Laws of Equilibrium - Physics - Solved Paper, Exams of Physics

Download Laws of Equilibrium - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! 2007 Leaving Cert Physics Solutions (Higher Level) 1 A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick. The student found that the centre of gravity of the metre stick was at the 50.4 cm mark and its weight was 1.2 N. (i) How did the student find the centre of gravity? By hanging the metre stick on a thread support and adjusting the position of the thread until the metre stick remained horizontal. (ii) How did the student find the weight, of the metre stick? By putting it on an electronic balance. (iii) Why is the centre of gravity of the metre stick not at the 50.0 cm mark? The material is not of perfectly uniform density. (iv) The student applied vertical forces to the metre stick and adjusted them until the metre stick was in equilibrium. How did the student know that the metre stick was in equilibrium? The metre stick was at rest. The student recorded the following data. (v) Calculate the net force acting on the metre stick. Fup = 4.5 + 5.7 = 10.2 N and Fdown = 2 + 3 +1.2 +4 = 10.2 N ⇒ net force = 0 (vi) Calculate the total clockwise moment about a vertical axis of the metre stick. (through zero) = 2(0.115) + 3(0.383) +1.2(0.504) +4.0(0.802) = 0.23+1.149+0.6048+3.208 = 5.2 N m (vii) Calculate the total anti-clockwise moment about a vertical axis of the metre stick. (through zero) = 4.5(0.262) +5.7(0.704) = 5.1918 N m = 5.2 N (viii) Use these results to verify the laws of equilibrium Fup = Fdown Total clockwise moments = Total anti-clockwise moments 2 The specific heat capacity of water was found by adding hot copper to water in a copper calorimeter. The following data was recorded. (i) Describe how the copper was heated and how its temperature was measured. It was heated using a hot-plate and temperature was measured using a thermometer. (ii) Using the data, calculate the energy lost by the hot copper E = m c Δθ E = (3.02 × 10-2)(390)(78.5) = 924.6 J (iii) Using the data, calculate the specific heat capacity of water. Heat lost by hot copper = heat gained by calorimeter + water 924.57 = (0.0557)(390)(4.5) + (0.0455)(cw)(4.5) ⇒ 924.57 = 97.75 + 0.2048 cw cw = 4.04 ×103 J kg-1 K-1 (iv) Give two precautions that were taken to minimise heat loss to the surroundings. Insulate calorimeter /use lid /transfer copper pieces quickly / use cold water (below room temperature) / polish calorimeter / low heat capacity thermometer (v) Explain why adding a larger mass of copper would improve the accuracy of the experiment. A larger mass of copper would result in a larger temperature change and therefore smaller percentage error . 2007 Question 3 In an experiment to measure the focal length of a concave mirror, an approximate value for the focal length was found. The image distance v was then found for a range of values of the object distance u. The following data was recorded. u/cm 15.0 20.0 25.0 30.0 35.0 40.0 v/cm 60.5 30.0 23.0 20.5 18.0 16.5 position on metre stick/cm 11.5 26.2 38.3 70.4 80.2 magnitude of force/N 2.0 4.5 3.0 5.7 4.0 direction of force down up down up down mass of calorimeter 55.7 g mass of calorimeter + water 101.2 g mass of copper + calorimeter + water 131.4 g initial temperature of water 16.5 oC temperature of hot copper 99.5 oC final temperature of water 21.0 oC (i) How was an approximate value for the focal length found? An image of a distant object was focused on a screen. Measure the distance from the screen to the mirror. (ii) What was the advantage of finding the approximate value for the focal length? To avoid placing object inside f during the experiment) which would have meant that the image couldn’t be formed on the screen. (iii) Describe, with the aid of a labelled diagram, how the position of the image was found. Apparatus: object, concave mirror, screen Adjust the position of the the screen until a clear image of the crosswire is obtained. (iv) Calculate the focal length of the concave mirror by drawing a suitable graph based on the recorded data. The question shouldn’t have specified the drawing of a graph as it wasn’t specified on the syllabus. As a result marking scheme was adjusted and you could get 15 marks out of 18 by using the normal approach. For the record, if you do graph the data then where the line cuts either axis corresponds to 1/f, so invert to get f. Do this for both axes and get the average. Calculate 1/u and 1/v values Label axes Plot at least five points Straight line Extrapolate to cut axis (or axes) Read axis (or axes) value = 0.085 Focal length = 12.0 cm For use of data table rather than graphical work: Correct formula Correct substitution One correct f value f average 4 The following is part of a student’s report of an experiment to investigate of the variation of current I with potential difference V for a semiconductor diode. I put the diode in forward bias as shown in the circuit diagram. I