Class: Life-Science Subject: Physics

Transcription

1 Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study the energy exchange between the syste (B, Earth) and the envronent A O For ths purpose, we launch (B) at te t =, fro O along the lne of greatest slope of the nclned plane Ox, wth an ntal velocty / s. Frctonal forces are v 6 equvalent to f at an opposte drecton to the velocty and of value f =,N.. The echancal energy of the syste (B, Earth) s not conserved. Justfed?. Deterne the echancal energy of the syste at pont O. 3. The ball (B ) passes at a te t by a pont A of abscssa OA = x. a) Deterne as functon of x, the expresson of the echancal energy of the syste (B, Earth) at te t. b ) Deterne as functon of x, the expresson of the gravtatonal potental energy of the syste at te t. 4 a) Draw n the sae syste of axs the curves gvng the varatons, dependng on x, of E and Epp. scale on the x-axs : c. on the energy axs : c.j b ) Use the graph to deterne the speed of (B) at x =. c) Fro the graph, deterne the value X of x for whch the speed s nll. d) The syste (B, Earth) then exchange energy wth the envronent. In what for and how uch?

2 Second year ( 7 pts ) Collson and echancal oscllator - ABC a track s consttuted by a horzontal plane BC, and nclned plane AB by an angle α = 3 wth the horzontal such that AB = 9 c. - A ass less sprng of stffness K= N /. t s fxed at one end n C, the other end beng connected to a punctual sold ( S ) of ass = 4g. The orgn O of the reference poston concdes wth the center of nerta of the sold ( S ) when the sprng s at rest. We neglect all the forces of frcton on (CB). - A punctual sold ( S ) of ass = 6 g placed n A. The horzontal plane BC s taken as the reference level of the gravtatonal potental energy of the syste. (g = /s ). A- Neglectng all frcton on (AB) : S S C B O. (S ), let go fro A wthout ntal speed. Deterne the velocty vector of (S v ) n O.. It copresses the sprng 6 c, then left the ass wthout ntal speed. Deterne the velocty vector of ( S ) at O. 3. ( S ) coes nto a frontal collson wth ( S ) at O ( equlbru poston ), thus forng a sngle ateral pont ( S ). Deterne the velocty vector of ( S ) edately after the shock. 4. The set ( S, R ) for a horzontal sprng pendulu, ( S ) oscllatng around ts equlbru poston O. a) Establsh the dfferental equaton of x of the oscllatons. b ) The soluton of the dfferental equaton s of the for x = X cos ( - Gve the eanng of each ter n ths expresson. ) t T

3 - Deterne the expresson of the proper perod T and calculate ts value. - Deterne nuercally the constants X and own the experence. Derve the nuercal expresson of x (t). B- In fact, the speed of ( S ) n O s / s. frcton are not neglgble n (AB) : a) Calculate the value of the assued constant frcton. b ) the syste ( S, R ) does not oscllate after pact. Justfed? Thrd year ( 7pts ) Use of a col A- Frst Experence A bar agnet ay be oved along the axs of a col ( x axs ), the ternals A and C are connected to an ohc conductor of resstance R = 3Ω N S x A R C The south pole of the agnet s approached to the sde A of the col. Gve the nae of the phenoenon deonstrated n ths experent?. Indcate the nductng source and the nductor. 3. Is there appearance of a current n the crcut? Why? 4. Indcate and justfy the drecton of the nduced current n R. 5. Represent the proper agnetc feld created n the col. B- Second experent The col s fored by N = turns at each secton of S = c, and nternal resstance of r = Ω. Assue that the agnet durng ts oveent through the col creates a unfor agnetc feld parallel to x x of vector B = B. The varaton of B as a functon of te s shown n the graph n the fgure aganst. ) Indcate on the segent the lne of acton and the drecton of the noral vector n ) Deterne the agnetc flux ( ) n the te nterval [, 3s ], [ 3 s, 5 s ] and [ 5s, 7s ]

4 3) Deterne the nduced electrootve force ( e) n the precedng ntervals. 4) Calculate n the prevous ntervals, the ntensty of the nduced current and deterne the drecton of the nduced current n R. 5) Represent the voltage U AC as functon of te. B(T) 3,5,5,5 t(s) O 4 6 Good Luck

5 The Correcton Preer exercse. We have frcton forces. Syste (B, Earth) Reference level E o E o E o c pp v,.36 3,6 j (/) 3. a) we apply the varaton of echancal energy between et t: E E t E o w. f E E o f x 3,6, x (x en ; E en j) (/) b) E pp (A) = gz A = gxsnα = x ( x en ; E en j) (/) 4. a) graph ( - ) b) At x = ; E pp = j et E = 3, j (/) E c = E - E pp = 3, =, j., v, v 3,46 (/), s c) v = E pp =E = 3 j. (/) X = 3. d) heat Q = ΔE = 3,6-3 =,6 j.

6 Second Exercse : A. Syste (S, Earth) Reference level f E s conserved E A = E o E co + E ppo = E ca + E ppa sn v gab v gab sn 9 3 s v 3. s. Syste (S, Earth) E = E o kx v k v x 3 s v 3 s. 3. Collson : the lnear oentu s conserved P av P ap v v v,6.3, 4.3 v

7 ,6 v,6 s 4. a) Syste (S, R, Earth) E = E c + E pél = v kx E de cte dt x x kx k x x b) - X : apltude ; T o : perod ; : ntal phase - x X cos t T x X sn t T T 4 x X cos t T T 4 x x T k 4 T T k,98 s. x - v,6 s

8 x X cos cos v X sn, 6 sn T (/) X,65c,65cos 33,3 x t t B- a) Syste (S, Earth) We have frcton between A et B. We apply the varaton of echancal energy A et B. E w f E E f AB A. v gab sn f. AB,5.,5.4 5.,9.,5,9.f f,5,389 N.,9 b) The speed of S after collson P av P ap v v v, 6., 4.3. v v v

9 The speed of S after collson s null at O then the syste does not oscllate. Thrd exercse A-. Electroagnetc nducton. agnet: source of nductng ; col: nductor 3. when we dsplace the agnet close to the col the value of B vared n the col the flux vared, close crcut ; we have current n the crcut 4. Accordng to Lenz law le pole the current passes n R fro C toa. 5. A B p C B-. Fgure. nb, NSB cos n, B,B Pour t ;3s 3 B t SI t SI Pour t 3 s;5s

10 B 5. 4 T 5 5. wb Pour t 5 s;7s 4 B t SI 3, t SI d 3. Faraday s law e dt t s;3s e = v. t 3 s;5s e =. t 5 s;7s e = - - v. 4. ub u R e r R e r R ,6. A crculate n the postve drecton A crculate n the negatve drecton 5. u R = R u = 4,8. -3 v. u = v. u 3 = v. fgure (/)