CENTRALE COMMISSIE VOORTENTAMEN NATUURKUNDE PHYSICS EXAM. Example exam 3

Transcription

1 CENTRALE COMMISSIE VOORTENTAMEN NATUURKUNDE PHYSICS EXAM Example exam 3 Time : 3 hours Number of questions : 5 Number of answer sheets : 1 (for question 2) Each question must be answered on a separate sheet (because each question is marked by different examiners). State your name on every sheet you hand in. Do not write in pencil and do not use Tipp-Ex or any similar product. Answers without argumentation will not be deemed correct. Additional data can be found in the BINAS science data reference book (5th or 6th edition). The standardized scores are: Question 1 Question 2 Question 3 Question 4 Question 5 : 14 points : 15 points : 11 points : 15 points : 19 points The marks are calculated as follows: mark = score/74 x Information concerning the procedure and progress of the proces of marking see: > verloop van de correctie

2 QUESTION 1 - Braking car A car (mass = 1200 kg) is driving on a test track at a constant speed of 90 km/h. At t = 0, the (front of) the car is at x = 0. At that exact moment, the driver decides to brake for a stationary car a little further along the track. The graph below shows the speed of the car. a. Calculate the force used by the car to brake in the time interval 0 # t # 2.0 s. At t = 2.0 s, the brakes of the car fail. The graph shows that the car was not experiencing any friction when its brakes failed. b. Explain how this is apparent from the graph. At t = 4.5 s, the moving car crashes into the stationary car (mass = 800 kg). c1. Calculate the distance travelled in the interval between t = 0 and t = 4.5 s (the moment of the crash). c2. Explain whether the car could have come to a standstill in time if its brakes had not failed. The cars crumple during the crash and become entangled. They continue down the track (without friction) as a single unit. d. Calculate how much energy was used to crumple the cars. CCVX voortentamen natuurkunde - Example 3 - blz. 1

3 QUESTION 2 - Gasses A cylinder sealed by a moveable piston contains a certain amount of an ideal gas. The piston has a surface area of 3.50 dm2. The scene is represented as a diagram in the figure. The gas passes through a thermodynamic cycle ABCDA, states A, B and C of which are shown on the p-t diagram below. This diagram can also be found on the answer sheet. In state A, the gas has a volume of m3. In state C, the gas has a volume of m3. Transition CD takes place at a constant temperature of 350 K. Transitions DA and BC take place at a constant volume. 4p a. Calculate the amount of gas (in mol) passing through this cycle. b1. Calculate the force exerted on the piston in state A. b2. Calculate the work performed by this force in transition AB. c1. Calculate the pressure in state D. c2. Draw the complete thermodynamic cycle ABCDA in the p-t diagram on the answer sheet. Draw the lines with their correct shape (straight or curved). c3. Describe the shape (using straight or curved) of each drawn line and explain why the line has that shape. CCVX voortentamen natuurkunde - Example 3 - blz. 2

4 QUESTION 3 - Stress in a spoke The wheels of a bicycle are constructed with steel spokes. When the spokes are fitted, they are tensioned like the strings on a musical instrument. In wheel building, this is referred to as pretension. A steel spoke is placed under a 180 MPa pretension stress. The Young modulus of elasticity for the steel used is Pa. The spoke has a cross-section of 2.50 mm2. a. Calculate the tension force in the pretensioned spoke. b. Calculate the strain of the pretensioned spoke. While cycling, the spoke is stretched and compressed during each revolution of the wheel as a result of the gravitational force FZ exercised on the bicycle and its rider. Eventually, the steel is weakened because of this continuous increase and decrease in stress. Even though the tensile strength of the steel is greater than the stress in the spoke while cycling, this weakening may cause the spoke to break. Figure 1 shows the stress in the spoke while cycling. c. Using figure 1, calculate to 3 significant figures the value of the frequency with which the stress changes while cycling. CCVX voortentamen natuurkunde - Example 3 - blz. 3

5 Lifespan N is the number of revolutions the spoke can withstand until it breaks. This lifespan is dependent on the stress amplitude óa of the spoke. The following applies to this stress amplitude: óa = ½ (ómax - ómin) In this equation, ómax and ómin are the maximum and minimum stress occurring in the spoke during one revolution of the wheel. Figure 2 shows the óa-n graph for the spoke. The horizontal axis has a non-linear scale. d1. Calculate the stress amplitude of the spoke. 7 1p d2. Using this amplitude, explain whether the spoke could withstand 1 10 wheel revolutions. 1p The wheel manufacturer claims you will be able to cycle at least 8300 km before breaking a spoke. The diameter of the wheel is 66 cm. e. Calculate the maximum stress amplitude in this case. CCVX voortentamen natuurkunde - Example 3 - blz. 4

