This exam is formed of three exercises in three pages. The use of a non-programmable calculator is allowed

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1 وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسن: الرقن: الدورة اإلستثنائية للعام 0 This exam is formed of three exercises in three pages. The use of a non-programmable calculator is allowed First Exercise (6 points) Determination of the inductance of a coil In order to determine the inductance L of a coil of negligible resistance, we connect this coil in series with a resistor of resistance R = 0 across the terminals of a generator G (Fig. ). The generator G delivers an alternating sinusoidal voltage u AD = u G = U m cost (u G in V, t in s). The circuit thus carries a current i. ) Redraw a diagram of figure (), showing on it the connections of an oscilloscope so as to display the voltage u G across the terminals of the generator and the voltage u R = u BD across the terminals of the resistor. G i Fig. A L N B R D ) Which of these two voltages represents the image of i? Justify your answer 3) In figure, the waveform () represents the variation of u G as a function of time. - Horizontal sensitivity: 5 ms/div. - Vertical sensitivity on both channels: V/div. a) Specify, with justification, which of the waveforms, () or (), leads the other. b) Determine: i. The phase difference between these two waveforms. ii. The angular frequency iii. The maximum value U m of the voltage across G. iv. The amplitude I m of i. div 0.63 div.8 div () () c) Write down the expression of i as a function of time t. div Fig 4) Determine the voltage u AB = u L across the terminals of the coil as a function of L and t.. Fig. 5) Determine the value of L by applying the law of addition of voltages and by giving t a particular value.

2 Second Exercise (7 points) Acceleration of a particle The object of this exercise is to determine the expression of the magnitude of the acceleration of a particle using two methods. The apparatus used is formed of two particles (S ) and (S ) of respective masses m and m, fixed at the extremities of an inextensible string passing over the groove of a pulley. (S ), (S ), the string and the pulley form a mechanical system (S). The string and the pulley have negligible mass. x (S ) may move on the line of greatest slope AB of an inclined plane that makes B (S an angle α with the horizontal AC and ) (S ) O' O (S ) hangs vertically. A h h At rest, (S ) is found at point O at a α x' height h above AC and (S ) is found at C O' at a height h (adjacent figure). At the instant t 0 = 0, we release the system (S) from rest. (S ) ascends on AB and (S ) descends vertically. At an instant t, the position of (S ) is defined by its abscissa x = OS on an axis x Ox confounded with AB, directed from A to B. Take the horizontal plane containing AC as a gravitational potential energy reference. Neglect all the forces of friction. ) Energetic method a) Write down, at the instant t 0 = 0, the expression of the mechanical energy of the system [(S), Earth] in terms of m, m, h, h and g. b) At the instant t, the abscissa of (S ) is x and the algebraic value of its velocity is v. Determine, at that instant t, the expression of the mechanical energy of the system [(S), Earth] in terms of m, m, h, h, x, v, α and g. c) Applying the principle of conservation of mechanical energy, show that : v (m m sin )gx =. (m m ) d) Deduce the expression of the value a of the acceleration of (S ). ) Dynamical method a) Redraw a diagram of the figure and show, on it, the external forces acting on (S ) and on (S ). (The tension in the string acting on (S ) is denoted by T of magnitude T and that acting on (S ) is denoted by T of magnitude T ). b) Applying the theorem of the center of mass ΣFext ma,on each particle, determine the expressions of T and T in terms of m, m, g, α and a. c) Knowing that T = T, deduce the expression of a.

