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2 Sample final exam PHYSICS 103 ρ w =1000 kg/m 3 p = F/A; p h = ρgh; 1 atm = x10 5 Pa, F B = ρgv A 1 1 = A A -olume flow rate, Mass flow rate = Aρ p 1 + 1/ρ 1 + ρgh 1 = p + 1/ρ + ρgh flow in horizontal pipe: p 1 + 1/ρ 1 = p + 1/ρ T( 0 C) = 9 5 [T( 0 F) - 3]; T( 0 F) = 5 9 T( 0 C) + 3; T(K) =[T( 0 C) + 73] L - L 0 =α L 0 (T-T 0 ); A - A 0 =α L 0 (T-T 0 ); V - V 0 = β V 0 (T-T 0 ) V - V 0 =3α V 0 (T-T 0 σ = Yα (T-T 0 ) ideal gas: PV = nrt T- in kelins, N A = 6.0x10 3 /mole N = nn a R = J/mol K m mass P absolute ρ = n = V molecular mass J heat lost = heat gained c water = 4186 ; L F = kg 0 C 4 4 P1 V1 T1 PV = ; T Heat: Q = mc(t - T 0 ), Q = ml F, L - latent heat J 3.35x10 5 ; c ice = kg J 100 kg 0 C T T Q = ka 1 t L Q = εσa(t T0 )t σ = 5.67x10-8 W/m K 4 Thermodynamics: ΔU = Q W W = PΔV Q h = W + Q c W T e = c Q e = 1 c T COP = COP = c Q h Th W Th Tc x = Acos(ωt) = - ω Asin(ωt) ω = πf = πr ω = πr f = πr F = kx period: T spring = πr ; T pend = πr max = Aω E = ½ m + ½ kx ; E = ½ ka ; = λf; f = 1/T m πr linear mass: µ = ; = sound: = 343 m/s I 0 = 10-1 W/m P I = L 4πR = 331 m/s πr I I 343m/s ± 0 β=10db log β β 1 = 10dB log f = f0 I 0 I1 343 m/s! s L standing waes on string and in open pipe: n = 1,, 3., f = n λ= closed pipe: n = 1, 3, 5,. L n 4L q f = n λ = Electric charge: q = Ne 1q q F = k E = k F = qe qe = ma qδv +ΔK=0 4L n r r K = ½ m ΔV = E k = 8.99x10 9 Nm /C e = 1.6 x C m e = 9.11x10-31 kg Circuits: V = I*R Δq Ne I = = ; Δt t E P = P = I R P = Δt V P = I*V; V = V m sinωt V rms = R V m I rms = in series : R eq = R 1 +R + +R n in parallel: R eq = m -1 r V P ag =½V m I m P ag =V rms I rms P ag = rms c P ag = I rms R Light: n = λ =λ 0 /n c = 3 x10 8 m/s n 1 sinθ 1 R = n sinθ n 1 sinθ cr = n sin90 0 mirror and lens equation m r m r I m grating: dsinθ = mλ; d = L/N tan θ= D y resolution: Dsinθ =1.λ tan θ= L y y 1.λ = L D

3 1. How large a force is necessary to stretch a.0-mm-diameter steel wire (E = N/m ) by 1.0%? a N b N c N d N e N Crew members attempt to escape from a damaged submarine 80 m below the surface. What force must they apply to a pop-out hatch of radius of 18 cm to push it out? Assume the density of ocean water 105 kg/m 3. A) 8 kn B) 14 kn C) 165 kn D) 186 kn E) 5 kn 3 A block of wood has density 0.50 g/cm 3 and mass g. It floats in a container of oil (the oil s density is 0.75 g/cm 3 ). What olume of oil does the wood displace? A) cm 3 B) 000 cm 3 C) cm 3 D) cm 3 E) 500 cm 3 4. A water hose of radius of 1. cm is used to fill a bucket of olume of m 3. If it takes. min to fill the bucket, what is the speed at which the water leaes the hose? A) 0.5 m/s B) 1.3 m/s C) 3.0 m/s D) 4.9 m/s E) 8.8 m/s 5. A sample of unknown material appears to weigh 300 N in air and 00 N when immersed in water. The density of the material is closest to A) 100 kg/m 3 B) 000 kg/m 3 C) 3000 kg/m 3 D) 4000 kg/m 3 E) 6500 kg/m 3 6. If wind (density of air =1.9 kg/m 3 ) blows at 30 m/s parallel to a flat roof haing an area of 475 m, what is the force exerted on the roof?

