This exam is formed of three exercises in three pages numbered from 1 to 3 The use of non-programmable calculators is recommended.

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1 009 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 exa is fored of three exercises in three pages nubered fro to 3 The use of non-prograable calculators is recoended. First Exercise (7 points) Horizontal elastic pendulu The free end of a spring of horizontal axis (O, i ), of negligible ass and of stiffness = 5 N/, is connected to a solid (S) of ass. (S) is free to ove on a horizontal table and G, center of ass of (S), ay ove along the horizontal axis (O, i ). The horizontal plane through G is taen as a gravitational potential energy reference. A Theoretical study G, shifted fro its equilibriu position O by a distance x 0 in the positive direction along the axis (O, i ), is released fro rest at the instant t 0 = 0. (S) thus perfors siple haronic oscillations of proper period. At an instant t, the abscissa of G is x and the algebraic value of its velocity is v =. ) Give the expression of the echanical energy of the syste [ (S),spring, Earth] at the instant t in ters of,, x and v. ) Derive the second order differential equation in x that governs the otion of G. 3) a) The solution of this equation has the for: x = X cos ( t + ). Deterine, in ters of the given constants, the expressions of and X and calculate the value of. b) Write down the instantaneous expression of v. Deduce the relation between x 0, and the axiu value V of v. B Experiental study I We record, as a function of tie, the variations of the abscissa x of G (figure ) and that of v (figure ). x(c) x V (c/s) (S) G O i x t(s) t(s) 3 Fig. Fig.

2 ) Referring to the graphs of figures and, specify the value of, that of V and the values of x and v at the instant t 0 = 0. ) Deterine the ass of (S). II ) Copy and coplete the table below, where K.E is the inetic energy of (S), P.E e is the elastic potential energy of the spring and M.E is the echanical energy of the syste [(S), spring, Earth] t(s) v(/s) K.E (J) x() P.E e (J) M.E (J) ) Deduce fro the table an indicator that confirs that the oscillations are siple haronic. Second Exercise (7 points) Measureent of the speed of a plane The ai of this exercise is to easure the speed of a plane using the phenoenon of electroagnetic induction. A Motion of a conductor in a unifor agnetic field A hoogeneous etallic rod MN of length l, slides on two horizontal and parallel etallic rails AA' and EE' at a constant velocity v. During its sliding, the rod reains perpendicular to the rails and its center of ass G oves along the axis Ox. At the instant t 0 = 0, G is at O, the origin of abscissa. At an instant t, the abscissa of G is x = OG and v = is the algebraic value of x its velocity. The whole set-up fored of the rod and the rails is put within a unifor agnetic field B perpendicular to the plane of the horizontal rails (Figure ). ) Deterine, at the instant t, the expression of the agnetic flux crossing the surface AMNE in ters of B, l and x, taing into consideration the chosen arbitrary positive direction on figure. ) Explain the existence of an induced e..f e across the ends M and N of the rod. 3) Deterine the expression of the induced e..f e in ters of B, l and v. 4) No current would pass in the rod. Why? 5) Deduce the polarity of the points M and N of the rod and give the expression of the voltage u NM in ters of e.. B Measureent of the speed of a plane M' A plane is flying horizontally along a straight path with a constant velocity v of agnitude v within the unifor agnetic field B of the Earth. The vector B, in the region of flight, has a horizontal coponent of agnitude B h =.3 T and a vertical coponent of agnitude B v = 4 T N' Fig. v