increased the potential difference across the diode until a current flowed. I measured the current flowing for different values of the potential difference. I recorded the following data. (i) Draw a circuit diagram used by the student. See diagram (ii) How did the student vary and measure the potential difference? Adjust rheostat / potential divider /variable power supply unit. To measure p.d. a voltmeter was used as shown in the diagram. (iii) Draw a graph to show how the current varies with the potential difference. u/cm 15.0 20.0 25.0 30.0 35.0 40.0 v/cm 60.5 30.0 23.0 20.5 18.0 16.5 1/u 1/v V/V 0.60 0.64 0.68 0.72 0.76 0.80 I /mA 2 4 10 18 35 120 9 (i) Define resistance. The resistance of a conductor is the ratio of the potential difference across it to the current flowing through it. (ii) Define resistivity. The resistivity of a material is defined as the resistance of a cube of material of side 1 m. A metre bridge was used to measure the resistance of a sample of nichrome wire. The diagram indicates the readings taken when the metre bridge was balanced. The nichrome wire has a length of 220 mm and a radius of 0.11 mm. (iii) Calculate the resistance of the nichrome wire R1/R2= L1/L2 R/20 = 282/718 R = 7.86 Ω (iv) Calculate the resistivity of nichrome ρ =RA/L ρ = (7.844)(3.801× 10-8)/ 0.220 ρ = 1.36 × 10-6 Ω m (v) Sketch a graph to show the relationship between the temperature and the resistance of the nichrome wire as its temperature is increased. Axes labelled R and T (or θ) Correct linear graph with intercept showing R greater than zero. (vi) What happens to the resistance of the wire as its temperature falls below 0oC? R decreases (vii) What happens to the resistance of the wire as its length is increased? R increases (viii) What happens to the resistance of the wire if its diameter is increased? (ix) R decreases (x) Name another device, apart from a metre bridge, that can be used to measure resistance. Ohmmeter / wheatstone bridge /multimeter. (xi) Give one advantage and one disadvantage of using this device instead of a metre bridge. Ohmmeter: compact, portable, faster method, etc. less accurate, fragile, difficult to calibrate/chec Wheatstone bridge: compact, portable, more accurate etc. ‘black box’ difficult to comprehend, expensive. 10 (a) Read the following passage and answer the accompanying questions. Ernest Walton was one of the legendary pioneers who made 1932 the annus mirabilis of experimental nuclear physics. In that year James Chadwick discovered the neutron; Carl Anderson discovered the positron; Fermi articulated his theory of radioactive decay; and Ernest Walton and John Cockcroft split the nucleus by artificial means. In their pioneering experiment Cockcroft and Walton bombarded lithium nuclei with high-energy protons linearly accelerated across a high potential difference (c. 700 kV). The subsequent disintegration of each lithium nucleus yielded two helium nuclei and energy. Their work gained them the Nobel Prize in 1951. (Adapted from “Ernest Thomas Sinton Walton 1903 –1995 The Irish Scientist” McBrierty; 2003) (i) Draw a labelled diagram to show how Cockcroft and Walton accelerated the protons. See diagram. (ii) What is the velocity of a proton when it is accelerated from rest through a potential difference of 700 kV? (iii) Write a nuclear equation to represent the disintegration of a lithium nucleus when bombarded with a proton. (accept p for H and α for He ) (iv) Calculate the energy released in this disintegration. Mass of reactants = 1.1646 × 10-26 + 1.6726 × 10-27 = 1.33186 × 10-26 kg Mass of products = 2(6.6443 × 10-27) = 1.32886 × 10-26 kg) Δm = 3.00 × 10-29 kg E = m c2 or E = (3.00 × 10-29)(9 × 1016) = E = 2.7 × 10-12 J (v) Compare the properties of an electron with that of a positron. Both have equal mass / charges equal / charges opposite (in sign) / matter and anti-matter (vi) What happens when an electron meets a positron? Pair annihilation occurs. (vii) In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive decay resolve this? Fermi (and Pauli) realised that another particle must be responsible for the missing momentum , which they called the neutrino. 11 Read the following passage and answer the accompanying questions. At present, nuclear fission reactors supply a sixth of the world’s electricity. Along with hydroelectric stations they are the major source of ‘carbon-free’ energy today. Nuclear reactors have shown remarkable reliability and efficiency even though the development of nuclear technology was held back by the nuclear accidents at Chernobyl and Three Mile Island. A nuclear revival is possible. The global reserves of uranium could support a much larger number of reactors than exist today. Nuclear power generation could increase from three hundred gigawatts today to one thousand gigawatts by the year 2050, saving the earth from 1.5 billion tonnes of carbon emissions a year. Already more than twenty gigawatts of nuclear capacity have come online