1 FOUNDATION STUDIES EXAMINATIONS January 2016 PHYSICS Seester 2 Exa July Fast Track Tie allowed 2 hours for writing 10 inutes for reading This paper consists of 4 questions printed on 11 pages. PLEASE CHECK BEFORE COMMENCING. Candidates should subit 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 INFORMATION a b = ab cos θ a b = ab sin θ ĉ = v dr dt i j k a x a y a z b x b y b z a dv dt v = a dt r = v dt v = u + at a = gj s = rθ x = ut + 1 2 at2 v = u gtj v = rω v 2 = u 2 + 2ax r = ut 1 2 gt2 j a t = rα a c = ω 2 r = v2 r p v N1 : N2 : if F = 0 then δp = 0 F = a N3 : F AB = F BA W = g F r = µr g = acceleration due to gravity = 10 s 2 Φ = E da = q ɛ 0 C q V C = Aɛ d E = 1 q 2 = 1qV = 1CV 2 2 C 2 2 C = C 1 + C 2 1 C = 1 C 1 + 1 C 2 R = R 1 + R 2 1 R = 1 R 1 + 1 R 2 V = IR V = E IR P = V I = V 2 = R I2 R K1 : In = 0 K2 : (IR s) = (EMF s) F = q v B F = i l B df = i dl B τ = ni A B τ r F v = E B r = q E BB 0 r = v qb Fx = 0 Fy = 0 τp = 0 T = 2π KE Bq ax = R2 B 2 q 2 2 W r 2 r 1 F dr W = F s KE = 1 2 v2 P E = gh db = µ 0 i dl ˆr 4π r 2 B ds = µ0 I µ0 = 4π 10 7 NA 2 P dw dt = F v φ = area B da φ = B A F = kx P E = 1 2 kx2 ɛ = N dφ dt ɛ = NABω sin(ωt) dv v e = d v f v i = v e ln( i f ) F = v e d dt F = k q 1q 2 r 2 k = 1 4πɛ 0 ɛ 0 = 8.854 10 12 N 1 2 C 2 E li δq 0 ( δf δq ) 9 10 9 N 2 C 2 E = k q r 2 ˆr f = 1 T ω 2πf y = f(x vt) k 2π λ v = fλ y = a sin k(x vt) = a sin(kx ωt) = a sin 2π( x t ) λ T P = 1 2 µvω2 a 2 v = s = s sin(kx ωt) F µ V W q E = dv dx V = k q r p = p cos(kx ωt)
3 I = 1 2 ρvω2 s 2 n(db s) 10 log I 1 I 2 = 10 log I I 0 where I 0 = 10 12 W 2 ( ) v±v f r = f r s v v s where v speed of sound = 340 s 1 1 λ = ke2 2a 0 ( 1 n 2 f 1 n 2 i ) = R H ( 1 n 2 f 1 n 2 i (a 0 = Bohr radius = 0.0529 n) (R H = 1.09737 10 7 1 ) (n = 1, 2, 3...) (k 1 4πε 0 ) E 2 = p 2 c 2 + ( 0 c 2 ) 2 ) y = y 1 + y 2 E = 0 c 2 E = pc y = [2a sin(kx)] cos(ωt) λ = h p (p = 0v (nonrelativistic)) N : x = ( λ 2 ) AN : x = ( + 1 2 )( λ 2 ) x p x h π E t h π ( = 0, 1, 2, 3, 4,...) y = [2a cos( ω 1 ω 2 2 )t] sin( ω 1+ω 2 2 )t f B = f 1 f 2 y = [2a cos( k 2 )] sin(kx ωt + k 2 ) = d sin θ Max : = λ Min : = ( + 1 2 )λ I = I 0 cos 2 ( k 2 ) E = hf c = fλ KE ax = ev 0 = hf φ L r p = r v L = rv = n( h 2π ) δe = hf = E i E f r n = n 2 ( h 2 4π 2 ke 2 ) = n 2 a 0 E n = ke2 2a 0 ( 1 ) = 13.6 n 2 n 2 ev dn dt = λn N = N 0 e λt R dn dt T 1 2 MATH: = ln 2 = 0.693 λ λ ax 2 + bx + c = 0 x = b± b 2 4ac 2a y dy/dx ydx x n nx (n 1) 1 n+1 xn+1 e kx ke kx 1 k ekx sin(kx) k cos(kx) 1 cos kx k 1 cos(kx) k sin(kx) sin kx k where k = constant Sphere: A = 4πr 2 CONSTANTS: V = 4 3 πr3 1u = 1.660 10 27 kg = 931.50 MeV 1eV = 1.602 10 19 J c = 3.00 10 8 s 1 h = 6.626 10 34 Js e electron charge = 1.602 10 19 C particle ass(u) ass(kg) e 5.485 799 031 10 4 9.109 390 10 31 p 1.007 276 470 1.672 623 10 27 n 1.008 664 904 1.674 928 10 27
PHYSICS: Seester 1 Exa. July Fast Track 2015 4 Question 1 ( (1 + 1 + 3 + 3 + 3 + 2) + (4 + 3) = 20 arks): Part (a): y R v W 4 z 3 2 S x Figure 1 A bead of ass = 50 g slides down under its own weight force along a wire RS, as illustrated in Figure 1. It takes the bead 1.2 s to reach the botto. Neglect any friction. Express the weight force F in ters of the unit vectors i, j and k. Find the displaceent vector s along RS in ters of the unit vectors i, j and k. (iii) Find the work done W by the force F, given that W = F s (iv) Find the final speed of the bead just before it reaches the botto. (v) What is the unit vector along RS in ters of the unit vectors i, j and k? (vi) Express the final velocity vector v of the bead along RS in ters of the unit vectors i, j and k.