3 The wings of the plane, considered as a straight and horizontal conductor of length l' = M'N' = 30, sweep with tie a surface area (Figure ). ) a) The agnetic flux of B h through the swept surface area is zero. Why? b) Give the expression of the induced e..f e that appears between the ends M' and N' of the wings in ters of B v, l' and v. ) Deterine v, if the potential difference across the wings has a value 0.36 V. Third Exercise (6 points) Sodiu vapor lap Sodiu vapor laps are used to illuinate roads. These laps contain sodiu vapor under very low pressure. This vapor is excited by a bea of electrons that cross the tube containing the vapor. The electrons yield energy to the sodiu atos which give bac this received energy during their downward transition towards the ground state in the for of electroagnetic radiations. Given: h = 6.6 l0-34 J.s; c = s - ; e = C ; n = 0-9. ) What do each of the quantities h, c and e represent? ) The analysis of the eission spectru of a sodiu vapor lap shows the presence of lines of welldeterined wavelengths. The figure below represents soe of the lines of this spectru n n Doublet and n 65.4 n 89.5 n 38. n a) The yellow doublet of wavelengths, in vacuu, = n and = n is ore intense than the other lines. i) To what range: visible, infrared or ultraviolet, does each of the other lines of the spectru belong? ii) The sodiu vapor laps are characterized by the eission of yellow light. Why? b) Is the visible light eitted by the sodiu lap onochroatic or polychroatic? Justify your answer. 3) a) Referring to the diagra of the energy levels of the sodiu ato in the adjacent figure: i) Specify an indicator that justifies the discontinuity of the eission spectru of the sodiu vapor lap. ii) Verify that the eission of the line of wavelength corresponds to the downward transition fro the energy level E to the ground state b) In fact, the energy level E is double, i.e., it is constituted of two energy levels that are very close to each other. Draw a diagra that shows the preceding downward transition as well as the downward transition corresponding to the eission of the radiation of wavelength. 4) The sodiu ato, being in the ground state, is hit successively by the electrons (a) and (b) of respective inetic energies.0 ev and 3.03 ev. a) Deterine the electron that can interact with the sodiu ato. b) Specify the state of the sodiu ato after each ipact. c) Deduce, after ipact, the inetic energy of the electron that interacts with the sodiu ato Energy (ev) E E E 7 E 6 E 5 E 4 E 3 Ground state 3

4 First Exercise (7 points) A ) Expression of the echanical energy: ME = ½ v + ½ x (¼) ) There is a conservation of the echanical energy: ME = constant, then ½ vv' + ½ xx' = 0 3) a) x = X cos( x( x x ) 0 ; as x 0 t + ) ; x = X sin( x = X we obtain: cos( x x 0, while coparing : = t, then: t + ) ; de = 0 x x 0 t + ) By replacing in the differential equation and by = أسس التصحيح الدورة العادية 009 امتحانات الشهادة الثانىية العامة الفرع : علىم الحياة مادة الفيزياء Second Exercise (7 points) A ) = B n Scos = - BS = -Blx. ) The agnetic flux varies, therefore an induced ef e appears across the extreities N and M of the rod (½) d 3) e = - B Bv. 4) The circuit is open i = 0. (½) 5) u NM = e ri (i = 0) u NM = e > 0, The point N is positive and the point M is negative. U NM = e = B v () For t 0 = 0, X cos() = x 0 > 0 and v = - X sin() = 0 = 0 or. But X > 0 cos = thus X = x 0 and = 0 b) v = x = - x0 sin( t) ; V x0 () B I ) = 0.8 s, x 0 = 3 c and V = 3.6 c/s or 0.36 /s At t 0 = 0, x 0 = 3 c and v 0 = 0. () 0.8 ) = = 5 = 0.43 g. II ) (¼) = B ) a) h = B h Scos90 0 = 0 (½) b) V = B V Scos0 0 = B V x d e = - Bv Bvv ) u NM = B v v v = () 300 /s. () t(s) v(/s) KE (J) x() EPE (J) ME (J) ) the echanical energy is approxiately the sae it is constant. (¼)

5 Third Exercise (6 points) ) h: Planc's constant; c: speed of light in vacuu, e: eleentary charge (½) ) a) i) n ultraviolet doain; n, 589 n and 65.4 n visible doain; 89.5 n and 38. n infra-red doain. ii) Because this yellow light is uch ore intense than the others (¼) b) It is polychroatic because it is ade of several radiations of different frequencies (¼) 3) a) i) The discontinuity of the eission spectru is justified by the discontinuous energy levels of the sodiu ato. (½) ii) E = hc 34 8 = = J or E = =. ev. E 9 + E = = ev (¼) b) (½) E E 4) a).0 + (-5.4) = ev, this energy level does not exist the electron (a) does not interact with the ato (-5.4) = -. ev, < -. < -.93 ev, the electron (b) interacts with the ato. () b) In case of the electron (a) the ato reains in the ground state. In case of the electron (b) the ato attains level E. (½) c) For the electron (b), K.E = 3.03 ( ) = 0.9 ev (½)