Physics Midterm #2 Two Hours, Closed Book

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1 Physics Midterm #2 Two Hours, Closed Book These are the same instructions as given on the first exam. Instructions for taking the exam in the Science Library: Pick up and return the exam from the circulation desk in the Collier Science Library. You may take the exam anywhere in the Park Science Center or another nearby building. You have two hours from the moment you open the exam. Be sure to time yourself. You may take a few extra minutes to walk the exam back to the library when you are done. When you are done, return your exam to the circulation desk. Discard the cover sheet and equation sheets. General instructions for everybody: This is a closed-book exam: do not use any references (text, notes, etc.). You will need a calculator capable of basic functions (arithmetic, logarithms, trigonometric functions, etc.), but you are not allowed to store formulas, etc., in the calculator memory. This booklet contains: This cover page. Three pages of formulas. The exam questions. Three blank pages in case you need extra work space. Remove the cover page and formula pages from your exam. Discard them when the exam is over. Write your name, start time, and end time on the first page of questions. Write your answers directly on the exam booklet. Show your work and box your final answers. If you write any final answers on blank pages, indicate that you have done so on the page on which the problem was posed. I don t want to miss any of your work when grading your exam. Good Luck!!!

2 Physics Formulas v = x t a = v t v f = v i + at x f = x i + v xi t a xt 2 v 2 xf = v 2 xi + 2a(x f x i ) a = v2 r = ω2 r F k = µ k n F s,max = µ s n F = mg F = Gm 1m 2 r 2 F = k x F = m a F = p t p = m v K = 1 2 mv2 K = 1 2 Iω2 U = 1 2 kx2 U = mgy U = Gm 1m 2 r P = E t or W t W = F r = F r cos θ τ = F r = F r sin θ g = Gm r 2 ( ) 4π T 2 2 = R 3 Gm F A = Y L L F A = B x s L = B s tan θ v = ωr = 2πfr = 2πr T a t = αr ω = θ t α = ω t ω f = ω i + αt θ f = θ i + ω i t αt2 ω 2 f = ω 2 i + 2α(θ f θ i ) ρ = m V p = F A p = ρgy Q = V t = va p ρv2 1 +ρgy 1 = p ρv2 2 +ρgy 2 F B = m displaced g v max = Aω a max = Aω 2 x(t) = A cos(ωt) or A sin(ωt) v(t) = v max sin(ωt) or v max cos(ωt) a(t) = a max cos(ωt) or a max sin(ωt) k ω = m g ω = l ω = 2πf f = 1 T The solution to ax 2 + bx + c = 0 is x = b ± b 2 4ac. 2a Volume of a sphere: V = 4 3 πr3 Surface area of a sphere: A = 4πr 2 Area of a circle: A = πr 2 Circumference of a circle: l = 2πr

3 Physics Formulas y(x, t) = A cos ( 2π x ωt) λ v = fλ F t v = µ, µ = m L f o = (1 ± vo v ) (1 vs v )f s f = 2 v r v f s f beat = f 1 f 2 ( I β = 10 db log I = P A I = P 4πr 2 I 0 ) v = c n λ = λ vac n n 1 sin θ 1 = n 2 sin θ 2 λ = h p = h mv 1 s + 1 = 1 s f M = h h = s s M angular = θ θ P = 1, P in diopters, f in m f θ λ D Q = ML Q = Mc T P = ka T L P = eσat 4 λ peak = nm K T String or open-open tube: Open-closed tube: Bragg scattering (X-rays): Interference in general: Single-slit interference: (small angle) Two-slit or Multi-slit interference: (any angle) f 1 = v 2L, f m = mf 1, m = 1, 2, 3,... f 1 = v 4L, f m = mf 1, m = 1, 3, 5,... 2d cos θ = mλ { m λ constructive L = (m + 1 )λ destructive 2 { L 1 L 2 m constructive = λ 1 λ 2 m + 1 destructive 2 0 constructive y = m L λ a destructive, m 0 sin θ = (small angle) y = m λ d ( ) m + 1 λ 2 d m L λ d ( ) m + 1 λ 2 L d constructive destructive constructive destructive

