Unit 1: Introduction and Kinematics Review

Transcription

1 Phyic Unit 1: Introduction and Kinematic Review 1. Know about cientific method, unit, fundamental unit, unit prefixe, preciion, accuracy, ignificant figure, vector, calar 2. Convert 120 Tm to m 3. In the proce of delivering milk, a milkman, walk 100 m due eat from hi truck. He then turn around and walk 20 m due wet. What i the milkman diplacement relative to hi truck (magnitude and direction)? What ditance did he travel? 4. A pigeon flew 10 km acro town with an average peed of 5 m/. How long, in hour, did it take the pigeon to make thi journey? 5. A car, tarting from ret, accelerate in a traight-line path at a contant rate of 2 m/ 2. How far will the car travel in 10 econd? 6. The minimum takeoff peed for a certain airplane i 50 m/. What minimum acceleration i required if the plane mut leave a runway of length 2000 m? Aume the plane tart from ret at one end of the runway. 7. Water drip from ret from a leaf that i 2 m above the ground. Neglecting air reitance, what i the peed of each water drop when it hit the ground? 8. What maximum height will be reached by a tone thrown traight up with an initial peed of 5 m/? 9. A cheetah i walking at a peed of 0.5 m/ when it oberve a gazelle 15 m directly ahead. If the cheetah accelerate at 3 m/ 2, how long doe it take the cheetah to reach the gazelle if the gazelle doen t move? 10. Be able to read graph and calculate peed, velocity, and acceleration from them. 11. A jumper in the long-jump goe into the jump with a peed of 5 m/ at an angle of 20 above the horizontal. What i the jumper horizontal peed a they jump? What i their vertical peed? 12. A ailboat leave a harbor and ail 21 km in the direction 15 north of eat, where the captain top for lunch. A hort time later, the boat ail 2 km in the direction 75 outh of eat. What i the magnitude of the reultant diplacement? 13. An eagle i flying due eat at 5 m/ carrying a gopher in it talon. The gopher manage to break free at a height of 50 m. What i the magnitude of the gopher velocity a it reache the ground? 14. A ball i thrown horizontally from the top of a 100 m tall building with an initial peed of 5 m/. How far from the bae of the building did the ball land? 15. A wimmer wim with a velocity of 15 m/ outh relative to the water. The current of the water i 2 m/ relative to the hore. If the current i moving wet, what i the velocity of the wimmer relative to the hore?

2 3. Diplacement: 100 m 20 m = 80 m; Ditance: 100 m + 20 m = 120 m 4. v = 5 m, Δx = 10 km Convert: 10 km ( 103 m ) = m 1 km v = Δx Δt 5 m t = m = t m 5 m = 2000 Convert: 2000 ( 1 h 3600 ) = 0.56 h 5. a = 2 m 2, t = 10, v 0 = 0 m, x =? x = x 0 + v 0 t at2 x = 0 m + (0 m ) (10 ) + 1 (2 m 2 2) (10 )2 x = 100 m 6. v = 50 m, x = 2000 m, v 0 = 0 m, a =? v 2 = v a(x x 0 ) (50 m )2 = (0 m )2 + 2a(2000 m 0 m) 2500 m2 = (4000 m)a 2 a = m/ 2 7. y 0 = 2 m, v 0 = 0 m, a = 9.8 m 2, v =? v 2 = v a(y y 0 ) v 2 = (0 m )2 + 2 ( 9.8 m 2) (0 m 2 m) v 2 = 39.2 m2 2 v = m 8. v 0 = 5 m, v = 0 m, a = 9.8 m 2, y =? v 2 = v a(y y 0 ) (0 m )2 = (5 m )2 + 2 ( 9.8 m 2) (y 0 m) 25 m2 = ( 19.6 m 2 2) y y = m 9. v 0 = 0.5 m, x = 15 m, a = 3 m 2, t =? r = = 21.1 km θ = tan = 9.67 N of E x: v 0x = 5 m, y: v 0y = 0 m, y 0 = 50 m, a y = 9.8 m 2, y = 0 m, v y =? v 2 y = v 2 0y + 2a y (y y 0 ) v 2 y = (0 m )2 + 2 ( 9.8 m 2) (0 m 50 m) v y 2 = 980 m v y = m combine: v = v x 2 + v y 2 v = (5 m )2 + (31.30 m )2 = m/ 14. x: v 0x = 5 m, x =? ; y: y 0 = 100 m, y = 0 m, a = 9.8 m 2, v 0y = 0 m find t: y = y 0 + v 0y t at2 0 m = 100 m + (0 m ) t + 1 ( 9.8 m 2 2) t2 100 m = ( 4.9 m 2) t m2 = 2 t2 t = find x: x = x 0 + v 0x t x = 0 + (5 m ) (4.52 ) = m 15. v SW = 15 m South, v WG = 2 m Wet v SG = v SW + v WG x y 15 m/ S m/ W v SG = ( 2) 2 + ( 15) 2 = 15.1 m/ θ = tan 1 15 = v SG = m at S of W x = x 0 + v 0 t at2 15 m = 0 m + (0.5 m ) t + 1 (3 m 2 2) t2 m 0 = ( 3 2 2) t2 + (0.5 m ) t 15 m t = 0.5± (0.5)2 4( 3 2 )( 15) 2( 3 2 ) = 3, Horizontal: v 0x = 5 m co 20 = m Vertical: v 0y = 5 m in 20 = m 12. x y N of E S of E