4 A).76x10 5 N, up B) 8.75x10 5 N, down C) 4.6x10 6 N, up D) 6.16x10 6 N, down E) 1.3x10 7 N, up 7. The temperature of the iron cube, 5 cm on edge, should be changed by what amount for the olume of the cube to increase by 0.35 cm 3. (The coefficient of linear expansion of iron is 1. x 10-5 per 0 C ) A) 55 0 C B) C C) 33 0 C D) C E) C 8.. For mercury to expand from 4.0 cm 3 to 4.08 cm 3, what change in temperature is necessary? (β = 180x10-6 / 0 C). A) C B) 67 0 C C) C D) 8. 0 C E) C 9.. Suppose the ends of a 0-m-long steel beam are rigidly clamped at 0 C to preent expansion. The rail has a cross-sectional area of 30 cm. What force does the beam exert when it is heated to 40 C? (α steel = /C, Y steel = N/m ). A) N B) N C) N D) N E) N 10. Approximately how many moles of argon ( atomic mass is 18g/mol) are needed to fill the space between two panes of glass in a window, if the absolute gas pressure is atm., the olume of the space is 0. m 3, and the temperature is 30 0 C? ( 1atm=1.013x10 5 Pa) What is the mass of the argon inside? A) 15 g B) 88 g C) 41 g D) 864 g E) Can t tell. 11. A helium-filled balloon has a olume of 1 m 3. As it rises in the earth's atmosphere, its olume expands. What will its new olume be (in m 3 ) if its original temperature and pressure are 0 o C and 1 atm, and its final temperature and pressure are -40 o C and 0.1 atm? a. 4 b. 6 c. 8 d. 10 3

5 e A scuba dier has his lungs filled to half capacity (3 liters) when 10 m below the surface. If the dier holds his breath while quietly rising to the surface, what will the olume of the lungs be (in liters) at the surface? Assume the temperature is the same at all depths. (The density of water is kg/m 3.) a. 5.9 b. 4.5 c. 6.4 d. 3.9 e An 500 g aluminum electric tea kettle has a 500-W heating coil. How long will it take to heat up 1 kg of water from 18 o C to 98 o C in this kettle? The specific heat of aluminum is 900 J/kg oc and the specific heat of water is 4186 J/kg oc A) minutes B) 7 minutes C) 1 minutes D) minutes E) 9 minutes 14. A 660 g of sample of water at 90 0 C is mixed with 400 g of water at 0 C. What is the final temperature of mixture? Assume no heat lost to the surrounding. A) C B) C C) C D) C E) C A 10 grams of ice at temperature 0 0 C added to water was able to decrease the temperature of water from 6 0 C to 11 0 C. What was the mass of the water? (latent heat of fusion for water is J/kg; specific heat of water is 4186 J/kg 0 C). A) 18 g B) 36 g C) 349 g D) 640 g E) 891 g 16. How much heat must be added to 0.05 kg of copper at 5 0 C to melt it completely? C cu = 387 J/kg. L f = 0.7x10 4 J/kg, melting point T = C A) 5 kj B) 1 kj C) 5 kj D) 0.5 kj E) 31 kj 17.. A thermopane window consists of two glass panes, each 0.6 cm thick, with a 1-cm-thick sealed layer of air in between. If inside the room temperature is 3 0 C and the outside temperature is 0 0 C, determine the rate of energy transfer through 1m of the window. ( k=0.84 J/smK k air = J/smK ) A) 6 W B) 58 W C) 55 W D) 65 W 4

6 E) 5 W 18 A radiator has an emissiity of 0.7 and its exposed area is 1. m. The temperature of the radiator is 85 0 C and the surrounding temperature is 0 0 C. What is the net heat flow rate from the radiator? (σ = 5.67x10-8 W/m K 4 ) A) 855 W B) 68 W C) 431 W D) 35W E) 100 W 19. A water heater is operated by a solar power. If the solar collector has an area of 6 m, and the intensity deliered by sunlight is 550 W/m, how long does it take to increase the temperature of 1000 kg of water from 0 0 C to 60 0 C? A) 0.55 h B).00 h C) 7.50 h D) 14.0 h E) 1.0 h 0. How long will it take to transfer 5.5 MJ of heat through a.5 m pane of 3 mm thick glass ( k=0.84 J/sm 0 C) if the temperature difference is 1 0 C. A) 08 hr B) 0.8 hr C) 1.1 min D) 75 s E) 15 s 1. Gas in a container expands at a constant pressure of 3 atm. Find the work done (in J) by the gas if the initial olume is 5 liters and the final olume is 10 liters.. ( 1 atm = 1.013x10 5 Pa, 1L = m 3 ) A) 0 B) 150 C) 15 D) E) 1.5. A Carnot engine takes 000 J from a hot reseroir at 500 K, does some work, and discards some heat to cold reseroir at 350 K. The work done by the engine is closest to A) 3600 J B) 3000 J C) 400 J D) 100 J E) 600 J 3. A refrigerator has a coefficient of performance of 4.0. When remoing J from inside the refrigerator, how much energy is sent into the enironment? A) J B) J C) J 5

