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 COMMENCING. Candidates should submit answers to ALL QUESTIONS. Marks on this paper total 80 Marks, and count as 35% of the subject. Start each question at the top of a new page.
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 = 4 0 9 0 9 Nm 2 C 2 0 =8.854 0 2 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 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 =0.0529 nm) (R H =.09737 0 7 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 2 4 2 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 = 0.693 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 =.660 0 27 kg =93.50 MeV ev =.602 0 9 J c =3.00 0 8 ms h =6.626 0 34 Js e electron charge =.602 0 9 C particle mass(u) mass(kg) e 5.485 799 03 0 4 9.09 390 0 3 p.007 276 470.672 623 0 27 n.008 664 904.674 928 0 27
PHYSICS: Semester One. February Main 203 4 Question ( 6 + (2+2+2+2+2) + (2+2)= 20 marks): Part (a): The pressure (i.e. force per area) P exerted on the bottom of a water tank is expected to depend on the density of water, the acceleration due to gravity g and the height h of water in the tank. Use dimensional analysis to determine the form of this dependence. Part (b): The equation of a transverse wave on a string is given (in SI units) by: y =0.05 cos 5 (x +30t) Find the (i) (ii) (iii) (iv) (v) amplitude, wavelength, frequency and speed of the wave. If the tension in the string is 9 N, calculate µ, themassperunitlengthofthe string. Part (c): Two ants are sitting on a turntable rotating at a constant rate. Ant is 20 cm from the centre of the turntable and its speed is measured at 5 m/s. Ant 2 s speed is measured to be 3 m/s. (i) How far from the centre of the turntable is Ant 2? (ii) Calculate the centripetal acceleration on Ant.
PHYSICS: Semester One. February Main 203 5 Question 2 ( (3+5+2) + (2+4+4) = 20 marks): Part (a): A bird enclosure at a zoo has the dimensions and position shown in Figure. A parrot is hanging on to the edge of the cage at point X, beforeflyingacrossthecagetopoint Y. (i) Find the displacement vector s of the bird s journey from X to Y. Express your answer in terms of the unit vectors i, j and k. (ii) A wind blows through the cage with a force F = 5 N, directed parallel to the! vector AB. Expressthisforceintermsofthesameunitvectors. (iii) Calculate the work done by the wind on the bird. y 3 m m m Y B F A 2 m O x m X 4 m z Figure :
PHYSICS: Semester One. February Main 203 6 Part (b): AnewinventionconsistsofauniformbeamAB of length 4 m and mass m =0kgwhich is hinged to a support H as shown in Figure 2. A mass M =00kgisattachedtoend A via a massless rope and a massless and frictionless pulley. A mass M 0 is attached to the other end B. (i) State the conditions for static equilibrium of the beam. (ii) Draw a diagram clearly showing all of the forces acting on the beam. (iii) Calculate the largest mass M 0 that can be placed at B before the mass M lifts o the ground and the beam moves. A α α H AH = m AB = 4 m M = 00 kg α = 30 degrees B M M Figure 2:
PHYSICS: Semester One. February Main 203 7 Question 3 ( (4+4+2) + (2+4+4) = 20 marks): Part (a): Astudentthrowsabasketballatanangleof45 as shown in Figure 3. The ball hits a nearby wall normally (i.e. at 90 to the wall) at a height 3.2 mabovethepointofrelease. Assume g =0m/s 2. (i) Calculate the speed V that the ball was initially thrown with. (ii) How far away from the wall was the ball when it was thrown? (iii) If the ball loses 36% of its kinetic energy in the collision with the wall, how far from the wall would the student need to stand to catch the ball without it bouncing on the ground? Assume the catching height is the same as the height from which the ball was thrown. V =? θ = 45 3.2 m Figure 3:
PHYSICS: Semester One. February Main 203 8 Part (b): Another student is playing pool. The white ball is propelled at a speed of 4 m/s toward a stationary red ball, as shown in Figure 4. Both balls have the same mass. After the collision, the red ball is travelling at 3 m/s at an angle to the x-axis, where tan =3/4. (i) Draw a clear, labelled diagram to show the approximate paths of the two balls after the collision. (ii) Calculate the magnitude and direction of the white ball s velocity after the collision. (iii) Is the collision between the balls elastic? Besuretoexplainyouranswer. y v = 3 m/s u = 4 m/s rest x θ (a) before collision (b) after collision Figure 4:
PHYSICS: Semester One. February Main 203 9 Question 4 ( (4+6) + 0 = 20 marks): Part (a): Two blocks of masses M and m (where M > m)areconnectedbyamasslessstring, running over a massless and frictionless pulley as shown in Figure 5. The coe cient of friction between block m and the level surface is µ,whilethecontactbetweenblockm and the incline is frictionless. (i) Draw two diagrams clearly indicating the direction of motion and the forces acting on each block. (ii) Hence use Newton s laws to find an expression for the acceleration a of block M in terms of the parameters shown in the diagram. g M µ m µ = 0 θ Figure 5:
PHYSICS: Semester One. February Main 203 0 Part (b): Ablockofmassm = 2 kg starts at rest and then slides down an inclined plane towards a spring as shown in Figure 6. The upper section AB of the plane is frictionless, and the lower section BC has a coe cient of friction µ =0.2. The block compresses the spring and is pushed back up the plane where it momentarily comes to rest at a point X. Use energy principles to calculate the distance AX. Take g =0m/s 2 in your calculations. rest A µ = 0 2 m B 2 m µ = 0.2 2 m k C Figure 6: END OF EXAM