4 More Physics Formulas F = K q 1q 2 r 2 E = K q r 2 E = Q ɛ 0 A F = qe V = 1 q 4πɛ 0 r U elec = qv E = V x Q = CV C = κɛ 0A d U = 1 Q 2 2 C = 1 2 QV = 1 2 CV 2 I = Q t V = IR R = ρl A P = IV = I 2 R = V 2 R 1 R equiv = 1 R R 2 R equiv = R 1 + R 2 ΣI in = ΣI out Σ V = 0 τ = RC V = V 0 e t τ V = V f (1 e t τ ) Fundamental Constants and Commonly Used Data gravitational constant 11 N m2 G = kg 2 electrostatic constant K = N m2 C 2 permittivity of free space 12 C2 ɛ 0 = N m 2 Stefan-Boltzmann constant σ = W m 2 K 4 Planck constant h = Js grav. acceleration at Earth surface g = 9.80 m s threshold of hearing I 0 = W m 2 speed of light in vacuum c = m s fundamental charge e = C electron mass m e = kg proton mass m p = kg speed of sound in air v = 343 m s air at 20 atmospheric pressure 1 atm = N m 2 specific heat capacity of water c water = 4186 J kg K density of water ρ water = 1000 kg m 3 power output of the Sun W radius of Sun m radius of Earth m radius of Moon m mass of Sun kg mass of Earth kg mass of Moon kg distance from Sun to Earth m

5 Physics Spring 2010 Midterm #2 Name Start Time End Time Grading note: There are six problems. Point values are given with each problem. They add up to 100 points. In multi-part problems, points are not necessarily evenly divided between the parts. 1. [20 points] The equipotentials in some region are shown. Equipotential contours are drawn at intervals of 10 V. Distances in meters are given along the axes. 3 40V 30V 20V 10V 0V 2 50V y(m) 1 A B C x(m) (a) Estimate the electric field at point B (direction and magnitude). This problem is continued on the next page... 1

6 (b) A proton is released from rest at point B. As it moves away from B, it passes through either point A or C. Which is it, point A or point C? (c) An electron is released from rest at point B. As it moves away from B, it passes through either point A or C. Which is it, point A or point C? (d) What is it the speed of the electron as it passes through this point? (Physical constants needed for this calculation can be found on the equation sheet at the front of the exam booklet.) 2

7 2. [20 points] Four identical resistors of resistance R = 1.0 kω, a capacitor of capacitance C = F, and a battery of voltage V b = 10 V are arranged as shown. Switch R1 R2 V b R4 R3 C (a) The three resistors R1, R2, and R3, can be reduced to a single equivalent resistor. What is the resistance of this equivalent resistor? (b) The switch has been closed for a long time. What is the charge on the capacitor? This problem is continued on the next page... 3

8 (c) The switch is opened at time t = 0. What is the charge on the capacitor as a function of time, t? Give a formula. Your formula should be a numerical expression with t as the only variable. (Substitute in numbers for any other variables.) (d) At what time is the charge on the capacitor one tenth of the value you calculated in part (b)? 4

9 3. [15 points] Imagine a space probe (satellite) in the shape of a cube, orbiting a star. The space probe orbits in such a way that the same face of the cube is always facing the star. The power output of the star is P = W. The distance from the star to the cubic probe is d = m. The edges of the cube are l = 2.0 m in length. The entire surface of the space probe (all six sides) always maintains the same temperature T. It has emissivity e = 1. What is T? This side always faces the Star STAR Drawing is not to scale! CUBE SHAPED SPACE PROBE 5

10 4. [15 points] Copper and aluminum are denoted by symbols Cu and Al, respectively. The resistivity of copper is ρ Cu = Ω m. The resistivity of aluminum is ρ Al = Ω m. Calculate the resistance of each of the following. The diagrams below show how each would be connected into a circuit. (a) A cube of copper, 0.1 m 0.1 m 0.1 m. (b) A cube of aluminum, 0.1 m 0.1 m 0.1 m. (c) A cube of copper and a cube of aluminum, each 0.1 m 0.1 m 0.1 m, next to each other. (d) A cube of copper and a cube of aluminum, each 0.1 m 0.1 m 0.1 m, one on top of the other. (a) (b) (c) (d) Cu Al Cu Al Al Cu 6

11 5. [15 points] A wall of a house is 7 m long and 3 m high. It is constructed of solid brick of thickness 0.2 m. There are two windows in the wall, each 1 m 1 m, made of glass m thick. Inside, it is 22 C. Outside, it is 2 C. Electricity costs $0.10 per kilowatt hour. How much does it cost to replace the heat lost through this wall in one day? Thermal conductivities: κ brick = 0.63 W, κ m C glass = 1.05 W. m C 7

12 6. [15 points] Sketch electric field lines and equipotential lines for the following charge distribution. There is a 6 µc charge in the center and two +3 µc charges, one to the left and one to the right, as shown below. Either make a single drawing or two separate drawings. +3 µ C 6 µ C +3 µ C 8

13 This is the first of three pages provided as extra work space for this exam. 9

14 This is the second of three pages provided as extra work space for this exam. 10

15 This is the third of three pages provided as extra work space for this exam. 11

Physics Final Exam Three Hours, Closed Book

Physics Final Exam Three Hours, Closed Book Physics 102-1 Final Exam Three Hours, Closed Book The instructions for this exam are identical to those of the midterm exams, except that this exam is three hours long. This is a closed-book exam: do not