Length of Pendulum - Physics - Solved Paper, Exams of Physics

Download Length of Pendulum - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! 2008 Leaving Cert Physics Solutions (Higher Level) 1 A student investigated the relationship between the period and the length of a simple pendulum. The student measured the length l of the pendulum. The pendulum was then allowed to swing through a small angle and the time t for 30 oscillations was measured. This procedure was repeated for different values of the length of the pendulum. The student recorded the following data: l /cm 40.0 50.0 60.0 70.0 80.0 90.0 100.0 t /s 38.4 42.6 47.4 51.6 54.6 57.9 60.0 Time for 1 swing/ s t2/ s2 l /m 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (i) Why did the student measure the time for 30 oscillations instead of measuring the time for one? To reduce percentage error in measuring the periodic time. (ii) How did the student ensure that the length of the pendulum remained constant when the pendulum was swinging? Use an inextensible string, string suspended at fixed point (e.g. split cork or two coins) (iii) Using the recorded data draw a suitable graph to show the relationship between the period and the length of a simple pendulum. (iv) What is this relationship? t2 is proportional to l (v) Use your graph to calculate the acceleration due to gravity. Slope = 0.25 (ms–2) [range: 0.24 – 0.25 m s–2] g = 9.72 m s–2 [range: 9.4 – 9.9 m s–2] 2 In an experiment to measure the specific latent heat of fusion of ice, warm water was placed in a copper calorimeter. Dried, melting ice was added to the warm water and the following data was recorded. Mass of calorimeter 60.5 g Mass of calorimeter + water 118.8 g Temperature of warm water 30.5 oC Mass of ice 15.1 g Temperature of water after adding ice 10.2 oC (i) Explain why warm water was used. To speed up the melting of the ice / in order to melt a larger mass of ice / (concept of) balancing energy losses before and after the experiment. (ii) Why was dried ice used? To remove any water/melted ice // melted ice would have already gained latent heat //so that only ice is added // so that no water is added (iii) Why was melting ice used? Melting ice is at 0 oC. (iv) Describe how the mass of the ice was found. Final mass of calorimeter + contents minus mass of calorimeter + water. (v) What should be the approximate room temperature to minimise experimental error? 20 0C / midway between initial and final temperatures (of the water in the calorimeter) (vi) Calculate the energy lost by the calorimeter and the warm water. {energy lost = } (mcΔθ )cal + (mcΔθ )warm water = (0.0605)(390)(20.3) + (0.0583)(4200)(20.3) = 5449.6365 / 5449.6 J (vii) Calculate the specific latent heat of fusion of ice. {Energy gained by ice and by melted ice =} (ml)ice + (mcΔθ )melted ice / (0.0151)l + (0.0151)(4200)(10.2) / 0.0151 l + 646.884 (equate:) 0.0151 l + 646.884 = 5449.6365 l = 3.181 × 105 ≈ 3.2 × 105 J kg–1 3 In an experiment to measure the wavelength of monochromatic light, a diffraction pattern was produced using a diffraction grating with 500 lines per mm. The angle between the first order images was measured. This was repeated for the second and the third order images. The table shows the recorded data: Angle between first order images Angle between second order images Angle between third order images 34.20 71.60 121.60 (i) Draw a labelled diagram of the apparatus used in the experiment. See diagram. Plus metre stick (ii) Explain how the first order images were identified. Nearest on either side of the central (zero order) image. (iii) Describe how the angle between the first order images was measured. Measure x between 1st order images Measure D from screen to grating θ = tan-1 (x/D) (iv) Use the data to calculate the wavelength of the monochromatic light. Use nλ = d sinθ 4 A student investigated the variation of the resistance R of a metallic conductor with its temperature θ. The student recorded the following data. θ/oC 20 30 40 50 60 70 80 R/Ω 4.6 4.9 5.1 5.4 5.6 5.9 6.1 (i) Describe, with the aid of a labelled diagram, how the data was obtained. The resistance was read from the ohmmeter, the temperature was read from the thermometer and the readings were varied using the heat source. (ii) Draw