since 2000. Nuclear power would significantly contribute to the stabilisation of greenhouse gas emissions. The type of reactor that will continue to dominate for the next two decades is the light water reactor, which uses ordinary water (as opposed to heavy water, containing deuterium) as the coolant and moderator. Solar cells, wind turbines and biofuels are becoming viable energy sources. Solar cells use semiconductor materials, such as silicon, to convert sunlight into electricity, but at the moment they provide only 0.15% of the world’s energy needs. Yet sunlight could be harnessed to supply 5000 times as much energy as the world currently consumes. (Adapted from “Scientific American; Energy’s Future beyond Carbon”; September 2006) (a) What is nuclear fission? Nuclear fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons). (b) How much energy is generated worldwide every minute by nuclear power today? (300 x 109)(60) J or 18,000 gigajoule (per minute) or 1.8 x 1013 J (c) At present, why is a fission reactor a more viable source of energy than a fusion reactor? Fission) can be more easily controlled / easier to initiate reaction or vice versa (d) Deuterium is an isotope of hydrogen, what is an isotope? Isotopes are atoms which have the same atomic number but different mass numbers. (e) What is the function of a moderator in a fission reactor? To slow down fast neutrons to facilitate fission. (f) Why is silicon a semiconductor? It has a resistivity between that of a conductor and an insulator. (g) A large number of solar cells are joined together in series and cover an area of 20 m2. The efficiency of the solar cells is 20%. If the solar constant is 1400 W m–2, what is the maximum power generated by the solar cells? (1400 × 20 × 1/5) W or 5600 J s-1 or 5600 W (h) What is the source of the sun’s energy? Nuclear fusion 12 (a) (i) What is friction? Friction is a force which opposes the relative motion between two objects. (ii) A car of mass 750 kg is travelling east on a level road. Its engine exerts a constant force of 2.0 kN causing the car to accelerate at 1.2 m s–2 until it reaches a speed of 25 m s–1. Calculate the net force acting on the car. Fnet = ma = (750)(1.2) = 900 N east. (iii) Calculate the force of friction acting on the car. Fnet = Fcar - Ffriction 900 = 2000 - Ffriction ⇒ Ffriction = 1100 N west (iv) If the engine is then turned off, calculate how far the car will travel before coming to rest? Friction causes deceleration: a = F ÷ m a = (-1100) ÷ 750 = - 1.47 ms-2 v 2 = u 2 + 2as 0 = 252 +2(-1.47) s or s = 213 m 12 (b) (i) Define sound intensity. Sound Intensity is defined as power per unit area. (ii) A loudspeaker has a power rating of 25 mW. What is the sound intensity at a distance of 3 m from the loudspeaker? Surface area of sphere = 4π r2 S.I at 3 m = (25 × 10-3 ) ÷ 4 π (3)2 S.I = 2.21 × 10-4 W m-2 (iii) The loudspeaker is replaced by a speaker with a power rating of 50 mW. What is the change in the sound intensity? Increased by: 2.21 × 10-4 W m-2 (iv) What is the change in the sound intensity level? Increased by: 0.30 B or 3 dB (v) The human ear is more sensitive to certain frequencies of sound. How is this taken into account when measuring sound intensity levels? dBA / decibel adapted / a frequency weighted scale is used // sound level meter (modified so that it) responds more to sounds between 2kHz and 4 kHz / just like the ear 12 (c) (i) State Faraday’s law of electromagnetic induction. Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux. (ii) Describe an experiment to demonstrate Faraday’s law. Move the magnet in and out of the coil slowly and note a slight deflection. Move the magnet quickly and note a greater deflection. (iii) A resistor is connected in series with an ammeter and an ac power supply. A current flows in the circuit. The resistor is then replaced with a coil. The resistance of the circuit does not change. What is the effect on the current flowing in the circuit? Current is reduced (iv) Justify your answer An emf induced in coil which induces a current which opposes the initial current. 12 (d) (i) Explain the term half-life. Time for half the radioactive nuclei in a sample to decay (ii) A sample of carbon is mainly carbon-12 which is not radioactive, and a small proportion of carbon-14 which is radioactive. When a tree is cut down the carbon-14 present in the wood at that time decays by beta emission. Write a nuclear equation to represent the decay of carbon-14. ( accept e in lieu of β) (iii) An ancient wooden cup from an archaeological site has an activity of 2.1 Bq. The corresponding activity for newly cut wood is 8.4 Bq. If the half-life of carbon-14 is 5730 years, estimate the age of the cup. 8.4 Bq to 2.1 Bq requires two half-lives. Answer =11,460 years (iv) Name an instrument used to measure the activity of a sample. Geiger Muller tube. (v) What is the principle of operation of this instrument? The gas is ionised and a pulse of charge/current flows.