 ; g() r = GM / r ; 1 r U = Gm m / r ; 4π 3 T = a GM 3 Math: 360 = π rad = 1 rev; Arc: s = rθ ; = 4 π R /3 ; = 4π R ; A = π R Vsphere Asphere b ± b 4ac quadratc formula to solve ax + bx + c = 0 : x = a Vectors: A= Aˆ ˆ x + Ay j ; Ax = A cos( θ ) ; Ay = A A y sn( θ ) ; A = Ax + Ay ; tanθ = Ax C = A+ B => Cx = Ax + Bx ; Cy = Ay + B ; y AA BB = AA BB cos θθ = AA xx BB xx + AA yy BB yy + AA zz BB zz ; ıı ıı = ȷȷ ȷȷ = kk kk = 1 ; ıı ȷȷ = ıı kk = ȷȷ kk = 0 A B= ABsnθ ; A B= ˆ( AB ) ˆ( ) ˆ y z AB z y + j AB z x AB x z + k( AB x y AB y x) ˆ ˆ= ˆj ˆj = kˆ kˆ= 0 ˆ ˆ ˆ ; j = k ˆ ˆ ˆ ; j k = ˆ ˆ ˆ ; k = j crcle 9

18 Name (prnt neatly): Secton #: Physcs 111 Exam 3 Frst, wrte your name on ths sheet and on the Scantron Card. The Physcs faculty would lke to help you do well: 1. Budget your tme: 80 mnutes/0 questons=4 mn each.. Questons vary n dffculty. Look for ones you can do frst. 3. If you get stuck on a queston, move on. 4. All answers are n standard unts of m, s, kg and J. 5. If you show your work on the exam sheet you wll do better and the work wll mprove your ablty to understand the exam afterward. 6. If any queston s unclear, ask a tutor to clarfy t mmedately. 7. Use a calculator. 8. Answers are approxmate; select the closest one. Snce the NJIT Student Councl asks for scrupulous farness n exams, we remnd you that you have pledged to comply wth the provsons of the NJIT Academc Honor Code. The tutors wll help by allowng no devces wth nternet access. Sgnature:

19 1. Glder A of mass.5 kg moves wth speed 1.7 m/s on a horzontal ral wthout frcton. It colldes elastcally wth glder B of dentcal mass.5 kg, whch s ntally at rest. After the collson, what s the value of the speed of glder A, n m/s? a. 1.7 b. 5 c. 1.3 d. 0 e A glder of mass 5.0 kg hts the end of a horzontal ral and bounces off wth the same speed, n the opposte drecton. The collson s elastc and takes place n a tme nterval of 0.s, wth an average force of 100N. What was the speed, n m/s, of the glder? a. 0.1 b. 1 c. d. 4 e. 10 a. 150 b. 60 c. 90 d. 10 e A man fell out of an arplane and barely survved. He was movng at a speed of 100m/s just before landng n deep snow on a mountan sde. Experts estmated that the average net force on hm was 600 N as he plowed through the snow for 10 s. What was hs mass, n kg?

20 4. A sker starts from rest and sldes down from a hgh hll and then, wthout losng energy, up a smaller hll. Hs speed s 10m/s at the top of the smaller hll. Ignore frcton. What was the dfference n heght of the two hlls, n m? a) Impossble to tell wthout knowng the mass of the sker and/or the shape of the slope b).5 c) 0.51 d) 5.1 e) A block sldes wth no frcton and hts a sprng wth sprng constant k=000 N/m. The block compresses the sprng n a straght lne for a dstance 0.15m. The block s knetc energy, n J, at that pont s 0 J. What was ts ntal knetc energy, n Joules? a. b. 19 c. 45 d. 9 e An elevator and counterweght are lke Atwood s machne. An elevator, M=100kg, has a counter weght m=90kg connected by a cable over a massless pulley wth no frcton. The elevator falls, startng from rest, a dstance 0.5 m and lands. What the fnal knetc energy of the system, n J, just before the elevator lands? a. 0,000 b. 18,000 c. 000 d e. 00

