Examination cover sheet

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1 Examination cover sheet Examination/course code: 3NBB1/3NBB Number of examinees: about 850 Date: January 23, 2017 Start time: End time: written open questions Number of pages: 5 Instructions for students and invigilators FOR ALL STUDENTS 3NBB, EXCEPT APPLIED PHYSICS Permitted examination aids (to be supplied by students): The printed formula pages from OASE (without annotations) Dictionary: English-Dutch Remarks : It is NOT allowed to use a calculator or any other electronic device. Important: Examinees are only permitted to visit the toilets under supervision it is not permitted to leave the examination room within 15 minutes of the start and within the final 15 minutes of the examination examination scripts (fully completed examination paper, stating name, student number, etc.) must always be handed in the house rules must be observed during the examination the instructions of examiners and invigilators must be followed no pencil cases are permitted on desks examinees are not permitted to share examination aids or lend them to each other During written examinations, the following actions will in any case be deemed to constitute fraud or attempted fraud: using another person's proof of identity/campus card (student identity card) having a mobile telephone or any other type of media-carrying device on your desk or on your person using, or attempting to use, unauthorized resources and aids, such as the internet, a mobile telephone, etc. using a clicker that does not belong to you having any paper at hand other than that provided by TU/e visiting the toilet (or going outside) without permission or supervision. These actions will therefore result in the student's immediate exclusion from further participation in the examination. Bijlage 3, behorende bij artikel 5 Regeling voor centrale tentamenafname

2 Technische Universiteit Eindhoven Bachelor College Eindtoets Toegepaste Natuurwetenschappen and final assessment Applied Natural Sciences (3NBB) Monday, January 23, 2017, hours This assessment consists of 9 exercises, containing one or two questions. The maximum score per question is shown in the exercise. Exercise number 9 is faculty/major specific. Which exercise number 9 you need to make, is clearly indicated. For all questions it is important that you explain how you obtain your result. You are allowed to use the following: 1. Summary files of the chapters of the Book University Physics of Young and Freedman. No additional notes to these files are allowed, 2. Dictionary (English-Dutch) It is NOT allowed to use a calculator or any other electronic device. Write on every paper you use during the assessment your name, student ID, and the faculty of your Bachelor. The answers to the questions will be posted on the OASE-website of the course. The grades will be announced before Tuesday February 14, 2017, through the OASE-website of the course. If you disagree with the result, you are requested to contact the responsible lecturer of the course, R.Engeln, via before Tuesday, February 28, 2017.

3 Exercise 1 A bullet is fired from a height H with a rifle that is aimed at a target a horizontal distance L away from the building. The target is kept at a height D. At the time the bullet exits the rifle the target is dropped. Air resistance can be ignored and the acceleration due to gravity equals g. a. What is the minimum speed the bullet should have to hit the target? Express your answer in the given constants. (HINT: realize that this situation is similar to the Wilhelm Tell demonstration, and ask yourself what happens if the bullet would be fired at a speed lower that this minimum speed). [10 pts] Exercise 2 A small sphere with mass m is attached at the end of a thin wire of length L. The sphere is moving with constant speed in a horizontal circle. The wire makes a fixed angle β with the vertical direction (see figure). The acceleration due to gravity equals g. a. Draw a free body diagram for the small sphere. Also, describe in words each force that is acting upon the small sphere. [2 pts] b. Express the time it takes the sphere to make one round trip in the given constants. [8 pts]

4 Exercise 3 In a region of space the force at a position (x, y) on an electron is F = Cxj, where C is a positive constant and j denotes the unit vector in the y- direction. The electron moves around a square loop in the xy-plane. The square has edge length L and is positioned as shown in the figure on the right. a. Determine the work done on the electron by the force F during a counter-clockwise trip around the square, and starting at (x = 0, y = 0). [10 pts] Exercise 4 On a horizontal surface a spring is attached at one end to a block and on the other end to a wall. The spring is initially not stretched or compressed and positioned perpendicular to the wall. The block is initially at rest. The kinetic friction coefficient between the block and the horizontal surface is μ k. The spring is ideal and has a spring constant k. A bullet with mass m, travelling perpendicular to the wall, hits the block with velocity v in a completely inelastic collision. The mass of the block is nine (9) times the mass of the bullet. The acceleration due to gravity equals g. a. Determine the maximum compression of the spring. Express your answer in the given constants. [10 pts] Exercise 5 A plane is flying at an altitude H above the ground and travels with constant velocity vp, which is larger than the (constant) speed of sound vs. A microphone on the ground detects the sonic boom (the shock wave). a. What is the horizontal distance between the plane and the microphone on the ground. Express your answer in the given constants. [10 pts]