3 Phyic Unit 2: Force and Uniform Circular Motion 1. Term like Velocity, Force, Acceleration, Equilibrium, Inertia, apparent weight, Normal force, True Weight, Gravitational Force, Applied force, Tenion, Uniform Circular Motion, Period, Revolution, radiu, centripetal acceleration, centripetal force, banked and unbanked curve, atellite, orbit, weightlene, artificial gravity, Kepler Law of Planetary Motion 2. Fundamental force 3. Difference between g and G 4. tatic and kinetic frictional force 5. Lit Newton Three Law of Motion. 6. difference between ma and weight 7. What force do you draw on a freebody diagram? 8. How i centripetal force different from all the other force we have tudied? 9. A 100-N force act on a 75-kg peron. What i the acceleration of the peron? 10. A 70-kg ice kater puhe on a box on mooth ice (no friction). He applie 200 N horizontally againt the 50-kg box. What are the acceleration of the ice kater and the box? 11. A 10-kg block ret on a frictionle plane inclined at 60. What i the acceleration of the block a it lide down the incline? 12. A toplight i upended by two cable over a treet. Weight of the light i 110 N and the cable make a 116 angle with each other. Find the tenion in each cable. 13. A 100-kg man i tanding on a bathroom cale while riding an elevator. What doe the cale read when the elevator i accelerating upward at 5 m/ 2? 14. A 5000-kg car kid to a top. k =.5. What i the magnitude of the friction force? 15. Find the terminal velocity of a falling moue in air (A = m 2, m = 0.02 kg, C = 0.5). 16. Convert the angular meaure of 40 degree to radian. 17. A tone i in a ling and a boy whirl it around in a circle. If the centripetal acceleration i 50 m/ 2 and the radiu of the circle i 10 cm, what i the peed of the tone? 18. Find the gravitational force of attraction between a 100-kg girl and a 200-kg boy itting 0.5 meter apart. 19. What i the acceleration due to gravity at an altitude of m above the earth urface? Note: the radiu of the earth i m. 20. Four people are having a tug-o-war game. Ahley pull left with 20 N, Bert pull left with 10 N, Charlie pull right with 30 N, and Dannie pull right with 5 N. What i the magnitude of the acceleration of the 5 kg rope and who win the game? 21. A 10-g nut i hanging from a pring that ha tretched 30 cm becaue a quirrel i pulling it down. If the quirrel i pulling with 300 N, what i the pring contant?

