FOUNDATION STUDIES EXAMINATIONS November PHYSICS Semester Two February Main

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FOUNDATION STUDIES EXAMINATIONS November 203 PHYSICS Semester Two February Main Time allowed 2 hours for writing 0 minutes for reading This paper consists of 5 questions printed on 0 pages.

1 FOUNDATION STUDIES EXAMINATIONS November 203 PHYSICS Semester Two February Main Time allowed 2 hours for writing 0 minutes for reading This paper consists of 5 questions printed on 0 pages. PLEASE CHECK BEFORE COMMENCING. Candidates should submit answers to ALL QUESTIONS. Marks on this paper total 70 Marks, and count as 35% of the subject. Start each question at the top of a new page.

2 2 INFORMATION a b = ab cos a b = ab sin ĉ = v dr dt i j k a x a y a z b x b y b z a dv v = R a dt r = R v dt dt v = u + at a = gj x = ut + 2 at2 v = u gtj v 2 = u 2 +2ax r = ut 2 gt2 j s = r v = r! a =! 2 r = v2 r p mv N : if P P F =0then p = 0 N2 : F = ma N3 : F AB = F BA W = mg F r = µr g =accelerationduetogravity=0ms 2 = H E da = P q 0 C q V C = A d E = q 2 = qv = CV 2 2 C 2 2 C = C + C 2 C = C + C 2 R = R + R 2 R = R + R 2 V = IR V = E IR P = VI = V 2 = R I2 R P K : P In =0 K2 : (IR 0 s)= P (EMF 0 s) F = q v B F = i l B df = i dl B = ni A B r F v = E B r = m q E BB 0 r = mv qb P Fx = 0 P Fy = 0 P P = 0 T = 2 m KE Bq max = R2 B 2 q 2 2m W R r 2 r F dr W = F s KE = 2 mv2 PE = mgh db = µ 0 i dl ˆr 4 r 2 H P B ds = µ0 I µ0 =4 0 7 NA 2 P dw dt = F v = R area B da = B A F = kx PE = 2 kx2 dv v e = dm m v f v i = v e ln( m i m f ) F = v e dm dt F = k q q 2 r 2 k = Nm 2 C 2 0 = N m 2 C 2 E lim q!0 F q E = k q r 2 ˆr = N d dt = NAB! sin(!t) f = k 2 T! 2 f v = f y = f(x vt) y = a sin k(x vt) =a sin(kx!t) = a sin 2 ( x t ) T P = 2 µv!2 a 2 v = s = s m sin(kx!t) q F µ V W q E = dv dx V = k q r p = p m cos(kx!t)

3 3 I = 2 v!2 s 2 m = ke2 2a 0 ( n 2 f )=R n 2 H ( i n 2 f ) n 2 i n(db 0 s) 0 log I I 2 =0log I I 0 where I 0 =0 2 Wm 2 v±v f r = f r s v v s where v speed of sound = 340 m s (a 0 = Bohr radius = nm) (R H = m ) (n =, 2, 3...) (k 4 " 0 ) E 2 = p 2 c 2 +(m 0 c 2 ) 2 y = y + y 2 E = m 0 c 2 E = pc y =[2a sin(kx)] cos(!t) N : x = m( 2 ) AN : x =(m + 2 )( 2 ) (m =0,, 2, 3, 4,...) y =[2a cos(!! 2 2 )t]sin(! +! 2 2 )t f B = f f 2 y =[2a cos( k 2 )] sin(kx!t + k 2 ) =d sin Max : =m Min : =(m + 2 ) I = I 0 cos 2 ( k 2 ) E = hf c = f KE max = ev 0 = hf L r p = r mv L = rmv = n( h 2 ) E = hf = E i E f r n = n 2 ( h mke 2 )=n 2 a 0 E n = ke2 2a 0 ( )= 3.6 n 2 n 2 ev = h p (p = m 0v (nonrelativistic)) h h x p x E t dn dt = N N = N 0 e t R dn dt T 2 MATH: = ln 2 = ax 2 + bx + c =0! x = b±p b 2 4ac 2a R y dy/dx ydx x n (n ) nx n+ xn+ e kx ke kx k ekx sin(kx) k cos(kx) cos kx k cos(kx) k sin(kx) sin kx k where k = constant Sphere: A =4 r 2 CONSTANTS: V = 4 3 r3 u = kg =93.50 MeV ev = J c = ms h = Js e electron charge = C particle mass(u) mass(kg) e p n

4 PHYSICS: Semester Two. February Main Question ( (6+) + (+3+2+)= 4 marks): Part (a): I i 4 V 3 Ω 5 Ω 2 Ω 3 V 2 V 6 Ω Figure : For the circuit shown in Figure : Use Kirchho s rules to determine the magnitude and direction of the current in the 2 resistor. What is the total power dissipated in the circuit?