5 Exercise 6 A cubical block of density ρ b and with edges of length L floats in water that has a density ρ w (ρ w > ρ b ). a. Express the fraction of the block s volume that is above the surface of the water in the given constants. [5 pts] b. An oil tanker passes by and leaks a thin layer of oil with density ρ oil and thickness d. The density of the oil is lower than that of water, but higher than that of the block. The oil forms a smooth layer on top of the water. Part of the block stays above the surface of the oil. Which fraction of the block is now above the surface of the oil? Express your answer in the given constants. [5 pts] Exercise 7 Two rods, 1 and 2, with cross-sectional area A are made of different materials and are joined end-to-end (see figure). The rods 1 and 2 have resp. lengths L1 and L2, and thermal conductivities k1 and k2. One of the ends is in an ice-water mixture, with temperature Ti, while the other end is immersed in boiling water, with temperature TB. There is no heat-loss to the surroundings. T =? a. What is the temperature at the point where both segments are joined? Express your answer in the given constants. [10 pts]

6 Exercise 8 A light ray with a wavelength of 500 nm in vacuum (refractive index n a ) strikes a quartz plate (thickness d and refractive index n b ) under an angle θ i (see Figure). d na nb θ i a. Show that θ i = θ o.[5 pts] na θ o a b. We now increase the wavelength of the incoming beam. Due to dispersion the displacement, a, of the beam will change. Explain whether the displacement, a, increases or decreases, and why. Use the information in the figure on the right. [5 pts] -- The exam continues with a faculty/major specific exercise --

7 Faculty/major specific exercise Faculty EE (major EE and AUT) Exercise 9 A doped semiconductor has an energy diagram as shown below. a. What type of doping has been applied to the semiconductor with the above energy diagram and which type of charge carrier (electrons or holes) dominates the charge transport for this semiconductor? Explain your answer. [5 pts] b. At a temperature of 0 Kelvin, the doped semiconductor is acting as an isolator. Explain by means of the Fermi-Dirac distribution how holes are created in the valence band in the doped semiconductor at higher temperatures. [5 pts]

8 Majors PT, SI and INFS/W Exercise 9 Protons with mass m p and charge +e are produced in a proton source. They are released in a homogeneous electric field (region 1) with negligible initial speed. The electric field in region 1 is created by applying a voltage difference V across a very large capacitor. After passing region 1 they enter region 2 in which there is a homogeneous magnetic field B perpendicular to the trajectory of the protons. In this region they move along a circular orbit with radius R until they hit a detector. a. What is the direction of the magnetic field in region 2? Explain your answer. [2 pts] b. Show that the protons hit the detector with a speed v = C V, where C is a constant. Calculate the constant C and express it in the given constants, but not in E. [4 pts] c. Calculate the voltage V that should be applied to have the protons hit the detector at distance R as indicated in the figure. [4 pts]

9 Major ST, TWk, and TBk Exercise 9 A light, nonstretching cable, is wrapped around a hollow cylinder of uniform mass density ρ with length L, inner radius R1 and outer radius R2. The cylinder rotates with negligible friction about a stationary horizontal axis through the symmetry axis of the cylinder. The thin spokes can be considered massless. The acceleration due to gravity equals g. The free end of the cable is tied to a block with mass m. The block is released from rest. As the block falls, the cable unwinds without stretching or slipping. a. Derive the moment of inertia for the hollow cylinder for the rotation axis through the symmetry axis of the cylinder. Express your answer in the given constants. [5 pts] b. What is the acceleration of the falling block? You are allowed to assume the moment of inertia, Ic, of the cylinder for the rotation axis through the symmetry axis of the cylinder as a given constant. Express your answer in the given constants. [5 pts]

10 Major BMT, MWT Exercise 9 A rod with length L and negligible weight is supported at its ends by wires A and B of equal length (see figure). The cross sectional area of wire A is OA, and of wire B is two times OA. a. At what distance from the point where A is attached to the rod should a weight W be suspended to produce equal stresses in A and B. Express your answer in the given constants. [5 pts] To decrease the distance from the ceiling to the rod and the weight W, two wires are attached to the ceiling further apart than the length L of the rod (see figure below). The rod stays horizontal and parallel to the ceiling. The wire on side A makes an angle θ with the ceiling. The Young s modulus for the rod is YR and the cross sectional area of the rod is OR. You can assume the distance determined in a to be D, and thus a known constant. b. Determine the change in length of the rod as compared to the situation in a. Assume that this change in length is much smaller than L and D. Express your answer in the given constants. [5 pts]