Technische Universiteit Eindhoven Bachelor College. Eindtoets Toegepaste Natuurwetenschappen and final assessment Applied Natural Sciences (3NBB)

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1 Technische Universiteit Eindhoven Bachelor College Eindtoets Toegepaste Natuurwetenschappen and final assessment Applied Natural Sciences (3NBB) Monday, January 20, 2014, hours This assessment consists of 10 exercises, containing one or more questions. Every question counts equally in determining your final score. Exercise number 10 is faculty/major specific. Which exercise number 10 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. (graphical) calculator, 3. dictionary. 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 11, 2014, 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 25, 2014.

2 1. A baseball is thrown into the air from the edge of a vertical cliff, as shown in the figure. Ignore air resistance. The gravitational acceleration is g. a. Express the initial speed, v 0, of the baseball in the constants P and Φ, depicted in the figure, and g. b. Express the height of the cliff, H, in the constants depicted in the figure (except H), the gravitational constant g, and the initial speed of the baseball, v Block B, with mass m B, rests on block A, with mass m A, which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is µ s. A light string, attached to block A, passes over a frictionless, massless pulley, and block C is suspended from the other end of the string (see figure on the right). a. What is the largest mass that block C can have so that blocks A and B still slide together when the system is released from rest? Express your answer in terms of m A, m B and µ s. 3. A net force along the x- axis that has x- component F x = A + B x 2 is applied to an object with mass m, that is initially at the origin and moving in the positive x- direction with a speed of v i. Both A and B are constant and are both larger than zero. a. What is the speed of the object when it has travelled on the x- axis over a distance L from the origin. Express your answer in the given 2

3 4. Two toy cars, one with mass m and one with mass 2m, are pressed against opposite ends of a light spring of force constant k, compressing the spring by an amount X from its normal length. The two toy cars are released at the same time. a. Find the speed of each car when it has moved free of the spring on a frictionless horizontal table. Express your answer in the given 5. A cube of ice (frozen water) with mass M is floating in glycerine. The glycerine is in a tall cylinder that has inside radius r. The level of the glycerine is well below the top of the cylinder. The density of water is ρ w and the density of glycerine is ρ g. a. If the ice completely melts, by what distance does the height of liquid in the cylinder change. Express your answer in the given 6. A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is v L (v L is larger than zero). a. What is the period of the SHM? Express your answer in the given 7. Three pieces of string, each of length L, are joined horizontally together end- to- end, to make a combined string of length 3L. The first piece of string has mass per unit length μ 1, the second piece has mass per unit length μ 2 =4μ 1, and the third has mass per unit length μ 3 = μ 1 /4. a. If the combined string is under tension, T, how much time does it take a transverse wave to travel the entire length 3L? Give your answer in terms of L, T, and μ the exam continues on the next page - - 3

4 8. Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, then listen to the frequency of the sound reflected from their prey to determine the prey's speed. (The "horseshoe" that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight). a. A Rhinolophus flying at speed v bat emits sound of frequency f bat ; the sound it hears reflected from an insect flying at speed v ins toward it has a frequency f r. Assume the speed of sound to be v s. Express f r in terms of v bat, f bat, v ins and v s. 9. A thin beam of white light is in vacuum directed at a flat sheet of silicate flint glass, thickness d = 9.1 cm, at an angle of 20.0 o to the surface of the sheet. Due to dispersion in the glass, the beam is spread out as shown in a spectrum. The index of refraction for silicate flint glass for blue and red light is 1.66 and 1.61 respectively. The index of refraction in vacuum is S a. What will be the distance S between the red and the blue part of the spectrum, as shown in the figure? - - the exam continues with a faculty/major- specific exercise - - 4

5 Faculty/major- specific exercise Faculty TN and ST, and major TWsk 10. You are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you are a good student, you know what to do. You measure the diameter of the wheel to be D and find that it has a mass M D. You mount the wheel, using frictionless bearings, on a horizontal axis through the wheel's center. You wrap a light rope around the wheel and hang a mass m from the free end of the rope. You release the mass from rest; the mass descends and the wheel turns as the rope unwinds. The gravitational acceleration is g. You find that the mass m has speed v after it has descended over a distance L. a. What is the moment of inertia of the wheel for an axis perpendicular to the wheel at its center? Express your answer in the given Faculty EE (major EE and AUT) 10. The Bohr model for the hydrogen atom leads to discrete energy states E! for the electron given by E! =!!"!".!"!" =, where R is!!!! the Rydberg constant with value m - 1, c is the velocity of light with value m/s, and h is Planck s constant with value Js. An electron jumps from the energy band at n=3 to the energy band at n=1. a. Compute the amount of energy that is released due to the transition and compute the wavelength of the photon that is generated. b. Sketch the curve of the Fermi- Dirac distribution, given by f E =!! (!!!")/!"!!, as a function of energy for the temperature T=0K and T=293K. Indicate the Fermi level Ef in the plot and explain what the Fermi- Dirac distribution expresses. 5

6 Faculty BMT (major BMT and MWT) 10. An adventurous archaeologist of mass m crosses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. As he stops to rest at the middle of the rope, the rope makes an angle θ with the horizontal plane, see figure below. The rope has a diameter d and a Young s modulus Y. The acceleration constant is equal to g. a. Express the strain in the rope in the quantities given. Major INFS/W and faculty IE&IS 10. An airplane flies in a loop (a circular path in a vertical plane) of radius R. The pilot's head always points toward the center of the loop. The speed of the airplane is not constant; the airplane goes slowest at the top of the loop and fastest at the bottom. The gravitational constant is g. a. At the top of the loop, the pilot feels weightless. What is the speed of the airplane at this point? Express your answer in the given 6