Principle of Conservation - Physics - Solved Paper, Exams of Physics

Download Principle of Conservation - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! 1 2011 Leaving Cert Physics Solutions (Higher Level) 2011 Question 1 A student carried out an experiment to verify the principle of conservation of momentum. The student adjusted the apparatus till a body A was moving at a constant velocity u. It was then allowed to collide with a second body B, which was initially at rest, and the two bodies moved off together with a common velocity v. The following data were recorded: mass of body A ........... = 230 g mass of body B ........... = 160 g velocity u .................... = 0.53 m s–1 velocity v .................... = 0.32 m s–1 (i) Draw a labelled diagram of the apparatus used in the experiment. Track/means of coalescing, two trolleys, labelled means of measuring time/velocity (e.g. motion sensor) (ii) What adjustments did the student make to the apparatus so that body A would move at constant velocity? Adjust gradient of track, lubricate trolley wheels, polish/brush track, clear holes (air track), etc. (iii)How did the student know that body A was moving at constant velocity? Dots on the ticker tape were equally spaced / same time interval shown by both light gates / horizontal line on v vs. t graph (datalogging method) (iv) Describe how the student measured the velocity v of the bodies after the collision. (v) Using the recorded data, show how the experiment verifies the principle of conservation of momentum. momentum = mass × velocity initial momentum = (0.230)(0.53) = 0.1219 final momentum = (0.390) (vi) How could the accuracy of the experiment be improved? Use digital balance / select more dots / select greater distance/displacement /avoid parallax error 2011 Question 2 During an experiment to verify Boyle’s law, the pressure of a fixed mass of gas was varied. A series of measurements of the pressure p and the corresponding volume V of the gas was recorded as shown. The temperature was kept constant. (i) Draw a labelled diagram of the apparatus used in the experiment. (ii) How was the pressure of the gas varied during the experiment? (iii)Describe how the pressure and the volume of the gas were measured. (iv) Why should there be a delay between adjusting the pressure of the gas and recording its value? (v) Draw a suitable graph to show the relationship between the pressure and the volume of a fixed mass of gas. (vi) Explain how your graph verifies Boyle’s law. p/kPa 325 300 275 250 200 175 150 125 V/cm3 12.1 13.0 14.2 15.5 19.6 22.4 26.0 31.1 2 5 2011 Question 6 (a) Define the moment of a force. Moment of a force = force × perpendicular distance between the force and the fulcrum When the toy is knocked over, it always returns to the upright position. Explain why this happens. (toy non-vertical) c.g. has a (turning) moment about fulcrum / point of support/contact / (c.g. has) zero turning moment when toy is in vertical position (b) State the conditions necessary for the equilibrium of a body under a set of co-planar forces. Algebraic sum of the forces = zero Sum of the moments about any point = zero Three children position themselves on a uniform see-saw so that it is horizontal and in equilibrium. The fulcrum of the see-saw is at its centre of gravity. A child of mass 30 kg sits 1.8 m to the left of the fulcrum and another child of mass 40 kg sits 0.8 m to the right of the fulcrum. Where should the third child of mass 45 kg sit, in order to balance the see-saw? 30g(1.8) = 40g(0.8) + 45g(x) x = 0.488 m / 0.49 m / 49 cm (c) A simple merry-go-round consists of a flat disc that is rotated horizontally. A child of mass 32 kg stands at the edge of the merry-go-round, 2.2 metres from its centre. The force of friction acting on the child is 50 N. Draw a diagram showing the forces acting on the child as the merry-go-round rotates. What is the maximum angular velocity of the merry-go-round so that the child will not fall from it, as it rotates? F = mω2r 50 = 30 ω2(2.2) ω = 0.842 rad s-1 If there was no force of friction between the child and the merry-go-round, in what direction would the child move as the merry-go-round starts to rotate? The child would remain stationary / any appropriate answer. 6 Question 7 (a) (i) When making a hot drink, steam at 100 °C is added to 160 g of milk at 20 °C. If the final temperature of the drink is to be 70 °C, what mass of steam should be added? You may ignore energy losses to the surroundings. energy gained by the milk = energy lost by the steam when condensing + energy lost by this condensed water cooling down (mcΔθ)m = (ml)steam + (mcΔθ)cond (0.160)(3.90×10-3)(50) = ms(2.34×106) + ms(4.18×103)(30) 𝑚𝑠 = 31.2×103 2.4654×106 = 12.655×10-3 kg = 12.66 g (ii) A metal spoon, with an initial temperature of 20 °C, is then placed in the hot drink, causing the temperature of the hot drink to drop to 68 °C. What is the heat capacity of the spoon? You may ignore other possible heat transfers. It looks like we are missing a value for the mass of the spoon, but we are being asked to calculate the heat capacity (C), not the specific heat capacity (c). The relationship between the two is as follows: C = mc Energy gained by the spoon = energy lost be the hot drink (CΔθ)spoon = (mcΔθ)hot drink 48C = (0.17266)(4.05×103)(2) = 1.3985×103 C = 29.14 J K-1 (b) (i) Name two processes by which a hot drink cools. (ii) How is the energy lost by each of these processes reduced for a hot drink supplied in a disposable cup? Conduction – The material the cup is made from is a good insulator Evaporation – use a lid Convection – Use a lid /insulation (c) (i) A thermocouple is used to measure the temperature of the steam. How would you demonstrate the principle of operation of a thermocouple? One junction (the reference junction) is held in cold water. The other junction is then heated Observation: e.g. emf /voltage is observed. (ii) Describe how to establish a calibration curve for a thermocouple. • Hold one junction at constant temperature, • Hold the other junction in water with beside an (already calibrated) thermometer. • Heat the water (in steps of 10 oC approx) and note temperature and emf values each time. • Plot a graph of emf vs. Temperature. 