21 7. A mass s revolvng n a horzontal crcle. The crcle has radus of m. The mass has a lnear speed of 0.63 m/s. What s the perod, n seconds? a. 0.5 b. 0.3 c. 0. d e A small ball s attached to one end of a rgd rod wth neglgble mass. The ball and the rod revolve n a horzontal crcle wth the other end of the rod at the center. The path of the ball has a constant lnear speed. The force exerted by the rod s 0.5 N. The centrpetal acceleraton s 0.5 m/s. What s the mass of the ball, n kg? a. Unknown: Need R b..5 c. 10 d e A ball s revolvng horzontally n a crcle and s held by a rgd, massless rod. The mass of the ball s 0.1 kg. The path of the ball has an angular velocty of 15 rad/s and a constant lnear speed of 7 m/s. What s the radus of the orbt n m? a. 1.8 b..3 c. 0.6 d. 5.4 e. 0.1

22 10. A car goes around a curve and then around another curve. The parameters are the followng: 1st, force F1 wth radus R and speed v. nd, force F wth radus 6R and speed 3v. What s the rato of the centrpetal forces, F1/F? a b. 1.3 c. 1 d. e A person s on a crcular carnval rde ( Ferrs Wheel ) that goes up and down wth an axs of rotaton parallel to the ground. It makes her feel twce her normal weght at the bottom and weghtless at the top. Her centrpetal acceleraton s constant. What s ts value, n m/s? a. 0 b..4 c. 4.9 d e A toy tran of m=0.60 kg moves at 0m/s along a straght track. It bumps nto another tran of M=1.5kg movng n the same drecton. They stck together and contnue on the track at a speed 1 m/s. What was the speed n m/s of the second tran just before the collson? a. 1 b. 1.1 c. 8.8 d. 4 e. 9.

23 13. A small ball s rotatng n a crcular horzontal path. The ball s held by a rgd, massless rod. Its angular rate of rotaton s 4.00 rad/s. The knetc energy of the ball s 19. J. What s the moment of nerta of the ball wth respect to the axs of rotaton, n kg m? a. 1. b..4 c. 4.9 d. 9.7 e A small ball s rotatng n a horzontal crcular path on a massless, rgd wre around a vertcal post. The radus of the ball s orbt s 1. m. The moment of nerta of the center of mass of the ball about the axs of rotaton s 8.6 kg m. What s the ball s mass, n kg? a. 7. b. 6.0 c. 3.1 d. 4. e Three partcles wth M1= kg, M=3 kg and M3=5 kg are located, respectvely, at r1=+j (n meters), r=+3j and r3=-j. Fnd the locaton of the center of mass. In m. a. 0.5 j b j c j d j e j

24 a b. 9.8 c..1 d e A mass of M=1.0 kg pulls down vertcally on a strng that unwnds around a sold cylndrcal rod attached to a dsk, wth a combned moment of nerta I=10 kg-m. The rod has a radus of r=0.1 m, the dsk has or radus R=1m and the system s ntally at rest. What s the angular acceleraton (n radans/s ) of the dsk. 17. A dsk wth mass M and radus R rolls down a 10 m long nclne startng from rest. The nclne makes 30 degrees wth horzontal. Fnd ts speed n m/s at the bottom of the nclne. a. Need to know M and R b. c. 4 d. 6 e. 8

25 18. A dsk (lke a yoyo) starts from rest and falls down from the poston shown n the fgure, unwndng a lght cord. The mass of the dsk s M=6.7 kg, ts radus s R=0.10 m. What s the ntal angular acceleraton, α, of the dsk, n rad/s? a. 100 b. 65 c. 00 d. 9.8 e To determne how well a bcycle wheel s lubrcated, the mechanc n the repar shop gves t a spn, measurng the tme t before t stops and countng the number of revolutons N. If t=1 mn and N=100 revolutons, what s the magntude of angular deceleraton n rad/s? a. 8.5 b c..3 d e. 3.

