ASSOCIATE DEGREE IN ENGINEERING TECHNOLOGY RESIT EXAMINATIONS. Semester 1 July 2012

Transcription

1 ASSOCIATE DEGREE IN ENGINEERING TECHNOLOGY RESIT EXAMINATIONS Semester 1 July 2012 COURSE NAME: ENGINEERING PHYSICS I CODE: PHS 1005 GROUP: ADET 2 DATE: July 4, 2012 TIME: DURATION: 9:00 am 2 HOURS INSTRUCTIONS: 1. This paper consists of SIX questions. 2. Candidates must attempt ANY FOUR questions on this paper. 3. All working MUST be CLEARLY shown. 4. Keep all parts of the same question together. 5. The use of non-programmable calculators is permitted. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO 1

2 Instructions: Answer any FOUR (4) questions. [Question 1] a) Using suitable examples, distinguish between systematic and random errors. [4 marks] b) A student measures the following quantities: A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m, C = 2.5 m/s ± 0.5 m/s, D = 0.10 s ± 0.01 s. Evaluate the error in the following expressions: i. 3A ii. B A iii. C x D [9 marks] c) A particle undergoes three consecutive displacements: d 1 = (15i + 30j + 12k) cm, d 2 = (23i- 14j 5.0k) cm, and d 3 = (-13i = 15j) cm. Find i. The components of the resultant displacement ii. The magnitude of the resultant displacement iii. The angle between the resultant displacement and the z axis [12 marks] [Question 2] (a) i) What is the distinguishing relationship in simple harmonic motion (SHM). [2] (ii) Explain the function of a shock absorber in a car s suspension system and state which degree of damping is best suited for this application. [4] 2

3 (b) For the system shown: At t = 0, x = m b = 0.364Nsm k = 75.0N/m m = 5.00kg i) What degree of damping exists here? [3] ii) What is the period, T of the oscillation? [3] 2(b) iii) What is the fractional decrease in amplitude per cycle? [6] iv) Write the displacement as a function of time. [3] (c) If a simple harmonic oscillator has velocity function of: v = 100πAsin(100πt 0.75π) find: 3

4 i) an expression for displacement, x. [2] ii) an expression for acceleration, a. [2] [Question 3] (a) Define stress and strain. (Include the defining equation or formula). (4 marks) (b) In an experiment to measure Young s modulus, a load of 500kg, hanging from a steel wire of length 3m and cross section 0.20cm 2, was found to stretch the wire 0.4cm above its no-load length. What were the stress, the strain, and the value of Young s modulus for the steel of which the wire was composed? (7 marks) (c) A solid lead sphere of volume 0.50 m 3, dropped in the ocean, sinks to a depth of 2.0 x10 3 m (about1 mile), where the pressure increases by 2.0 x 10 7 Pa. Lead has a bulk modulus of 4.2 x Pa. What is the change in volume of the sphere? (4 marks) (d) Suppose a rocket has a strap-on booster supported by eight horizontal steel bolts, each 9.00 cm in diameter and oriented horizontally. (i) What maximum load can be placed on these bolts before they are sheared off? Assume the load is shared equally by the eight bolts. The ultimate shear strength of steel is 2.50 x10 8 Pa. (ii) If the booster has a mass of 3.00 x 10 5 kg, calculate the shear deformation of one of the bolts if the length of the bolt between rocket and booster is 8.00 cm. (10 marks) (Question 4) (a) (i) State the principle of superposition. (2 marks) (ii) State three conditions that must be satisfied in order that two waves may interfere. (3 marks) (b) The apparatus illustrated in fig. is used to demonstrate two-source interference using light. 4

5 The separation of the two slits in the double slit arrangement is a and the interference fringes are viewed on a screen at a distance D from the double slit. When light of wavelength λ is incident on the double slit, the separation of the bright fringes on the screen is x. (i) 1. Suggest a suitable value for the separation a of the slits in the double slit. 2. Write down an expression relating λ, a, D and x. (2 marks) (ii) Describe the effect, if any, on the separation and on the maximum brightness of the fringes when the following changes are made. 1. The distance D is increased to 2D, keeping a and λ constant. 2. The wavelength λ is increased to 1.5λ, keeping a and D constant. 3. The intensity of the light incident on the double slit is increased, keeping λ, a, and D constant. (6 marks) (c) A wave whose wavelength is 0.30m is travelling a 300m long wire whose total mass is 15kg. If the wire is under tension of 1000N, what are the speed and frequency of this wire? (5 marks) (d) Monochromatic light from a helium laser (λ = nm) is incident normally on a diffraction (Question 5) grating containing 6.00 x 10 3 lines/cm. Find: (i) the angle at one would observe the first-order maximum and (ii) the maximum possible order (7 marks) (a) An ideal gas has its pressure cut in half slowly, while being kept in a rigid wall container. In the process, 1300 kj of heat left the gas. i) How much work was done during this process? [1] ii) What was the change in internal energy of the gas during this process? [2] (b) A nuclear power plant operates at 75 percent of its maximum theoretical (Carnot) efficiency between temperatures of C and C. If the plant produces 5

6 electric energy at a rate of 1.1 GW, how much exhaust heat is discharged per hour? [7] (c) A gas cylinder holds 0.10 mol of O 2 at C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final: i) pressure? [6] ii) temperature? [4] [ γ for a diatomic gas = 1.40] (d) A heat engine with 0.20 mol of a monatomic ideal gas initially fills a 2000 cm 3 cylinder at 600 K. The gas goes through the following closed cycle: Isothermal expansion to 4000 cm 3 Isochoric cooling to 300 K Isothermal compression to 2000 cm 3 4 d) Isochoric heating to 600 K. Sketch a PV graph for this cycle. [5] (Question 6) a) Briefly explain heat transfer by conduction, convection and radiation [6 marks] b) State the factors that affect the rate of heat transfer by conduction. [4 marks] c) A cylindrical rod of cross-sectional area 5.0mm 2 is made by joining a 0.30m rod of silver to a 0.12m rod of nickel. The silver end is maintained at 290K and the nickel end at 440K. given the thermal conductivities of silver and nickel are 0.42kWm -1 K -1 and 91Wm - 1 K -1 respectively, calculate: i. the temperature of the join under steady conditions, and ii. the rate of conduction of heat down the rod State any assumptions you need to make. [15 marks] 6