4 7. Only force acting on the object 9. F = ma 100 N = 75 kg (a) 10. a = m F y : F N W = 0 F N = W F N = (5000 kg) (9.8 m 2) = N F x : f k = μ k F N = 0.5(49000 N) = N 15. Moue: v = 2mg ρca F N 200 N 200 N F N v = 2(0.02 kg)(9.8m 2) (1.21 kg )(0.5)(0.004 m2 ) = m ( π 180 ) = 2π 9 W kater W box W kater = 70 kg (9.8 m 2) = 686 N W box = 50 kg (9.8 m 2) = 490 N x y x y 200 N F N 200 N F N W = 686 N W = 490 N F = ma 200 N = 70 kg (a) a kater = m/ 2 F = ma 200 N = 50 kg (a) a box = 4. 0 m/ W = 10 kg (9.8 m 2) = 98 N F N 60 W W y W x x y F N W x = W in 60 W y = W co 60 Force in x: F = ma W in 60 = ma 98 N in 60 = 10 kg (a) a = m F X : T 2 co 32 T 1 co 32 = 0 T 2 (. 8480) T 1 (. 8480) = 0 T 1 = T 2 F y : W + T 1 in 32 + T 2 in 32 = N + T 1 (. 5299) + T 1 (. 5299) = N T 1 = T 1 = 110 N T 1 = T 2 = N 13. F N W = ma F N (100 kg) (9.8 m 2) = (100 kg) (5 m 2) F N = 1480 N 1 W 17. a c = v2 r 50 m 2 = v m v 2 = 5m 2 / 2 v = m/ 18. F g = G mm r 2 11 Nm2 (100 kg)(200 kg) F g = = kg 2 (0.5 m) N 19. g = G M r 2 g = ( Nm2 kg 2 )( kg) = m/ 2 ( m m) F net = ma 20 N 10 N + 30 N + 5 N = (5 kg)a a = 1 m/ 2 ince thi i to the right Charlie and Dannie win 21. kx mg F q = ma = 0 k(0.3 m) (0.01 kg) (9.8 m 2) 300 N = 0 k = 1000

5 Phyic Unit 3: Work, Energy, and Momentum 1. Meaning and concept of term like work, kinetic energy, gravitational potential energy, Conervation of mechanical energy, work-energy theorem, conervative force, nonconervative, elatic and inelatic colliion, impule, momentum, iolated ytem, conerved 2. Know how force and time are related to colliion and impule. 3. When i linear momentum and kinetic energy i conerved. 4. Mike i cutting the gra uing a human-powered lawn mower. He puhe the mower with a force of 100 N directed at an angle of 20 below the horizontal direction. Calculate the work that Mike doe on the mower in puhing it 5 m acro the yard. 5. The kinetic energy of a car i 7000 a it travel along a horizontal road. How much work i required to top the car in 20? 6. A 15-kg block i lifted vertically 10 meter from the urface of the earth. To one ignificant figure, what i the change in the gravitational potential energy of the block? 7. An engineer i aked to deign a playground lide uch that the peed a child reache at the bottom doe not exceed 4.0 m/. Determine the maximum height that the lide can be. 8. A ball of ma 5-kg i dropped from a height of 1.4 m (from the ground) onto a male pring (the pring ha an equilibrium length of 0.5 m). The ball compree the pring by an amount of 0.29 m by the time it come to a top. Calculate the pring contant of the pring. 9. A warehoue worker ue a forklift to lift a crate of pickle on a platform to a height 5 m above the floor. The combined ma of the platform and the 1.4 m 0.29 m 0.5 m crate i 100 kg. If the power expended by the forklift i 2000 W, how long doe it take to lift the crate? 10. ennifer i walking at 0.5 m/. If ennifer weigh 980 N, what i the magnitude of her momentum? 11. A 10.0-kg teel ball i dropped traight down onto a hard horizontal floor and bounce traight up. It peed jut before and jut after impact with the floor i 100 m/. Determine the magnitude of the impule delivered to the floor by the teel ball. 12. A 5000-kg cannon at ret contain a 100-kg cannon ball. When fired, the cannon ball leave the cannon with a peed of 20 m/. What i the recoil peed of the cannon? 13. A 2000-kg car traveling eat at 50 m/ collide with a 500-kg car traveling wet at 30 m/. The car tick together after the colliion. What i their common velocity after the colliion? 14. A driver lam on the brake of a 900-kg car going at 40 m/ o that the wheel lock. The road i loping upward. If the car top 20 m higher than it tarted, what i the work that friction did to top the car?