26 0. An Atwood machne, smlar to an elevator, wth a counter-weght, s ntally at rest. On one sde s a mass of.00 kg and on the other sde s a mass of 1.00 kg. A massless cord that passes over a pulley connects the two weghts. The pulley has a mass of 4.00 kg, a radus of 0.0 cm and no frcton, and can be treated as a unform dsk. When the heaver mass has fallen for 50.0 cm, what s ts lnear speed, n m/s? a. 14 b. 4 c. 3.4 d. 1.8 e. 1.4

27 Constants: 1 nch =.54 cm; 1 m =1.61 km; 1 cm=10 - m; 1 mm= 10-3 m; 1 gram=10-3 kg; g = 9.8 m/s 11 ; G = N m /kg 4 6 ; M Earth = kg ; R Earth = m 1D and D moton: x=x+vt (constant v); 1 1 x = x + vt + at ; v = v + at ; v = v + ax ( x) ; r = r + vt + at ; v = v + at Crcular moton: T = π R/ v ; T = π / ω ; a c = v / R Force: F = ma ; F1 = F1 ; Frcton: ff ss μμ ss NN ; ff kk = μμ kk NN Energes: KK = 1 mmvv ; UU gg = mmmmmm ; UU ss = 1 kkxx ; WW = FF ddrr = FF rr Etotal = K + Ug + US ; Emech = K+ Ug + Us = fd P = dw / dt = F v s K = W ; ; Momentum and Impulse: p = mv ; I = Fdt = p Center of mass: r mr / m ; v mv / m = cm = cm Collsons: p = const and E const (nelastc) or p = const and E= const (elastc) Rotatonal moton: ω = π /T ; ω = dθ / dt ; α = dω/ dt ; vt = rω ; at = rα ac = ar = vt / r = ω r ; atot = ar + a ; t vcm = rω (rollng, no slppng) ; acm = rα ω = ωo + αt ; θ = θ + ω t+ α f o t / ; ωf = ω + αθ ( f θ) ; θθ θθ = ωω 0+ωω tt = MR ; I = MR ; I = MR /; I = MR /5; I = MR /3; I pont hoop dsk sphere I rod ( center ) = ML / 1 Irod ( end ) = ML /3 ; I = mr ; I = Icm + Mh ; τ = r F ; τ = Iα ; L = r p ; L = Iω Energy: K rot = Iω / ; K = Krot + Kcm ; K + U = 0 ; W = τ θ ; Pnst = τω Flud: ρρ = MM ; PP = PP VV oo + ρρρρh ; AA 1 vv 1 = AA vv ; PP 1 + ρρρρyy ρρ(vv 1)^ = PP + ρρρρyy + 1 ρρ(vv )^ ; BB = ρρ ffffffffff VV oooooooooooo gg Gm1m Gravtaton: F ˆ g = r 1 ; g() r = GM / r ; 1 r U = Gm m / r ; 4π 3 T = a GM 3 Math: 360 = π rad = 1 rev; Arc: s = rθ ; = 4 π R /3 ; = 4π R ; A = π R Vsphere shell Asphere b ± b 4ac quadratc formula to solve ax + bx + c = 0 : x = a Vectors: A= Aˆ ˆ x + Ay j ; Ax = A cos( θ ) ; Ay = A A y sn( θ ) ; A = Ax + Ay ; tanθ = Ax C = A+ B => Cx = Ax + Bx ; Cy = Ay + B ; y AA BB = AA BB cos θθ = AA xx BB xx + AA yy BB yy + AA zz BB zz ; ıı ıı = ȷȷ ȷȷ = kk kk = 1 ; ıı ȷȷ = ıı kk = ȷȷ kk = 0 A B= ABsnθ ; A B= ˆ( AB ) ˆ( ) ˆ y z AB z y + j AB z x AB x z + k( AB x y AB y x) ˆ ˆ= ˆj ˆj = kˆ kˆ= 0 ˆ ˆ ˆ ; j = k ˆ ˆ ˆ ; j k = ˆ ˆ ˆ ; k = j crcle