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1 Andrzej Czajkowsk PHY/ exam Page out o Prncples o Physcs I PHY PHY Instructor: Dr. Andrzej Czajkowsk Fnal Exam December Closed book exam pages questons o equal value 5 correct answers pass the test! Duraton: hrs REURN ONLY HE SCANRON SHEE!

2 Andrzej Czajkowsk PHY/ exam Page out o kg mass hangs an the strng. Strng makes angle π/4 wth the celng. he tenson n the strng s: A N B 9.4N C N 4.7N E none o the above he poston o a partcle o mass kg s gven by r t 4t j + k (t s n seconds and r n meters). he magntude o the nstantaneous acceleraton at t s s: A 8m/s B 5m/s C a 8 j D -8 m/s E none o the above A partcle o mass M, s at the orgn whle the partcle o the mass 4M s at xm. he centre o mass o ths system s at: A x.m B x.m C x.4 m D.8 m E none o the above. kg π/4 4. A cart o mass M movng at speed v colldes wth another statonary cart o mass M on ar track (no rcton), and the two stck together ater the collson. What s ther velocty ater colldng? A.5 v B.5v C -.5v D -v E none o the above 5. A constant orce o N n the postve x drecton acts on a 4.-kg object as t moves rom the orgn to the pont (6 8j) m. How much work s done by the gven orce durng ths dsplacement? A) +6 J B) +84 J C) +48 J D) +57 J E) +7 J 6 An object moves rom x m to x 7 m subject to the orce shown n the dagram. How much work n J s done on the object by the orce when the object moves rom x4m to x5m? A. 4 B. C. D. - E. -4 F ( x) (N) x (m) 7. he work done n the expanson rom an ntal to a nal state A. depends only on the end pont. B. s ndependent o the path. C. s the slope o a P curve. D equals P( F ) E. s the area under the curve o a P dagram.

3 Andrzej Czajkowsk PHY/ exam Page out o 8. In order or two objects to have the same temperature, they must a. be n thermal equlbrum. b. be n thermal contact wth each other. c. have the same relatve hotness or coldness when touched. d. have all o the propertes lsted above. e. have only propertes (b) and (c) above. 9. A gasolne engne absorbs 5 J o heat and perorms J o mechancal work n each cycle. he ecency o the engne s a.8% b.6% c.5% d.4% e.%. A Carnot cycle, operatng as a heat engne, conssts, n the order gven, o a. an sothermal expanson, an sothermal compresson, an adabatc expanson and an adabatc compresson. b. an adabatc expanson, an adabatc compresson, an sothermal expanson and an sothermal compresson. c. an sothermal expanson, an adabatc compresson, an sothermal compresson and an adabatc expanson. d. an adabatc compresson, an sothermal compresson, an sothermal expanson and an adabatc expanson. e. an sothermal expanson, an adabatc expanson, an sothermal compresson and an adabatc compresson When the partcle s at x m t has J o knetc energy, and moves under nluence o conservatve orce whose potental energy s shown n the dagram. What s ts knetc energy, and what s the drecton o the orce actng on the partcle at xm? U(J) 6 4 A) KJ, F s negatve B) KJ, F s postve C) K J, F s negatve D) K 4J, F s postve E) none o the above x(m). A bullet s red through a board, 4. cm thck, wth ts lne o moton perpendcular to the ace o the board. I t enters wth a speed o 45 m/s and emerges wth a speed o m/s, what s the bullet s acceleraton as t passes through the board? A) 5 km/s B) 55 km/s C) 6 km/s D) 5 km/s E) 75 km/s

