General Physics 95.104. Exam 4. Spring 2011 1 Final Exam REQUIRED: Scientific Calculator Pen (Blue or Black) Formula Sheet (provided) OPTIONAL: Pencil (and eraser) Ruler NOT PERMITTED: Cellphone Smartphone Computer Notes Books Talking NAME: SECTION: Section 1. Multiple Choice /50 Section 2. Concepts /30 Section 3. Problem /40 Total = /120 GENERAL INSTRUCTIONS: Write your answers and working on the exam paper. Partial Credit can only be given if your work is clear and intelligible i.e. it doesn t further require a verbal explanation! Use the Formula Sheet this isn t a memorization test. Think through each question before trying to answer it. ANSWER TWO PROBLEMS
General Physics 95.104. Exam 4. Spring 2011 2 Section 1. Multiple Choice. /50 1. What is the force exerted between charge of +30 µc and a charge of - 2 µc, separated by 40 cm? a. 3.37 N, attractive b. 1.34 N, attractive c. 3.75x10-10 N, attractive d. 3.37 N, repulsive 2. What is the maximum amount of energy that could be stored by wiring together ten 1.5 F capacitors and charging the circuit to 30 volts? a. 225 kj b. 135 kj c. 67.5 kj d. 5.06 MJ 3. A hair dryer is rated at 900 watts (according to its label) when plugged into a 120 v electrical outlet. How much current does it draw? And what is its effective resistance? a. 3.5A, 4Ω b. 15A, 16Ω c. 7.5A, 8 Ω d. 7.5 A, 16Ω 4. A diver shines a flashlight upward from beneath the water at a 35 angle to the vertical. At what angle does the beam leave the water? a. 49.5 b. 29.7 c. It doesn t d. 35 5. A spy satellite orbiting at an altitude of 190 km needs to resolve features as small as 5cm on the ground. What is the minimum diameter of its objective mirror? a. 23 cm b. 2.3 m c. 1.5 m d. It could be any size.
General Physics 95.104. Exam 4. Spring 2011 3 6. What is the magnifying power of an astronomical telescope consisting of a reflecting mirror whose radius of curvature is 7 m, and an eyepiece whose focal length is 25 mm? a. 280 X b. 560 X c. 3.57 X d. 35.7 X 7. Calculate the Magnetic Field 12m below an overhead electric utility cable carrying a 300A current. a. 5 x10-6 T (less than the Earth s natural field) b. 0.75 x10-5 T (about equal to the Earths field) c. 3.5 x10-4 T (slightly larger than the Earth s field) d. 3 T (much greater than the Earth s field) 8. What is the energy of a photon of light whose wavelength is 350 nm? a. 3.6 ev, ultraviolet b. 5.7e - 19 ev, microwaves c. 13.6 ev, ultra violet d. 4.5 kev, X- ray 9. Radioactive Iodine ( 131 I) was released into the air by the Fukushima nuclear accident. If the half- life of 131 I is 8.02 days, how long will it take to decay until less than 1% remains in the environment? a. 53.5 days b. 8.02 days c. 5.3 years d. 80 years 10. If your eyeglass prescription is +3.0 Diopters, what is the focal length of your spectacle lenses? a. 66 cm b. 6.6 cm c. 33 mm d. 33 cm
General Physics 95.104. Exam 4. Spring 2011 4 Section 2. Conceptual Questions: /30) 1. According to Coulomb s law, like charges and opposite charges. [2] 2. When electricity passes through a wire, some of the energy is lost due to,. The energy loss can be reduced by using wire, or the voltage using a [4]. 3. A filter would enable your camera to take pictures of objects behind glass (say in a museum) without any distracting spoiling the view. [3] 4. Say a very fast train (v=0.8c)) approaches a tunnel that is slightly shorter than the train. According to Special Relativity, can the train fit completely inside the tunnel? [4] a. As seen by a person standing watching both ends of the tunnel (yes / no) b. As seen by a passenger on the train? (yes / no) 5. Imagine you have 3 identical lightbulbs connected in series to a small battery, and another 3 identical bulbs connected in parallel to an identical battery. The circuit will be brightest. [2] 6. Microphones and Speakers make use of the principle of electromagnetic [2] 7. When white- light is focused by a converging lens, the red rays converge from the lens than the blue rays. This problematic phenomenon is called aberration. [2] 8. When a Uranium atom undergoes, the mass of the fragments always adds up to the mass of the original atom. [2] 9. Different Isotopes of the same element contain the same number of, and differ in the number of. [2] 10. The three types of nuclear radiation are, and. [3] 11. are ejected during the decay of unstable nuclei, while are emitted during the rearrangement of the neutrons and protons within the nucleus. [2] 12. Briefly explain what is meant by Wave- Particle Duality [2]