a suitable graph to show the relationship between the resistance of the metal conductor and its temperature. (iii) A bar magnet is attached to a string and allowed to swing as shown in the diagram. A copper sheet is then placed underneath the magnet. Explain why the amplitude of the swings decreases rapidly. An emf is induced in the copper because is its experiencing a changing magnetic field. This produces a current. This current has a magnetic field associated with it which opposes the motion of the magnet. (iv) What is th main energy conversion that takes place as the magnet slows down? Kinetic (or potential) to electrical (or heat). (v) A metal loop of wire in the shape of a square of side 5 cm enters a magnetic field of flux density 8 T. The loop is perpendicular to the field and is travelling at a speed of 5 m s–1. How long does it take the loop to completely enter the field? t = dist/velocity = 5 cm / 500 cm s-1 = 0.01 s (vi) What is the magnetic flux cutting the loop when it is completely in the magnetic field? Φ = BA = (8)(.05 × .05) = 0.02 webers. (vii) What is the average emf induced in the loop as it enters the magnetic field? Induced emf = (Final Flux –Initial Flux) / Time Taken = (0 - 0.02)/0.01 = 2 Volts 9 (i) What is meant by refraction of light? Refraction is the bending of light as it passes from one medium to another (of different refractive index). (ii) State Snell’s law of refraction. The ratio of the sin of the sin of the angle of incidence to the sin of the angle of refraction is a constant. (iii) An eye contains a lens system and a retina, which is 2.0 cm from the lens system. The lens system consists of the cornea, which acts as a fixed lens of power 38 m–1, and a variable internal lens just behind the cornea. The maximum power of the eye is 64 m–1. Calculate how near an object can be placed in front of the eye and still be in focus. Pmax = 64 m-1 = 1/f f = 0.0156 m = 1.56 cm 1/u = 1/v +1/f ⇒ 1/u = 1/2 = 1/1.56 ⇒ u = 7.14 cm (iv) Calculate the maximum power of the internal lens. Pmax = P1 + P2 ⇒ 64 = 38 + P2 ⇒ P2 = 26 m-1 (v) Light is refracted as it enters the cornea from air as shown in the diagram. Calculate the refractive index of the cornea. ⇒ n = sin 37/sin 27 ⇒ n = 1.33 (vi) Draw a diagram to show the path of a ray of light as it passes from water of refractive index 1.33 into the cornea. Both media have the same refractive index so there is no bending of light. Draw a straight line passing from one medium to the other without bending. (vii) A swimmer cannot see properly when she opens her eyes underwater. When underwater why does the cornea not act as a lens? Because light does not refract at the cornea since there is no change in refractive index. (viii) What is the maximum power of the eye when underwater? The maximum power of the eye is 64 m–1, but this includes the focusing power of the cornea (38 m-1) which doesn’t work underwater, so maximum power = 64 – 38 = 26 m–1. (ix) Why do objects appear blurred when underwater? Because the internal lens by itself is not powerful enough to focus light on retina. (x) Explain how wearing goggles allows objects to be seen clearly. Because light which hits the cornea is coming from air and so there will be refraction here (the cornea will now act as a lens). 10 (a) Baryons and mesons are made up of quarks and experience the four fundamental forces of nature. (i) List the four fundamental forces and state the range of each one. Strong (short range), Weak (short range), Gravitational (infinite range), Electromagnetic (infinite range). (ii) Name the three positively charged quarks. Up, top, charm. (iii) What is the difference in the quark composition of a baryon and a meson? Baryon: three quarks Meson: one quark and one antiquark (iv) What is the quark composition of the proton? Up, up, down (v) In a circular accelerator, two protons, each with a kinetic energy of 1 GeV, travelling in opposite directions, collide. After the collision two protons and three pions are emitted. What is the net charge of the three pions? Justify your answer. Zero, because electric charge must be conserved. (vi) Calculate the combined kinetic energy of the particles after the collision. Energy equivalent of a pion:) E = mc2 E = (2.4842 )( 2.9979 × 108)2 E = 2.2327 × 10–11 J E = 1.3935 × 108 eV For 3 pions E = 6.6980 × 10–11 J / 1.58195 × 109 eV Energy after collision = (2 × 109) - (4.18047 × 108) = 1.58195 × 109 eV = 2.535 × 10–10 J (vii) Calculate the maximum number of pions that could have been created during the collision. Number of pions = (1.58195 × 109) / 1.3935 × 108 = 11.3524 = 11 pions. Maximum number of pions = 3 + 11 = 14 pions. 