4 Andrzej Czajkowsk PHY/ exam Page 4 out o. he horzontal surace on whch the objects slde s rctonless. I M. kg, the tenson n strng s N. Determne F n N. M M M F a. 5 b. c. d. 5 e A sh weghs. N at rest. When t s weghed on a sprng scale n an elevator acceleratng upwards at 6. m s, the scale reads N. a. 7.5 b..7 c..7 d..7 e he specc heat at constant volume at C o one mole o an deal datomc gas s 5 a. R. b.r. c. R. d.r. e. R. 6 Some speces o whales can dve to depths o klometer. What s the total pressure they experence at ths depth? (ρ sea kg/m and 5 N/m AM.) A) 9 AM B) 9 AM C) AM D) AM E) AM 7. A hole s punched n a ull mlk carton, cm below the top. What s the ntal velocty o outlow? A.4 m/s B. m/s C.8 m/s D.9 m/s E.8 m/s 8 A heat pump wth a coecent o perormance o 4.9 absorbs heat rom the atmosphere at a rate o kw. At what rate s t dong work? A 6 kw B 47 kw C 7 kw D 6 kw E none o the above 9 Fve moles o an deal gas expands sothermally at C to ve tmes ts ntal volume. Fnd the heat low nto the system. A).5 4 J B). 4 J C) 6.7 J D).9 J E) 7. J. I M. kg, what s the tenson n N n strng? a.. b. c. 4 d..5 e. 4 In an adabatc process 6 J o work are done on each mole o a gas. I the gas has 5 degrees o reedom, how much does ts temperature change? Answer n terms o R. A) 4/R (K) B).4/R (K) C) 6.4/R (K) D)./R(K) E) none o the above M

5 he dstrbuton o car speeds measured by a Polce patrol or a partcular stretch o the 4 hghway between Kngston and Ottawa s shown on the gure. Whch o the ollowng conclusons about the v rms [root mean square speed], and the P (85;5) [probablty that the car has speed between 85km/h and 5 km/h] are true: A v rms 7km/h P(85,5).6 B v rms km/h P(85,5).6 C v rms 5km/h P(85,5).84 D v rms 7km/h P(85,5).66 E none o the above Andrzej Czajkowsk PHY/ exam Page 5 out o number o cars speed Speed km/h). A.8 kg stone you throw rses 4. m n the ar. he mpulse your hand receves rom the stone whle t throws the stone s A. 7. N s, up. B. 7. N s, down. C. 7. N s, up. D. 7. N s, down. E N s, up. 4. he gure shows the dstrbuton o the molecular speeds o gas or two derent temperatures (sold) and (dashed). Whch o the ollowng sentences s true: (v) a) <, and the pont labeled corresponds to the average speed o molecules whose temperature s b) > and the pont labeled corresponds to the average speed o molecules whose temperature s c) > and the pont labeled corresponds to the most probable speed o molecules at v d) <, and the pont labeled corresponds to the average speed o molecules at e) <, and the pont labeled corresponds to the most probable speed o molecules at 5. A.6 kg mass s swung n a vertcal crcle. It s astened to a strng.5 m long. What s the tenson n the strng n N at the bottom o the crcle when the speed o the mass at that pont s 5.5 m/s? A. 5 B. 4 C. 49 D. 58 E. 6

6 Andrzej Czajkowsk PHY/ exam Page 6 out o 6 Four objects o the same volume are placed careully n the contaner lled wth water (shown on the gure). None o the object s movng wth respect to the water. Whch o the ollowng statements about the masses o these objects s true: A) m() m() < m() < m(4) B) m() m() < m() < m(4) C) m() < m() m() < m(4) D) m() < m() m() m(4) E) m() < m() m() m(4) 4 7 A -kg block on a horzontal rctonless surace s attached a lght sprng (orce constant.8 kn/m). he block s ntally at rest at ts equlbrum poston when a orce (magntude P 8 N) actng parallel to the surace s appled to the block, as shown. What s the speed o the block when t s cm rom ts equlbrum poston? A B C D E.78 m/s.8 m/s.7 m/s.58 m/s.64 m/s P 8. An 8,-kg alumnum lagpole -m long s heated by the sun rom a temperature o C to C. Fnd the work done (n J) by the alumnum the lnear expanson coecent s 4 6 ( C). (he densty o alumnum s.7 kg/m and atm. 5 N/m.) A. 87 B. 45 C. D. 7 E.66 9 grams o molten lead (6 C) s used to make musket balls. I the lead shot s allowed to cool to room temperature ( C), what s the change n entropy (n J/K) o the lead? (For the specc heat o molten and sold lead use.9 J/g C; the latent heat o uson and the meltng pont o lead are.45 4 J/kg and 7 C.) a. 4 b. 5 c. d. 49 e.