3 Third Exercise (6 points) Provoked Nuclear Reactions The object of this exercise is to compare the energy liberated per nucleon in a nuclear fission with that liberated in a nuclear fusion. Given: Symbol n H 3 H 4 He 35 U 94 Sr A Xe 0 9 Z 54 Mass in u u = 93.5 MeV/c A Nuclear fission The fission of uranium 35 is used to produce energy. ) The fission of one uranium 35 nucleus takes place by bombarding this nucleus by a slow (thermal) neutron of kinetic energy around 0.05 ev.the equation of this reaction is written as : A 9 U 0n ZSr 54Xe 30n a) Calculate A and Z specifying the laws used. b) Show that the energy E liberated by the fission of one uranium nucleus is MeV. c) i) The number of nucleons participating in this reaction is 36. Why? ii) Calculate then E, the energy liberated per nucleon participating in this fission reaction. E ) Each of the obtained neutrons has an average kinetic energy E 0 =. 00 a) In this case, the obtained neutrons do not, in general, provoke fission. Why? b) What then should be done in order to obtain a fission reaction? B Nuclear fusion Nowadays, many researches are performed in order to produce energy by nuclear fusion. The most accessible is the reaction between a deuterium nucleus H and a tritium nucleus 3 H. ) The deuterium and the tritium are two isotopes of hydrogen. Write down the symbol of the third isotope of hydrogen. ) Write down the fusion reaction of a deuterium nucleus with a tritium nucleus knowing that this reaction liberates a neutron and a nucleus A ZX. Calculate Z and A and give the name of the nucleus A X. Z 3) Show that the energy liberated by this reaction is E' =7.596 MeV. 4) Calculate E the energy liberated per nucleon participating in this reaction. C Conclusion Compare E and E and conclude. 3

4 وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات هشروع هعيار التصحيح اهتحانات الشهادة الثانىية العاهة الفرع : علىم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسن: الرقن: الدورة اإلستثنائية للعام 0 First exercise (6 points) Part of the Q. Answer A G i L N B R Ch A Ch B Mark u R = Ri, u R is proportional to i. 3-a u becomes zero before u, thus u = u G leads i (u = u R represents i). 3-b-i 3-b-ii T 5 div rad div = 5 T = 5 (div) 5 ms/div = 5 ms = T π = 5.3 rad/s = 0.79 rd 3-b-iii Um = 4 (div) V/div = 4 V 3-b-iv U Rm =.8 =.8 V ¾ U I m = Rm. 8 = = 0.8 A R 0 3-c i lags u G by 0.79 rad; i = I m cos(t 0.79) i = 0.8 cos (80 t 0.79) 4 u L =L di dt = 70.37L sin (80t 0.79) 5 u G = u R + u L = Ri + u L 4 cos (80 t) =.8 cos (80 t 0.79) 70.37L sin (80 t 0.79) For t = 0 ; L = 0.04 H = 40 mh. D ¾

5 Second exercise (7 points) Part of the Q Answer Mark.a M.E = K.E + P.E g + K.E + P.E g = 0 + m gh m gh.b M.E = KE + P.E g + K.E + P.E g M.E = m v + m g (h + xsinα )+ m v + m g (h x).c m v + m g (h + xsinα )+ m v + m g (h x)= m gh + m gh (m + m ) v = (m m sinα) gx v (m m sin )gx =. (m m ).d Derive the expression of v w.r.t time, we get: (mmsin )g (m va = v msin )g a =. (m m ) (m m ) T A..a.b The relation ΣFext m a applied on S gives: mg + N T m a.. () N mg Projecting () on the axis ox we get : m gsin + T = m a T = m gsin + m a (with a = a = a). The relation ΣFext m a applied on S gives : mg + T ma. () Projecting () on the vertically downward axis we get: m g T = m a T = m g m a. T mg ¾ ¼.c The relation T = T gives: m gsin + m a = m g m a m msin a = ( )g. m m

6 Third exercise (6 points) Part of the Q Answer Mark A..a Conservation of nucleons number: 35 + = 94 + A +3 then A = 39 Conservation of charge number: 9 = Z + 54 then Z = 38 A..b E = Δmc = ( )93.5 Energy = MeV A..c.i We have 35+ = 36 nucleons ¼ E = = 0.76 MeV/nucleon 36 A..a E 0 = = MeV; which is much greater than 0.05 ev 00 A..b They should be slowed down, ¼ B. H ¼ A..c.ii B. 3 A Z 0 H H X n +3 = A + then A = 4 + = Z then Z = The helium nucleus 4 He B.3 E' = Δmc = ( )93.5 = MeV B We have + 3 = 5 nucleons E = = 3.59 MeV/nucleon 5 C E is greater than E ; fusion is more efficient. ¼ 3

This exam is formed of three exercises in three pages. The use of non-programmable calculators is recommended.

This exam is formed of three exercises in three pages. The use of non-programmable calculators is recommended. 011 وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسن: الرقن: الدورة العادية للعام This