6 4. F = 100 = 5 m W = F co θ = (100 N)(5 m) co 20 = KE 0 = 7000, t = 20 W = KE f KE 0 = = m = 15 kg, h = 10 m PE = mgh = (15 kg) (9.8 m 2) (10 m) = v f = 4 m PE f + KE f = PE 0 + KE 0 mgh f mv f 2 = mgh mv 0 2 (9.8 m 2) (0 m) (4 m )2 = (9.8 m 2) h (0 m )2 8 m2 2 = 9.8 m 2 h 0 h 0 = m 8. m = 5 kg, h 0 = 1.4 m, h f = 0.5 m 0.29 m = 0.21 m, x = 0.29 m KE 0 + PE 0 = KE f + PE f 0 + mgh 0 = 0 + mgh f kx2 (5 kg) (9.8 m 2) (1.4 m) = (5 kg) (9.8 m 2) (0.21 m) + 1 k(0.29 m) = ( m 2 )k = ( m 2 )k 12. m c = 5000 kg, v 0c = 0, v fc =? m b = 100 kg, v 0b = 0, v fb = 20 m m c v 0c + m b v 0b = m c v fc + m b v fb (5000 kg)(0) + (100 kg)(0) = (5000 kg)v fc + (100 kg) (20 m ) 0 = (5000 kg)v fc kg m 2000 kg m = (5000 kg)v fc v fc = m 13. m 1 = 2000 kg, v 01 = 50 m, v f1 =? m 2 = 500 kg, v 02 = 30 m, v f2 =? m 1 v 01 + m 2 v 02 = m 1 v f1 + m 2 v f2 (2000 kg) (50 m ) + (500 kg) ( 30 m ) = (2000 kg)v f + (500 kg)v f kg m = 2500 kg v f v f = 34 m/ 14. E 0 + W nc = E f 1 2 mv W nc = mgh f 1 2 (900 kg) (40 m 2 ) + W nc = (900 kg) (9.8 m 2) (20 m) W nc = W nc = k = 1387 N m 9. h = 5 m, m = 100 kg, P = 2000 W P = W t = F t = ma t 2000 W = (100 kg)(9.8m 2)(5 m) t t = W = mg 980 N = m (9.8 m 2) m = 100 kg p = mv p = (100 kg) (0.5 m ) = 50 kg m 11. m = 10 kg, v 0 = 100 m, v f = 100 m = F t = mv f mv 0 = (10 kg) (100 m ) (10 kg) ( 100 m ) = 2000 N

7 Phyic Unit 5: Fluid 1. Meaning and concept of term like fluid, denity, barometer, Pacal principle, Bernoulli principle, Archimede principle, continuity equation, preure, buoyant force, gauge preure, abolute preure, Poieuille Law, laminar flow, turbulent flow, omoi, dialyi, diffuion 2. The denity of mercury i kg/. What i the ma of a 10- ample of mercury? 3. The average denity of the material in intergalactic pace i approximately kg/. What i the volume of a gold ample, ρ = kg/, that ha the ame ma a of intergalactic pace? 4. A barometer i taken from the bae to the top of a 10-m tower. Auming the denity of air i 1.29 kg/, what i the meaured change in preure? 5. How much force doe the atmophere exert on one ide of a vertical wall 10-m high and 20-m long? 6. A force of 500 N i applied to a hydraulic jack piton that i 0.01 m in diameter. If the piton which upport the load ha a diameter of 2 m, approximately how much ma can be lifted by the jack? Ignore any difference in height between the piton. 7. A balloon inflated with helium ga (denity = 0.2 kg/ ) ha a volume of 5. If the denity of air i 1.3 kg/, what i the buoyant force exerted on the balloon? 8. Water enter a pipe of diameter 10 cm with a velocity of 5 m/. The water encounter a contriction where it velocity i 20 m/. What i the diameter of the contricted portion of the pipe? 9. A large tank i filled with water to a depth of 17 m. A pout located 8 m above the bottom of the tank i then opened a hown in the drawing. With what peed will water emerge from the pout? 10. A mall crack occur at the bae of a 10.0-m-high dam. The effective crack area through which water leave i m 2. Ignoring vicou loe, 17 what i the peed of the water flowing through the crack? 11. Water flow through a pipe with radiu 2 m and peed of 10 m/. The denity 8 of water i 1000 kg/ and it vicoity i Pa. Calculate the Reynold number for thi ituation. 12. About how long will it take a perfume molecule to diffue a ditance of 2 m in one direction in a room if the diffuion contant i m 2 /? Aume that the air i perfectly till. 13. The denity of ice i 800 kg/ ; and the denity of eawater i 900 kg/. A large iceberg float in Arctic water. What fraction of the volume of the iceberg i expoed?