5 PHYSICS: Semester Two. February Main Part (b): Two charges Q =3µC andq = 2 µc are positioned as shown in Figure 2 Q 4 m q 90 3 m C Figure 2: Calculate: (iii) (iv) the magnitude of the Coulomb force acting on the charge q the electric feld vector at point C the scalar potential at point C the work done in placing a third charge of µc atpointc

6 PHYSICS: Semester Two. February Main Question 2 ( (2+2+8) + (2+2) = 6 marks): Part (a): AchargeQ is distributed uniformly over a sphere of radius R. Draw a diagram clearly showing the sphere and the shape of the electric field around and inside it Clearly show on your diagram a Gaussian surface suitable for determining the electric field strength E at a distance r from the centre of the sphere (iii) Use this surface and Gauss Law to determine an expression for the electric field strength E at a distance r from the centre of the sphere, where r<r.besuretoexplain your steps, as marks will be given for this. Part (b): AlongstraightwirecarriesacurrentI. Draw a clear diagram showing the magnetic field flux lines around the wire. Show on your diagram an Amperian path, which you could use to determine the magnetic field strength B at a distance r from the wire.

7 PHYSICS: Semester Two. February Main Question 3 ( (4++) + (2+2++) = 2 marks): Part (a): Aprotontravelsataspeedofv =0 5 m/s and enters a region of uniform magnetic field Bata90degreeangleasshownbelow. B θ = 60 v = 00,000 m/s d = 5 mm Figure 3: It leaves the field at an angle of 60 degrees to its initial direction and at a point displaced d =5mmfromitsoriginalpath. Calculate (iii) the magnetic field strength B the work done on the proton by the magnetic field the de Broglie wavelength of the proton before entering the field.

8 PHYSICS: Semester Two. February Main Part (b): ArectangularmetallooptravellingataspeedV enters a region of uniform magnetic field B as shown in in Figure 4. V B R b a Figure 4: If the loop begins to enter the field at time t =0,writedownanexpressionfor the magnetic flux through the loop at time t, intermsoftheparametersgiven. Hence determine a formula for the magnitude of the current i flowing in the loop at time t. (iii) What is the direction of this current i? (iv) At what time will the current in the loop become zero?

9 PHYSICS: Semester Two. February Main Question 4 ( (2+2+2) + (2+2) + (2+2) = 4 marks): Part (a): The work function of magnesium is 3.66 ev. Calculate the cuto wavelength of a photocell containing a magnesium surface. When light of wavelength 400 nm is directed on to this photocell, determine: the stopping voltage that would be measured in the photocell (iii) the maximum speed of the emitted electrons Part (b): ABalmerseries(iewithn final =2)photonismeasuredtohaveawavelengthof486nm. What was the value of n initial for this transition? How much energy is required to remove an electron in this n initial state from the Hatom? Part (c): Calculate the rest mass energy of a neutron What is the momentum of a neutron with energy equal to 5 times this rest mass energy?

10 PHYSICS: Semester Two. February Main Question 5 ( (3+2+2) + (2+5) = 4 marks): Part (a): While tidying up in their lab, some scientists find a mysterious black box labelled DAN- GER - RADIOACTIVE at the back of a cupboard. They immediately measure the activity of the box to be 200 MBq. Exactly one week later a second measurement is taken, of 90 MBq. Calculate the half-life of the box. How many radioactive nuclei were present at the time of the first measurement? (iii) The lab s safety regulations state that the maximum activity of material that can be thrown into the rubbish is 0. MBq. How much longer after the second measurement must the box be stored before it can be safely disposed of? Part (b): Identify the mystery particle X in the following reaction: 2 H+ 6 3Li! 4 2He + X Calculate the Q-value for this reaction (express your answer in MeV) Masses that may be useful (all in u) H H H He He Li Li END OF EXAM

FOUNDATION STUDIES EXAMINATIONS June PHYSICS Semester One February Main

FOUNDATION STUDIES EXAMINATIONS June 203 PHYSICS Semester One February Main Time allowed 2 hours for writing 0 minutes for reading This paper consists of 4 questions printed on 0 pages. PLEASE CHECK BEFORE