Physics 1252 Exam #2A

Transcription

1 Physics 1252 Exam #2A Instructions: This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet, except for your name: it must be handed in, signed but clean, with your exam. There is space after each question to show your work; if you need more space, you may use the back of the page, or request more paper. Please clearly indicate where your work for each problem is. Underline or draw a box around your final answer. The exam consists of four sections. Read all the questions at the start so that you can allocate your time wisely. Do easy ones first! You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put away throughout the exam. Do not open the exam until told to begin. You have the one entire class period to finish the exam. Put your last name on every page of the exam and on the formula sheet. You must provide explanations and/or show work legibly to receive full credit for Sections II and III. Make sure that your answers include appropriate units and significant digits. (Note: For intermediate steps in your calculation, it s best to carry more significant digits.) Fundamental constants and unit prefixes are on the Formula Sheet, last page. By signing below, you indicate that you understand the instructions for this exam and agree to abide by them. You also certify that you will personally uphold the university s standards of academic honesty for this exam, and will not tolerate any violations of these standards by others. Unsigned exams will not be graded. Signature: UGACard #: Copyright c 2015 University of Georgia. Unauthorized duplication or distribution prohibited.

2 Section I II III Score /30 /35 /35 I: Multiple-Choice Questions (30 points) For each question below, choose the single best response and write the corresponding capital letter in the box provided. There is no penalty for guessing the wrong answer. 1. In the figure below, Q 1 is a positive and Q 2 is a negative point charge with Q 1 and Q 2 being of comparable magnitude. Which arrow drawn at P could correctly represent the electric field vector E generated by Q 1 and Q 2 at P? P (C) Q 2 (D) (E) (B) (A) Fig Q 1 A. B. C. D. E. 2. If two point charges Q 1 and Q 2 at some distance r repel each other with a force of 80µN, what force would they exert on each other if Q 1 is tripled ( 3) without change of sign; r is quadrupled ( 4), and the sign of Q 2 is reversed? The two charges will A. attract each other with a force of 15µN B. repel each other with a force of 60µN C. repel each other with a force of 15µN D. attract each other with a force of 60µN E. attract each other with a force of 45µN Copyright c 2015 University of Georgia. 2

3 3. A beam of coherent (laser) light of wavelength λ is incident upon a diffraction grating with line spacing d, with λ < d, as shown in the figure below. Assume y is the distance (in cm) between the two 1st-order intensity maxima, observed on a screen at a distance L on the other side of the grating. This distance y will 1st order maxima Δy Fig Screen L θ Diff. Grating Laser Beam A. decrease if we increase λ (keeping L and d fixed); B. increase if we increase d (keeping λ and L fixed); C. increase if we decrease λ (keeping L and d fixed); D. decrease if we increase d (keeping λ and L fixed); E. decrease if we increase L (keeping λ and d fixed). 4. The figure below shows the volume, V, enclosed by an ellipsoidal surface, S, both displayed by their intersections with the x-y-plane. Also shown are three point charges, located in the x-y-plane as shown, with charge amounts Q 1 = 2mC, Q 2 = +10mC and Q 3 = 4mC. The three charges produce a net electric field, E, present everywhere inside, outside and on the surface of V. What is the net electrical flux, Φ, out of the surface S, due to this electrical field E, when multiplied by ɛ o 1/(4πk)? Fig surface S Q 2 volume V Q 1 Q 3 A. ɛ o Φ = +8mC B. ɛ o Φ = +12mC C. ɛ o Φ = +4mC D. ɛ o Φ = 8mC E. ɛ o Φ = +6mC Copyright c 2015 University of Georgia. 3