7 D) J E) J 4. One kilogram of chilled water at (0 0 C) is placed in a freezer which is kept at (-18 o C). Approximately how much electric energy is needed to operate the compressor to cool this water to (-18 o C).if the room temperature is maintained at (4 0 C)? (L ice = 3.33 x 10 5 J/kg; c ice =.09 x10 3 J/kg o C) A) 13 kj B) 1.5 kj C) 61 kj D) 16 kj E) 33 kj 5. A mass of 0.40 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moing through the equilibrium point? The starting displacement from equilibrium is 0.10 m. A) zero B) 1.4 m/s C).0 m/s D) 3.4 m/s E) 6.5 m/s 6. A 0.3-kg block, attached to a spring, executes simple harmonic motion according to x = 0.8 cos (35 rad/s t), where x is in meters and t is in seconds. Find the spring constant of the spring. A) N/m B) 1500 N/m C) 368 N/m D) 160 N/m E).8 N/ m 7. A string of linear mass kg/m is under a tension of 40 N. What should its length be if the frequency of the second harmonic is 440 Hz? A) 0.6 m B) 0.37 m C) 0.41 m D) 0.85 m E) 1.5 m 8. A standing wae of frequency 45 Hz is set up on a string 6 m long as shown. What is the speed at which wae propagates on the string? A) 5 m/s B) 45 m/s C) 100 m/s D) 180 m/s E) 0 m/s 6

8 9. The intensity at a distance of 4.0 m from a source that is radiating equally in all directions is 9.85 x 10-7 W/ m. What is the intensity leel in db at a distance of 6 m? A) 17.8 db B) 0.0 db C) 6.5 db D) 3. db E) 56.4 db 30. The intensity of a certain sound wae is x10-7 W/m. If its intensity is raised by 30 decibels, what is the new intensity in W/m? A) 6x10-5 W/m B) 5x10-4 W/m C) x10-4 W/m D) 6 x10-3 W/m E) x10 - W/m 31. A 500-Hz whistle is moed toward a listener at a speed of 10.0 m/s. At the same time, the listener moes at a speed of 0.0 m/s in a direction away from the whistle. What is the apparent frequency heard by the listener? (The speed of sound is 340 m/s.) A) 463 Hz B) 485 Hz C) 533 Hz D)547 Hz E) 56 Hz 33. An organ pipe, open at both ends, is. m long. If the elocity of sound in air is 343 m/s, the frequency of third harmonic of this pipe is: A) 116 Hz B) 34 Hz C) 366 Hz D) 499 Hz E) 5640 Hz 34. A mg particle carrying a charge of 4nC is placed in an uniform electric field of magnitude of 100 N/C. Find the particle s acceleration. A.) 0. m/s B.) 0.85 m/s C.) 7. m/s D.) 80.0 m/s E.) m/s 35. Determine the magnitude and direction of the electric field midway between a -8nC and a +6 nc charge 60 cm apart. A) 00 N/C to the right B) 00 N/C to the left C) 1400 N/C to the left D) 1400 N/C to the right E) none of the aboe 7

9 36. The wiring in a house must be thick enough so it doesn't become so hot to start a fire. What diameter must a copper wire (ρ = 1.68 x 10-8 Ωm) be if it is to carry a maximum current of 30 A and produce no more than 1.6 W of heat per meter of length? A) 0.05 mm B) 0.44 mm C) 3.5 mm D) 8.4 mm E). cm 37. What is the resistance of a light bulb that uses an aerage power of 15 W when connected to ac power source with maximum oltage of 50 V? A) 50 Ω B) 90 Ω C) 10 Ω D)150 Ω E) 50 Ω 38. An electric heater is rated at 1300 W, a toaster is rated at 1000 W, and an electric grill is rated at 1500 W. The three appliances are connected in parallel to a common 10 V circuit. For what current the circuit breaker be rated for you to operate all of these appliances at the same time? A) 6.0 A B) 8.0A C) 1.5 A D) 17.0 A E) 3.0 A 39. If the terminal oltage of the 9- V battery connected across 10- Ω resistor R is 8.4 V, what is the internal resistance of the battery? A) 0. 9 Ω B) 8.0 Ω C) 0.7θ Ω D) 6.4 Ω E) 0.5 Ω 40. The power dissipated in the 6 Ω resistor is: A).5W B)8.64W C)9.56W D)1.5W E)4.0W 8