PHYSICS: Seester 1 Exa. July Fast Track 2015 5 Part (b): A 1 0.1s 15/s B Figure 2 The diagra shows ball A being dropped fro a building and at the sae tie ball B is thrown up with an initial velocity of 15 /s. Ball A will take 0.1 s to pass a 1 high window. Neglect any air resistance. Find the tie for ball A to reach the botto of the window fro the oent it was dropped. What is the height ball B will achieve in that tie interval?
PHYSICS: Seester 1 Exa. July Fast Track 2015 6 Question 2 ( (3 + 5 + 2) + (4 + 2 + 4) = 20 arks): Part (a): 2 μ table 4 Figure 3 A pulley syste is set up as shown in Figure 3. There is friction only between the table and the ass 2. Assue that the pulleys are assless and frictionless. The entire syste will ove with an acceleration a. Draw a labeled diagra of each of the blocks of the set-up showing the individual forces that act on each. Label also the acceleration of each block. Write a set of Newton s laws of otion for each of the asses. (iii) Find an expression for the acceleration, a, in ters of, µ, and g.
PHYSICS: Seester 1 Exa. July Fast Track 2015 7 Part (b): A 4 wire 4 μ=0 Figure 4 x B A bea AB of ass 50 kg and length L leans against a window, as shown in Figure 4. There is no friction between the bea and floor. The bea is held to the wall via a wire with a axiu tension of 150 N. The reaction at A is perpendicular to the bea. A cat of ass 6 kg is clibing up the bea. The wire is just about to break and the bea will slip when the cat is at a distance x fro B. Draw a labeled diagra showing all of the forces that will act on the bea. State the static equilibriu conditions. (iii) Find how far up the bea the cat will be able to go before the bea slips.
PHYSICS: Seester 1 Exa. July Fast Track 2015 8 Question 3 ( 6 + (1 + 4 + 4) = 15 arks): Part (a): H spring Figure 5 A block of ass is pushed against a spring with a spring constant k. The spring is copressed by a distance of y. When released, the block will be ejected upwards. There will be a total 10% loss of its initial energy as the block travels out of the hole. Use conservation of energy principle to find the axiu height H reached by the block.
PHYSICS: Seester 1 Exa. July Fast Track 2015 9 Part (b): 5/s before collision Figure 6 2/s 30 o 2/s θ after collision v Figure 6 shows three blocks of equal ass. The first block will collide with the other two stationary blocks, as shown. The initial block will keep travelling in its original direction after the collision. The other two blocks will ove of with different velocities and angles. State the principle/law that will be used. Find the velocity v of the block just after ipact. (iii) Is the collision elastic? State your reasoning.
PHYSICS: Seester 1 Exa. July Fast Track 2015 10 Question 4 ( (1 + 1 + 2) + 4 + (2 + 2 + 3) = 15 arks): Part (a): A wave with a function y = 2 sin(20x 400t) travels down a taut wire which is under a tension T. length of µ = 0.25 kg/. The wire has a ass per unit State the frequency of the wave. Find the velocity of the wave. (iii) What is the tension T for such a wave to travel through it? Part (b): It is given that the net force F acting on any body is dependent on the ass of the body, its speed v and the tie duration t that the force acts. Use diensional analysis to find this dependence.
PHYSICS: Seester 1 Exa. July Fast Track 2015 11 Part (c): t = 0s t = 2s r = 0.5 x Figure 7 A ass is rotating on a turn-table without slipping. It starts fro rest and after 2 s, the ass has an angular velocity of π 6 rad/s. Find its angular acceleration. What is the angular displaceent of the ass in that tie interval? (iii) Find the position vector of the ass at tie t = 2 s, in ters of the unit vectors i, j and k. END OF EXAM