7 ****END OF PAPER***** ASSOCIATE DEGREE IN ENGINEERING SOLUTIONS SEMESTER DECEMBER COURSE NAME: CODE: [COURSE NAME] [8 CHARACTER COURSE CODE] GROUP: "[AD-ENG 1 OR 2]" DATE: TIME: DURATION: "[EXAM DATE]" "[TIME OF PAPER]" "[LENGTH OF PAPER]" Solutions [Question 1] 7

8 [Question 2] (a) (i) acceleration is directly proportional to negative displacement. [2] ii) A piston situated within a spring is attached to the car s frame is placed in a viscous fluid and the base of is attached to the spring and the car s axle. When the car s spring is displaced by say a pothole, its vibration is damped by the piston in the viscous fluid. [3] The damping attained should be near critical damping so that equilibrium is re-established in the shortest possible time. [1] (b) i) b 2 < 4mk [1] (0.364) 2 < 4(5)(75) therefore system is lightly damped. [2] ii) T I = 4m 2 [1] 4mk b 2 = 4(5) 2 [1] 4(5)(75) (0.364) 2 T I = 1.62s [1] (b) iii) x = x o e- αt [1] x = 0.004e 0.364(1.62)/2(5) [3] x = 3.77X10-3 m [1] 3.77 X 10-3 X100% / 4X10-3 = 94% of amplitude remains [1] iv) x = 0.004e t cos3.88t [3] c) i) x = -Acos(100πt 0.75π) [2] ii) a = (100π) 2 Acos(100πt 0.75π) [2] [Question 3] Solution 8

9 (a) Stress is the force acting per unit cross-sectional area or = F/A [2] Strain is the extension per unit length or = e /l [2] (b) = Pa [3] = [2] = 1.84 x Pa [2] (c) B = -ΔP/(ΔV/V) ΔV = -VΔP/B = x 2.0 x 10 7 / 4.2 x = x 10-4 m 3 [4] (d) (i) Shear stress, F/A = F/πr 2 = 2.50 x10 8 Pa(USS) F = π(4.50 x10-2 ) 2 ( 2.50 x10 8 ) = 1.59 x10 6 N F= 8 F total = 1.27x10 7 N [5] (ii) F total = mg = 3.00x10 5 x 9.80 = 2.94x10 6 N F/A = SΔx/h Δx = (F total /8)h/AS = (1.27x10 7 /8)(0.080)/π(4.50 x10-2 ) 2 ( 8.40 x10 10 ) Δx = 5.51 x10-5 m [5] (Question 4) (a) (i) Principle of Superposition at a point where two or more waves meet, the instantaneous displacement is the vector sum of the individual displacement due to each wave at the point. [2] (ii) Conditions for double slit interference (Any three is enough) 1. Two sources should be coherent 2. Two sources should produced wavetrains that are sufficiently distributed in order to overlap 3. Two sources should be close enough (about 0.5mm for light) for their wavetrains to interfere. 4. The wavetrains should be polarised in the same plane [3] (b) (i) 1. a = 1 mm to 2mm 2. x = Dλ/a [2] (ii) 1. Separation increased to 2x [6] Brightness - decreased 2. Separation increased to 1.5x 9

10 Brightness not affected 3. Separation not affected Brightness - increased (c) = = 140m/s [3] f =v/λ = 140/0.30 = 470 Hz [2] (d) (i) d = 1/6.00 x 10 3 = 1.67 x 10 3 nm sin θ = λ/d = 632.8/1.67 x 10 3 = θ = sin -1 (0.379) = 22.3 [4] (ii) n < d/λ n < 1.67 x 10 3 /632.8 n < 2.6 Maximum possible order, n =2 [3] (Question 5) (a) i) Work, W = 0 as vessel has a fixed volume. [1] ii) ΔQ + ΔW = ΔU [1] As W = 0, ΔQ = ΔU = -1300kJ [1] (b) e ideal = T H - T L [1] T H = X 100% = 32.2% [1] % of Carnot = 75% of 32.2% = 24.1% [2] 24.1% = 1.1 GW X 100% [2] heat Exhaust Heat = 4.56 GW [1] (c) i) P f V f γ = P i V i γ [1] P f = P i V i γ [1] V f γ 10

11 P i V i = nrt i [1] V i = (0.1)(8.31)( ) [1] 3 X 1.01 X 10 5 P f = 3(1.065 X 10-3 ) 1.40 [1] (2.13 X 10-3 ) 1.40 = atm [1] ii) T f V f γ-1 = T i V i γ-1 [1] T f = (423) (1.065 X 10-3 ) 0.40 [2] (2.13 X 10-3 ) 0.40 = 321 K = 48 0 C [1] 11

12 (d) P [5] t 1 = 600 K t 2 = 300 K V / cm (Question 6) Heat transfer by conduction is the transfer of heat energy from one particle to the next through a substance. There is no net movement of mass in conduction. The factors that affect conduction are i. Thermal conductivity (which expresses the type of substance) ii. Surface area of the conducting substance iii. Temperature difference between hot and cool side of conducting substance iv. Thickness of conducting substance 5ci. 343K ii. 0.37W 12