10 41. What is the current in the 15-Ω resistor when emf = 9.0 V? I am a straight A student with a 4.0 GPA A) 0.0 A B) 0.30 A C) 0.10 A D) 0.6 A E) 0.60 A 4. The current in a wire is I = 15x10-3 A. How many electrons will pass a point in this wire in 4 min? (e = 1.6x10-19 C) A) B) C) D) E) None 43. A slab made of glass ( n= 1.5) has a thickness of 5 m. How long does it take light to pass perpendicularly through the slab? A) ns B) 1 ns C) 5 ms D) 5 ns E) 15 s 44. A 1.5 cm high object is placed 0 cm from the concae mirror with radius of curature 30 cm. Determine the position of the image and its magnification A) 60 cm, -3 B) 60 cm, 3 C) 30 cm, D) 15 cm, -5 E) 30 cm, Light enters a substance from air at C to the normal. It continues through the substance at to the normal. What would be the critical angle for this substance? A) B) C) D) E)

11 46. An optical fiber consists of a core made of glass of n 1 = 1.68 surrounded by a cladding made layer of plastics with index of refraction n = 1.4. The critical angle θ c for the interface between the glass and the plastics is closest to A) B) C) D).0 0 E) A 8-cm tall object is placed 40 cm away from a conerging lens of a focal length 30 cm. What is the nature and location of the image? A) The image is real,.5 cm tall, 60 cm on the same side as object. B) The image is irtual,.5 cm tall, 60 cm on the other side of the lens. C) The image is irtual, 4 cm tall, 10 cm on the same side as object. D) The image is real, 4 cm tall, 10 cm on the other side of the lens. E) none of the aboe. 48. An object 50-cm high is placed 1.0 m in front of a conerging lens whose focal length is 1.5 m. Determine the image height (in cm). a. 77 b. 150 c. 5 d. 17 e An object 0-cm high is placed 50.0 cm in front of a lens whose focal length is 5.00 cm. Where will the image be located (in cm)? a..13 b c. 6.7 d e What is the minimum aperture diameter of a camera that can resole detail on the ground of size of m from an airplane flying at an altitude of 14 km? Assume light with a waelength of 55 nm. A) 4.5 mm B) 9.6 mm C) 17 mm D) 3 mm E) 38 mm 10

12 51. Monochromatic light from a helium-neaon laser ( waelength 63.8 nm) is incident normally on a diffraction grating containing 6000 lines/cm. At what angle the first order maximum can be obsered? A) 5. 0 B) C).3 0 D) E) Light of waelength 475 nm falls on a double-slit grating with slit separation of 0.0 mm. The diffraction pattern is obsered on the iewing screen.5 m away from the grating. What is the distance on the iewing screen between the central bright fringe and the first bright fringe? A) 5.0 cm B) 8.6 cm C) 15.1 cm D).4 cm E) 5.9 cm 53. The pupil of a person s eye has a diameter of 5.0 mm. What distance apart must two small objects be if their images are just resoled when they are 50 mm from the eye and illuminated with light of waelength 500 nm? A) 1 x 10-5 m B) 3 x10-5 m C) 8 x 10-5 m D) 3 x10-4 m E) 7 x 10-3 m 54. A diffraction grating produces a first-order bright fringe that is 0.18 m away from the central bright fringe on a flat screen. The separation between the slits of the grating is.5 x 10-6 m, and the distance between the grating and the screen is 0.8 m. What is the waelength of the light shining on the grating? A) 345 nm B) 490 nm C)550 nm D) 60 nm E) 760 nm 55. A conex meniscus lens is made of glass with n = 1.5. The radius of curature surface is cm. The surface on the right is concae with radius of curature 46 cm. What is the power of this lens? A).6 D B) 0.55 D C) 1. D D).4 D E) 1.8 D 56. A 1.5 cm high object is placed 0 cm from the concae mirror with radius of curature 30 cm. Determine the position of the image and its magnification A) 60 cm, -3 B) 60 cm, 3 C) 30 cm, D) 15 cm, -5 11

13 E) 30 cm, - 1