8 2. ρ = kg m3, V = 10 m3 ρ = m V kg = m 10 m = kg 27 kg 3. ρ pace = , ρ gold = kg, V pace = ρ = m V kg = m m = kg kg kg = m3 V V = h = 10 m, ρ air = 1.29 kg P = hρg P = (10 m) (1.29 kg ) (9.8 m 2) = 126 Pa 5. h = 10 m, l = 20 m P = F A F Pa = (10 m)(20 m) F = N 6. F 1 = 500 N, d 1 = 0.01 m, d 2 = 2 m F 1 = F 2 A 1 A N π(0.005 m) 2 = F 2 π(1 m) 2 F 2 = N W = mg m = W g = N 9.8 m/ 2 = kg 7. ρ He = 0.2 kg, V = 5 m3, ρ air = 1.3 kg F B = w fl F B = m air g ρ = m V 1.3 kg = m air 5 m air = 6.5 kg F B = (6.5 kg) (9.8 m 2) = N 8. d 1 = 10 cm, v 1 = 5 m, v 2 = 20 m A 1 v 1 = A 2 v 2 (π(0.05 m) 2 ) (5 m ) = (πr 2 2 ) (20 m ) r 2 = m d 2 = m 9. h 1 = 17 m, h 2 = 8 m, ρ = 1000 kg P ρv ρgh 1 = P ρv ρgh 2 1 atm (1000 kg ) (9.8 m 2) (17 m) = 1 atm + 1 kg ( ) v (1000 kg ) (9.8 m 2) (8 m) N kg = (500 m2 ) v N m N kg = (500 m2 m 2) v 2 2 v 2 = m 10. P ρv ρgh 1 = P ρv ρgh 2 1 atm (1000 kg ) (9.8 m 2) (10 m) = 1atm + 1 kg ( ) v kg = 500 m2 v 2 2 v 2 = 14 m 11. r = 2 m, v = 10 m kg, ρ = 1000 m3, η = Pa 2ρv r N R = η 2 (1000 kg m N R = 3) (10 m ) (2 m) Pa N R = m2 12. x = 2 m, D = 5 10 x rm = 2Dt m2 2 m = 2 ( ) t 4 m 2 m2 3 = t t = ρ ice = 800 kg kg m3, ρ = 900 Fraction ubmerged = ρ obj ρ fl Fraction ubmerged = 800 kg 900 kg Fraction ubmerged = 8 9 = 88.9 % Fraction expoed = 1 Fraction ubmerged Fraction expoed = Fraction expoed = 1 = % 9