7 Andrzej Czajkowsk PHY/ exam Page 7 out o A 5 g lead bullet at C moves at 75 m/s and strkes a block o ce at C. What quantty o ce n kg s melted all o the knetc energy o the bullet s converted to heat? he block o ce does not move. (he latent heat o uson o ce s 8 kcal/kg and the specc heat o lead s.5 kcal kg C. cal 486. J) A 4. E 5. 8 B C D 5. 5 A potter's wheel (a sold, unorm dsk) o mass 6. kg and radus.65 m spns about ts central axs. A. kg lump o clay s dropped onto the wheel at a dstance.4 m rom the axs. It stcks to the wheel and rotates wth t Calculate the moment o nerta o the system. A. kg m B.4 kg m C. kg m D.6 kg m E none o the above A sold, unorm sphere o mass. kg and radus.7 m rolls wthout slppng down an nclned plane o heght 7. m. What s the angular velocty o the sphere at the bottom o the nclned plane? A 5.8 rad/s B 9.9 rad/s C. rad/s D 7. rad/s E none o the above. A 5-g con, s dropped rom a -m buldng. I t reaches a termnal velocty o 45 m/s, and the rest o the energy s converted to heatng the con, what s the change n temperature (n K ) o the con? (he specc heat o copper s 87 J/kg C.) What s the entropy change assocated wth ths heatng ( con ntal emperature was K)? A 9K; S.6J/K B K; S.J/K C 5K; S.J/K D K; S.9J/K E none o the above

8 Andrzej Czajkowsk PHY/ exam Page 8 out o Mechancs dx v x v d r dv a x d v x a r r v t a t o + o + dv a t v a c r F m a F o b v µn R DρAv F ρ l g B. F k x W F. d s mv k U g mgh d p P m v F U e kx m r rcm r CM rdm M M 4 π r π A 4 r Flud Mechancs: A πr C πr v Av p po + ρgh A p o + ρ gy + ρ v const

9 Andrzej Czajkowsk PHY/ exam Page 9 out o Rotatonal moton About a Fxed Axs Angular speed ω dθ Angular acceleraton α dw Net torque τ Iα ω ω + αt Iα const. θ θ + ωt + αt ω ω + α ( θ θ ) Work W θ θ τ dθ Rotatonal knetc energy K R Power P τ ω Angular momentum L Iω Net torque dl τ Iω Crcular Hoop I CM MR Hollow cylnder I CM M ( R + R ) where R : nner radus, R : outer radus Sold cylnder or dsc I CM MR hn Rectangle I CM M ( a + b ) Long thn rod wth rotatonal axs through center I CM ML Long thn rod wth rotatonal axs through edge Sold sphere I CM MR 5 hn sphercal shell I CM MR I CM ML

10 Integrals: v MP Andrzej Czajkowsk PHY/ exam Page out o HERMODYNAMICS Probablty o ndng the speed o a partcle n the range (v;v+dv )s: k m p ρ < v e ax x dx e ax m P( v) dv 4π π k π a dx a > 4 x v rms v k m xe ax dx a e ax dx 8 π 5 a e mv k dv x e ρ ax v avg Nm dx 4 4 x π dx x e 5 8k π m Ent Q + W pnr dq S Change Ent W Q S P const nc v -p( - ) nc p nc p ln const nc v nc v const nr ln Q nc v ( p p ) γ p const. W Q Q H L CRN Q QH C γ P γ C p Cv R C C H COP what we want what we pay or t nr ln π a nc ln nr ln L αl S βs γ P e σ A 4; σ 5.67x -8 W/(K 4 m d ) P ka dx Q mc Q Lm c(water) 486 J/(kg C); c(ce) 9 J/(kg C); c(steam) J/(kg C) L(meltng).x 5 J/kg L (vaporzaton).6x 6 J/kg

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