4 5. In a triple slit (3-slit) interference experiment, a 3 rd order principal intensity maximum is observed at an angle θ 3 = o, measured from the central axis, and sin θ 3 = How many principal maxima, total, including the central maximum, can be observed across the entire, very wide (infinite-width) screen, i.e., between θ = 90 o and θ =+90 o? A. 11 B. 9 C. 6 D. 7 E A diffraction grating (in air or vacuum), is illuminated by coherent (laser) light with wavelength λ and wave oscillation period τ = λ/c. The 5th order intensity maximum, to the right of the central intensity maximum M, is located at point Q, as shown in the figure below. A wave crest A, from slit R, and a wave crest B, from the neighboring slit S to the right of R, have departed at the same time from their respective slits of origin. Therefore, at Q, M Q Fig R S Diffr. Grating Laser Beam A. B will arrive 6 periods before A. B. B will arrive 9/2 periods before A. C. B will arrive 5 periods before A. D. A will arrive 5 periods before B. E. A and B will arrive at the same time. Copyright c 2015 University of Georgia. 4

5 II: Electric Field from Point Charges (35 points) Four point charges of unknown charge amounts, Q 1, Q 2, Q 3, Q 4, are positioned at various unknown locations in the x-y-plane, excluding origin O (0, 0, 0). They jointly produce a net electric field vector E f [E f,x, E f,y, E f,z ] with components E f,x =+6.0N/C, E f,y = 8.0N/C, E f,z =0, at an observation point, P (x P, 0, 0) with x P =+3m, on the x-axis. The subscript f here is to remind you that E f is produced by the four point charges. A fifth point charge, Q 5 = 20nC, is now added, placed at the origin, O, and all five point charges, Q 1, Q 2,..., Q 5, then jointly produce a net electric field, E = [E x, E y, E z ]. (a) Draw this: big, on full blank page attached! Show: x-axis, y-axis, O, P, and E f with its tail end attached to P. Also show field contribution E 5, produced by Q 5 at P. It does not have to be to scale, but all vectors must point into the correct quadrant or along the correct coordinate axis direction. (b) Calculate the components of E at P ; its strength, E ; and its angle, θ, measured from the +x-direction, with θ > 0 if E points above the x-axis, else θ < 0. Then also show E in the drawing from (a), as the resultant in a vector addition parallelogram. (c) Now Q 5 is removed again and a muon is placed, at rest, at point P and then released, to accelerate subject to the electric field produced by the other four point charges. A muon is a sub-atomic particle carrying the same charge as an electron, but with a mass of kg. Find the muon s acceleration, a, immediately after its release at P. State the magnitude of the acceleration, a, and its angle, φ, measured from the +x-direction, with φ > 0 if a points above the x-axis, else φ < 0. Then also show a in the drawing from (a), correctly aligned with the relevant electric field vector. Copyright c 2015 University of Georgia. 5

6 Drawing for Problem II (a): Copyright c 2015 University of Georgia. 6

7 III: Sound Interference in Air and Water (35 points) Two small sound sources, oscillating at the same frequency and in phase, are positioned 90m below the x-axis, 2m to the left and 2m to the right of the y-axis, respectively. A sound detector (microphone), P, moving slowly along the x-axis, observes a maximum in sound intensity at x 0 = 0m, and, closest to that, an intensity minimum, at x 1/2 = 10.89m, if the experiment is performed in air with a speed of sound of v A = 340m/s. (a) Draw this: big, on full blank page attached! Show: x-, y-axes, detector, sources, line connecting sources, observation angle θ, all given distances. It need not to be to scale. Then find the oscillation frequency of the sources. (b) How many intensity maxima, total, and how many intensity minima, total, will the detector observe if it travels along the x-axis from very far to the left (x = ) to very far to the right (x = + )? (c) If the entire experimental apparatus (sources, detector, and the entire space in between sources and x-axis) is now submerged in salt water the intensity minimum, closest to the central maximum, is observed on the x-axis at x 1/2 = 41.65m. From this, calculate the speed of sound in salt water. Hint: the frequency of the sources, the spacing between them, and their distance from the x-axis is the same as before. Copyright c 2015 University of Georgia. 7

8 Drawing for Problem III (a): Copyright c 2015 University of Georgia. 8