7 2011 Question 8 (a) Destructive interference can occur when waves from coherent sources meet. Explain the underlined term. Coherent waves are waves which are the same frequency (or wavelength) and are in phase.in phase / constant phase difference 3 Give two other conditions necessary for total destructive interference to occur. The waves must have the same amplitude and be out of phase by 1800 (crests over troughs). The diagram shows a standing wave in a pipe closed at one end. The length of the pipe is 90 cm. (i) Name the points on the wave labelled P and Q. P represents a node, Q represents an anti-node. (ii) Calculate the frequency of the standing wave. 5𝜆 4 = 0.90 𝑚 λ = 0.720 m v = fλ 𝑓 = 340 0.720 f = 472.2 Hz (iii) What is the fundamental frequency of the pipe? 𝜆 4 = 0.90 λ = 3.60 m 𝑓0 340 3.60 f0 = 94.44 Hz The clarinet is a wind instrument based on a pipe that is closed at one end. What type of harmonics is produced by a clarinet? Odd harmonics 2011 Question 8 (b) An audio speaker at a concert emits sound uniformly in all directions at a rate of 100 W. Calculate the sound intensity experienced by a listener at a distance of 8 m from the speaker. 𝑆𝐼 = 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 𝑆𝐼 = 100 4𝜋82 SI = 0.124 W m-2 The listener moves back from the speaker to protect her hearing. At what distance from the speaker is the sound intensity level reduced by 3 dB? (speed of sound in air = 340 m s–1) SIL decreased by 3dB means SI was halved. 0.062 = 100 4𝜋𝑅2 𝑅2 = 100 4𝜋(0.062) R = 11.33 m 10 2011 Question 10 (a) (i) List three quantities that are conserved in nuclear reactions. Momentum, charge, mass-energy (ii) Write an equation for a nucleus undergoing beta-decay. (iii)In initial observations of beta-decay, not all three quantities appear to be conserved. What was the solution to this contradiction? The discovery of the neutrino which accounted for the missing momentum. (iv) List the fundamental forces of nature in increasing order of their strength. gravitational < weak (nuclear) < electromagnetic < (strong) nuclear (v) Which fundamental force of nature is involved in beta-decay? The weak force. (vi) Why are new particles produced in the collision? The kinetic energy of the protons is converted into mass. (vii) Write an equation to represent the collision. p + p → p + p + 𝜋P+ + π- (viii) Show that the kinetic energy of each incident proton must be at least 140 MeV for the collision to occur. Mass of π+ = 273 me = 273(9.109×10-31) kg E = 2mec2 E = 2(2.4869×10-28)(3×108)2 = 44.76 ×10-12 J 𝐸 = 44.76 × 10−12 1.602 × 10−19 E = 279.94 ×106 eV ≈ 280 MeV This is the total kinetic energy that must be available to produce the two pions so the energy each proton has must be greater than 140 MeV. 11 2011 Question 12 (a) State Hooke’s law. For a stretched string the restoring force is proportional to displacement A body of mass 250 g vibrates on a horizontal surface and its motion is described by the equation a = – 16 s, where s is displacement of the body from its equilibrium position. The amplitude of each vibration is 5 cm. Why does the body vibrate with simple harmonic motion? The acceleration is proportional to the displacement Calculate the frequency of vibration of the body? ω2 = 16 ω = 4 F = ω/2π F = 0.64 Hz s-1 What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s motion? a max = (–)16(0.05) = 0.80 (Fmax occurs when acceleration / displacement is a maximum) Fmax = (0.250)(0.80) = 0.20 N Fmin = 0 2011 Question 12 (b) State the laws of refraction of light. The incident ray, refracted ray and normal all lie in same plane sin i/sinr is a constant A lamp is located centrally at the bottom of a large swimming pool, 1.8 m deep. Draw a ray diagram to show where the lamp appears to be, as seen by an observer standing at the edge of the pool. At night, when the lamp is switched on, a disc of light is seen at the surface of the swimming pool. Explain why the area of water surrounding the disc of light appears dark. No light emerges from this area of the pool due to total internal reflection Calculate the area of the illuminated disc of water. 𝜂 = 1 sin 𝑖𝑐 η = 1.33 ic = 48.760 radius of disc = r = 1.8 tan(48.76) r = 2.053 m area = πr2 = 13.24 m2 12 2011 Question 12 (d) (i) Name a suitable detector. GM tube (linked with a ratemeter/scaler)/ Solid state detector (ii) Describe how the reading on the detector may vary as the paper passes by. The count rate would decrease with increasing paper thickness. (iii)Why would the radioisotope Am-241, which emits alpha-particles, not be suitable for this process? The alpha-particles have poor penetrating power so would be easily blocked by the paper. (iv) Calculate the number of atoms present in a sample of Sr-90 when its activity is 4250 Bq. The half-life of Sr-90 is 28.78 years. 1 year = 365 days OR 365.25 days T½ = 0.693 / λ λ = 0.693/ T1/2 λ = 7.77 × 10-10 s-1 / 7.63 × 10-10 s-1 Activity = dN/dt = (-) λN 4250 = 7.77 × 10-10(N) OR 4250 = 7.63 × 10-10(N) N = 5.47 × 1012 (atoms) OR N = 5.57 × 1012 (atoms)