11 (i) The SI unit is named in honour of Lord Kelvin. What is the temperature of the boiling point of water in kelvin? 273.15 + 100 = 373.15 K (ii) Define the newton, the unit of force. A force of 1 N gives a mass of 1 kg an acceleration of 1 m s-1. (iii) A force of 9 kN is applied to a golf ball by a golf club. The ball and club are in contact for 0.6 ms. Using Newton’s laws of motion, calculate the change in momentum of the ball. From Newton II: Force ∝ rate of change of momentum F ∝ (mv – mu)/t F = (mv – mu)/t {proportional constant = 1} (mv – mu) = F × t = (9 × 103)( 0.6 × 10-3) = 5.4 kg m s-1. (iv) Nam three different electromagnetic radiations. x-rays, microwaves, ultra-violet etc. (v) What is the photoelectric effect? The Photoelectric Effect is the emission of electrons from a metal due to light of a suitable frequency falling upon it. (vi) Why as the quantum theory of light revolutionary? light has a particle nature (as well as a wave nature) (vii) High-energy radiation of frequency 3.3 × 1014 Hz is used in medicine. What is the energy of a photon of this radiation? E = h f E = (6.6 × 10–34)( 3.3 × 1014) = 2.18 × 10–19 J. (viii) 100 MJ of energy are released in a nuclear reaction. Calculate the loss of mass during the reaction. E = mc2 ⇒ m = E/c2 ⇒ m = (1 × 108) / (9 × 1016) = 1.11 × 10-9 kg. 12 (a) (i) State the principle of conservation of energy. The Principle of Conservation of Energy states that energy cannot be created or destroyed but can only be converted from one form to another. (ii) In a pole-vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints from rest and reaches a maximum velocity of 9.2 ms–1 after 3.0 seconds. He maintains this velocity for 2.0 seconds before jumping. Draw a velocity-time graph to illustrate the athlete’s horizontal motion. See diagram (iii) Use your graph to calculate the distance travelled by the athlete before jumping. Distance (s) = area under curve s = ½ (3)(9.2) + 2 (9.2) / 13.8 + 18.4 / 32.2 m (iv) What is the maximum height above the ground that the athlete can raise his centre of gravity? K.E. = P.E. ½ mv2 = mgh h = v2/2g = (9.2)2/2(9.8) = 4.32 Max height above the ground = 4.32 + 1.1 = 5.42 m. 12 (b) (i) The pitch of a musical note depends on its frequency. On what does (i) the quality, (ii) the loudness, of a musical note depend? Quality depends on number and relative strengths of overtones. Loudness depends on amplitude of the wave. (ii) What is the Doppler Effect? The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer. (iii) A rally car travelling at 55 m s–1 approaches a stationary observer. As the car passes, its engine is emitting a note with a pitch of 1520 Hz. What is the change in pitch observed as the car moves away? uc fcf ± =′ ⇒ 55340 )340(1520 + =′f ⇒ f1 = 1308.35 Hz ⇒ change in frequency = 1520 – 1308.35 = 211.65 Hz. (iv) Give an application of the Doppler Effect. Calculate speeds of stars or galaxies, speed traps. 12 (c) (i) In 1939 Lise Meitner discovered that the uranium isotope U–238 undergoes fission when struck by a slow neutron. Barium–139 and krypton–97 nuclei are emitted along with three neutrons. Write a nuclear reaction to represent the reaction. (ii) In a nuclear fission reactor, neutrons are slowed down after being emitted. Why are the neutrons slowed down? Only slow neutrons cause fission. (iii) How are they slowed down? They collide with the molecules in the moderator. (iv) Fission reactors are being suggested as a partial solution to Ireland’s energy needs. Give one positive and one negative environmental impact of fission reactors. Positive: no CO2 emissions / no greenhouse gases / no gases to result in acid rain / less dependence on fossil fuels. Negative: radioactive waste / potential for major accidents etc. 12 (d) (i) Define capacitance. The Capacitance of a conductor is the ratio of the charge on the conductor to its potential.