9 Phyic Unit 6: Temperature, Heat, and Thermodynamic 1. Meaning and concept of term like thermal expanion, equilibrium, condenation, evaporation, ublimation, freezing, melting, humidity, heat, calorimeter, convection, conduction, radiation, blackbody radiator, thermodynamic, heat engine, heat pump, Carnot engine, entropy 2. The coefficient of linear expanion of aluminum i /C. A circular hole in an aluminum plate i 10 cm in diameter at 10 C. What i the diameter of the hole if the temperature of the plate i raied to 100 C? 3. A ample of a monatomic ideal ga i originally at 20 C. What i the final temperature of the ga if both the preure and volume are quadrupled? 4. Late on an autumn day, the relative humidity i 60% and the temperature in 30 C. What will the relative humidity be that evening when the temperature ha dropped to 10 C, auming contant water vapor denity? 5. A 5-kg lead hot i heated to 200 C and dropped into an ideal calorimeter containing 10 kg of water initially at 20.0 C. What i the final equilibrium temperature of the lead hot? The pecific heat capacity of lead i 128 /(kg C ); and the pecific heat of water i 4186 /(kg C ). 6. What i the minimum amount of energy required to completely melt a 5-kg lead brick which ha a tarting temperature of 20 C? The melting point of lead i 328 C. The pecific heat capacity of lead i 128 /(kg C ); and it latent heat of fuion i /kg. 7. A blue upergiant tar ha a radiu of m. The pherical urface behave a a blackbody radiator. If the urface temperature i K, what i the rate at which energy i radiated from the tar? 8. At what rate i heat lot through a 5 m 10 m rectangular gla windowpane that i 0.5 cm thick when the inide temperature i 20 C and the outide temperature -5 C? The thermal conductivity for gla i 0.80 W/(m C ). 9. A ytem containing an ideal ga at a contant preure of Pa gain 100 of heat. During the proce, the internal energy of the ytem increae by 500. What i the change in volume of the ga? 10. An engine i ued to lift a 5000 kg truck to a height of 2 m at contant peed. In the lifting proce, the engine received of heat from the fuel burned in it interior. What i the efficiency of the engine? 11. A Carnot heat engine i to be deigned with an efficiency of 60%. If the low temperature reervoir i 20 C, what i the temperature of the hot reervoir? 12. If the coefficient of performance for a refrigerator i 6 and 1000 of work are done on the ytem, how much heat i rejected to the room? 13. A 20-kg ample of team at C condene to water at C. What i the entropy change of the ample if the heat of vaporization of water i /kg?

10 2. α = /C, d 1 = 0.05 m, T 1 = 10 C, T 2 = 100 C ΔL = αlδt ΔL = ( /C )(0.05 m)(100 C 10 C) ΔL = m d 2 = 0.05 m m = m 3. T 1 = 20 C, P 2 = 4P 1, V 2 = 4V 1 PV = nrt PV T = nr ince nr i contant P 1 V 1 = P 2V 2 T 1 T 2 P 1 V 1 20 C = (4P 1)(4V 1 ) T C = 16 T 2 T 2 = 320 C 4. % hum 1 = 60 %, T 1 = 30 C, T 2 = 10 C % relative humidity vapor denity = aturation vapor denity 100% vapor denity 60 % = 30.4 g 100% vapor dentiy = g % humid = g 9.4 g 100% % humidity = 194 % Thi can't really happen. It tarted raining and the humidity tayed at 100%. 5. m l = 5 kg, T l = 200 C, m w = 10 kg, T w = 20 C, c l = 128, c kg C w = 4186 kg C = mcδt l = w (5 kg) (128 kg C ) (T f 200 C) = (10 kg) (4186 kg C ) (T f 20 C) 640 C T f = C T f C T f = T f = C 6. m = 5 kg, T 0 = 20 C, T melt = 328 C, c = 128, L kg C f = kg = mcδt = (5 kg) (128 ) (328 C 20 C) kg C = melt = ml f melt = (5 kg) (23200 ) = kg tot = = r = m, T = K, e = 1 t = σeat4 t = ( m 2 K 4) (1)(4π( m) 2 )( K) 4 t = A = (5 m)(10 m) = 50 m 2, d = m, T 2 = 5 C, T 1 = 20 C, k = 0.80 W m C t = ka(t 2 T 1 ) d t = (0.80 W m C ) (50 m2 )( 5 C 20 C) m t = P = Pa, = 100, ΔU = 500 ΔU = W 500 = 100 W W = 600 W = PΔV (iobaric proce) 600 = ( Pa)ΔV ΔV = m = 5000 kg, h = 2 m, = Eff = W h (5000 kg) (9.8 m Eff = 2) (2 m) = Eff C = 0.60, T c = 20 C Eff C = 1 T c T h 20 C 0.60 = 1 T h 0.40 = 20 C T h 20 C T h = = 50 C COP ref = 6, W = 1000 COP ref = c W 6 = c 1000 c = m = 20 kg, T = 100 C, L v = ΔS = T ΔS = kg (20 kg) ( kg ) = C K