6 QUESTION 4 - Wear in a steel bearing To determine the wear in a steel bearing (mass m = 150,0 g), the object is exposed to neutron radiation in a nuclear reactor for a certain amount of time This radiation forms Mn and Fe isotopes in the bearing material. Both isotopes are homogeneously distributed throughout the bearing. Both isotopes decay under emission of beta radiation. 59 a. Write down the decay equation for Fe Immediately after the neutron radiation, the activity of the formed Fe is Bq, and the activity of Mn is Bq. The activity of a certain amount of a radioactive substance is given by: A(t) = A(0) e ët In this equation: A(t) is the activity at time t, A(0) is the activity at time 0, and ë is the decay constant The decay constant for Fe is day, for Mn, the decay constant is 6.48 day. (NB e 2,7183; your calculator has special keys for the e function and In(x).) 59 b1. Calculate the activity of Fe 2.0 days after the radiation of the bearing b2. Demonstrate that the activity of Mn is less than 1.0% of the activity of Fe at that moment. Following radiation, the bearing is installed in a machine. 2.0 days after the end of radiation, the machine is run for six hours. While the machine is running, the bearing experiences wear; it sheds small metal parts which end up in the bearing grease. When the machine stops running, the bearing is taken out. The bearing grease is dissolved, and the metal parts are filtered out. This wear material is placed before the window of a GM tube. The GM tube counts 25% of all the particles emitted during the radioactive decay process. The scene is represented as a diagram in the figure. Without the wear material, the GM tube counts 135 pulses across a test period of 10 minutes. When the wear material is added, the GM tube counts 1820 pulses across a period of 10 minutes. 1p c. Explain why the GM tube detects radiation even before the wear material is introduced. d. Calculate the activity of the wear material. (If you were unable to calculate this part, assume a value of 108 Bq for the remainder of this assignment. Please note that this value is incorrect.) 4p e. Calculate the amount (in grams) of wear material released by the bearing per hour of operation The activity of Mn and Fe decreases rapidly as soon as radiation is stopped, and becomes ever less measurable as a consequence. However, there is still a good reason to wait two days before producing and measuring the wear material. 1p f. Explain this reason. CCVX voortentamen natuurkunde - Example 3 - blz. 5

7 QUESTION 5 - Mercury vapour Source B releases electrons that all have the same energy. They are released into space I, which exclusively contains mercury vapour under low pressure. See Figure 1. Some electrons collide with mercury atoms. When these collisions change the course of the electrons sufficiently, they enter space II via two narrow gaps, S 1 and S 2. A vacuum is maintained in space II as far as possible. a. Using a drawing, explain why the beam in space II becomes narrower as the distance between gaps S and S is increased. 1 2 Figure 2 details a part of space II. K and L are two cylindrically shaped conducting plates. The intention is to move the electrons between the plates along the dotted line shown in Figure 2. To achieve this, the plates are connected to a (controllable) voltage supply. b. Which plate should have the highest potential? Explain your answer. The electrical field strength E between plates K and L along the dotted line can be calculated using the following formula: E = ÄU/d. In this formula, ÄU is the potential difference between the plates and d is the distance between the plates. Electrons with a certain kinetic energy E k move in a uniform circular motion along the dotted line between K and L. The following applies to the kinetic energy Ek of the electrons: E k = ½ (ÄU e R) / d In this equation: R is the radius of the (quarter) circle travelled by the electrons, and e is the elementary charge quantum. 1p c1. Provide the name of the force that occurs as a centripetal force in this example. c2. Prove the above formula for the kinetic energy E of the electrons. In the example, d = 2.00 cm and R = 10.0 cm. Voltage ÄU is set at V. 1p d. Demonstrate that the kinetic energy E k of the electrons that now travel along the dotted line is 50 ev. Continued on the next page k CCVX voortentamen natuurkunde - Example 3 - blz. 6

8 The electrons emitted by source B (see Figure 1) all have an energy of ev. The collisions between these electrons and the mercury atoms in space I can be divided into two types: 1. Elastic collisions. In these collisions, the electrons change direction while retaining almost all of their kinetic energy. 2. Non-elastic collisions. In these collisions, the electrons not only change direction, but also transfer energy to the mercury atoms. To establish how much energy the electrons transfer to the mercury atoms during non-elastic collisions, the voltage between K and L is slowly reduced. The electrons moving along the dotted line at the set voltage are captured by a detector D via a third gap, S 3. See Figure 1. The number of electrons reaching detector D per second at different voltages is shown in Figure 3. The number of electrons counted by D per second (n/t) is plotted on the vertical axis, and the kinetic energy E (calculated using the formula in question c) of the captured electrons is plotted on the horizontal axis. According to the Bohr s atomic theory, mercury atoms can only exist at highly specific energy levels. e. Explain how the result of the experiment described above (see Figure 3) supports this theory. f. Draw the energy level diagram of mercury as can be deducted from this experiment. The mercury vapour emits light. One of the lines in the line spectrum is yellow and has a wavelength of 579 nm. g1. Calculate the energy of a photon in this yellow light. g2. In the diagram you have drawn for question f, indicate with an arrow how the emission of this yellow light is achieved and explain your answer. Alternatively, explain the same using Figure 3. END CCVX voortentamen natuurkunde - Example 3 - blz. 7

9 ANSWERSHEET - QUESTION 2 Name :...