General Physics 95.104. Exam 4. Spring 2011 5 13. Give 3 exam Problem 1. (You must complete TWO problems only) /20 An Oil droplet with a radius of 0.03 mm is observed to hover motionless in space between two vertically separated metal plates. The plates are 3cm apart and are charged to a potential difference of 500 Volts. The density of oil used for this experiment is 500 kg/m 3. A. Draw a free body diagram for the oil drop suspended between the high voltage plates. [6] Label the Forces due to: the Weight of the drop the Electric Field B. What is the magnitude of the Electric Field produced by the plates? [2] (if you cannot figure this out, use E= 20 kv/m for the rest of the problem) C. What is the net charge on the oil drop? [10] D. How many excess electrons must the oil drop have? [2]
General Physics 95.104. Exam 4. Spring 2011 6 Problem 2. (You must complete TWO problems only) /20 Your car s (passenger side) rearview mirror is designed to provide a wide view of the road behind and alongside your car. A. What type of mirror is it? [1] B. What magnification does this mirror afford, if it is to provide a view of twice as much road compared to a flat mirror (e.g. the internal rearview mirror mounted on the windshield) [2] C. Draw a diagram, and label: The Mirror Your Eye Radius of curvature (R ) [8 points total] Focal length (f) Location of a truck behind your car (do) Location of the Image of the truck formed by the mirror (di) D. Calculate the radius of curvature of the mirror [8] (if you don t trust your answer from part B, use M=0.65) D. Why do objects in the rearview mirror appear to be further away than they really are? [1]
General Physics 95.104. Exam 4. Spring 2011 7 Problem 3. (You must complete TWO problems only) /20 Nuclear reactors use the energy released by the Fission of Uranium nuclei to produce power. Data. Atomic masses: 235 U = 235.043923 u 88 Sr = 87.905614 u 136 Xe = 135.90722 u A. Draw a simple diagram to illustrate this nuclear fission reaction: [2] 235 U + n - > 88 Sr + 136 Xe + 12n B. Calculate the energy (in either MeV or Joules) released per 235 U atom in the above fission reaction. Assume the initial KE of the neutron is very small. [10] B. Calculate the mass of 235 U needed to produce the same amount of energy as burning 1kg of Coal, which yields about 3x10 7 J/kg. (If you don t trust your answer to part B, use 120 MeV for the energy released by a single 235 U Fission reaction.) [8]
General Physics 95.104. Exam 4. Spring 2011 8 Constants and Data: Speed of Light, c = 3.0 x10 8 m/s Ground State of Hydrogen Atom: E1=- 13.6 ev Plank s Constant, h = 6.63x10-34 Rydberg Constant = 1.0974x10 7 m - 1 Electron Mass = 9.11 x10-31 kg Electron Charge = 1.6 x10-19 C Permittivity of Free space (ε0 ) = 8.85 x10-12 C 2 /N.m 2 Sphere: Permeability of Free Space (µ0) = 4π x10-7 T.m/A Volume = 4/3 π r 3 Coulomb s Law constant (k) = 8.988 x10 9 N.m 2 /C 2 Area = 4π r 2 Density of Water = 10 3 kg/m 3 Brewster s Angle for Air- Water = 53 Density of Air = 1.29 kg/m 3 Refractive Index of Air = 1.00 Resistivity of Copper ρ= 1.68 x10-8 Ω.m Critical Angle for Water- Air = 49 Resistivity of Aluminum ρ= 2.65 x10-8 Ω.m Refractive Index of Water = 1.33 Resistivity of Silver ρ= 1.59 x10-8 Ω.m Refractive Index of Glass = 1.5 Direct Current Alternating Current: Capacitance Ohm s Law: V=IR Vrms = V0/ 2 C= Q/V (Farad) Electrical Power: P=VI = I 2 R Irms=Io/ 2 C = kε0 A/d Resistance: R = ρl/a PE = ½ CV 2 Electric Field and Potential: E = F/q (unit is N/C or V/m), V=PE/q (unit is Volts or J/C) Magnetic Field due to a current- carrying wire: B = µ0i/2πr Nuclear Data: Unified Atomic Mass Unit u = 1.6605x10-27 kg = 931.5 MeV/c 2 Proton Mass = 1.6726 x10-27 kg Neutron Mass = 1.6749 x10-27 kg 4 2He Mass = 4.02603 u 235 U Mass = 235.043923 u 14 C half- life = 5730 yr Radioactive Decay Law N = N 0 2 T t 12 N = N 0 e λt t 12 = ln(2) /λ = 0.69/λ t1/2 is the half- life λ is the decay constant Relation between half- life and decay constant Logarithms: if y = a x then loga(y) = x y= e x then ln(y) = x log(a x ) = x log a (useful if your calculator only has one type of log button)
General Physics 95.104. Exam 4. Spring 2011 9 Wave speed equation Focal length and image formation distance Magnification for a mirror or lens Power of a lens in diopters (f in meters) c = "f 1 f = 1 d i + 1 d o m = # d i d o P = 1 f Refractive Index Snell s Law of refraction Critical Angle for total internal reflection Diffraction angle for double- slits or grating Resolution limit of optical instruments (Rayleigh criterion) Magnification of a Telescope n = c v n 1 sin$ 1 = n 2 sin$ 2 sin$ C = n 2 n 1 sin90 = n 2 n 1 sin$ = m" d $ =1.22 " D m = # f O f E
General Physics 95.104. Exam 4. Spring 2011 1 0 γ = 1 1 v c Δt = γδt O L = L O γ 2 E 2 = p 2 c 2 + m 2 c 4 E = mc 2 λ D = h / p E = hf E = hf W c = λf 1 λ = R 1 m 1 2 n 2 E n = (13.6eV ) Z 2 λ max = 2.9 10 3 T n 2 Relativistic Gamma factor Time Dilation Length Contraction Total Energy De Broglie Wavelength Photon Energy Photoelectric Effect Rydberg Formula (n=1,2,3 m=1,2,3..) Bohr Atom Energy Levels Wien s Law