Steps in Measuring Acceleration - Physics - Solved Paper, Exams of Physics

Download Steps in Measuring Acceleration - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! 2010 Leaving Cert Physics Solutions (Higher Level) 1. [2010] In an experiment to investigate the relationship between the acceleration of a body and the force applied to it, a student recorded the following data. (i) Describe the steps involved in measuring the acceleration of the body. Measure/calculate the initial velocity/speed Measure/calculate the velocity/speed again (t seconds later) Measure time interval from initial to final velocities / distance between light gates Use relevant formula Datalogging method: Align motion sensor with body (e.g. trolley) / diagram Select START and release body (Select STOP and) display GRAPH of ‘a vs. t’ // ‘v vs. t’ (Use tool bar to) find average value for a // use slope (tool) to find a (= dv /dt) (ii) Using the recorded data, plot a graph to show the relationship between the acceleration of the body and the force applied to it. Label axes correctly on graph paper Plot six points correctly Straight line Good distribution (iii) What does your graph tell you about this relationship? Acceleration is proportional to the applied force. (iv) Using your graph, find the mass of the body. The mass of the body corresponds to the slope of the graph = 2.32 kg [range: 2.1 - 2.4 kg] (v) On a trial run of this experiment, a student found that the graph did not go through the origin. Suggest a reason for this and Friction / dust on the track slowing down the trolley. (vi) Describe how the apparatus should be adjusted, so that the graph would go through the origin. Elevate/adjust the track/slope F/N 0.20 0.40 0.60 0.80 1.00 1.20 1.40 a/m s–2 0.08 0.18 0.28 0.31 0.45 0.51 0.60 2. [2010] In an experiment to measure the specific latent heat of vaporisation of water, a student used a copper calorimeter containing water and a sensitive thermometer. The water was cooled below room temperature before adding dry steam to it. The following measurements were recorded. Mass of copper calorimeter = 34.6 g Initial mass of calorimeter and water = 96.4 g Mass of dry steam added = 1.2 g Initial temperature of calorimeter and cooled water = 8.2 °C Final temperature of calorimeter and water = 20.0 °C (i) How was the water cooled below room temperature? Ice was added to the water / the water was taken from fridge (ii) How was the steam dried? By using a steam trap (or ensure that the delivery tube is sloped upwards) (iii) Describe how the mass of the steam was determined. Final mass of calorimeter plus contents – initial mass of calorimeter and contents (iv) Why was a sensitive thermometer used? For greater accuracy / to reduce (%) error / more significant figures / e.g. to read to 0.1 oC (v) Using the data, calculate the specific latent heat of vaporisation of water. ms = 1.2×10-3 kg and mw = 6.18 × 10-2 kg Δθs = 80 (K) and Δθw (= Δθcu) = 11.8 (K) [heat lost by steam = heat gained by water and calorimeter] (ml)s + (mcΔθ )s = (mcΔθ )w + (mcΔθ )cu (1.2×10-3)l + (1.2×10-3)(4180)(80) = (6.18 × 10-2)(4180)(11.8) + (3.46 × 10-2)(11.8)(390) (1.2×10-3)l + 401.3 = 3048.2 + 159.2 l = 2.34 × 106 J Kg-1 6 [2010] (Radius of the earth = 6.36 × 106 m Acceleration due to gravity at the earth’s surface = 9.81 m s−2 Distance from the centre of the earth to the centre of the moon = 3.84 × 108 m Assume the mass of the earth is 81 times the mass of the moon.) (i) State Newton’s law of universal gravitation. Force between any two point masses is proportional to product of masses and inversely/indirectly proportional to square of the distance between them. (ii) Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which is twice the radius of the earth. Note that 2d above surface is 3d from earth’s centre 2d GMg = 2)3( d GMgnew = where d = 6.36 × 10 6 m gnew = 1.09 m s-2 (iii) A spacecraft carrying astronauts is on a straight line flight from the earth to the moon and after a while its engines are turned off. Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off. There are no external forces acting on the spacecraft so from Newton’s 1st law of motion the object will maintain its velocity. (iv) Describe the variation in the weight of the astronauts as they travel to the moon. Weight decreases as the astronaut moves away from the earth and gains (a lesser than normal) weight as she/he approaches the moon (v) At what height above the earth’s surface will the astronauts experience weightlessness? Gravitational pull of earth = gravitational pull of moon 2 1d mGmE = 2 2d mGmm 2 2 2 1)81( d d M M M E == 2 19 d d = dE = 9 dm and dE + dm = 3.84 × 108 m 10 dm = 3.84 × 108 dm = 3.84 × 107 dE = 3.356 × 108 Height above the earth = (3.356 × 108) – (6.36 × 106) = 3.39 × 108 m (vi) The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second? v = 2πr T v = 2π(3.84 × 108) 27.3 × 24 × 24 × 60 v = 1022.9 m s-1 (vii) Why is there no atmosphere on the moon? The gravitational force is too weak to sustain an atmosphere. 7 [2010] (i) What is the Doppler effect? The Doppler effect is the apparent change in frequency due to the relative motion between a source and an observer. (ii) Explain, with the aid of labelled diagrams, how this phenomenon occurs. Diagram: Labelled moving source of waves Shorter wavelength approaching observer Longer wavelength receding Correct reference to frequency change (iii) Describe a laboratory experiment to demonstrate the Doppler effect. Attach a string to a buzzer. Swing the buzzer over your head. An observer will note a frequency change as the buzzer approaches then recedes from source the observer. (iv) What causes the red shift in the spectrum of a distant star? Distant stars are moving away from us therefore the wavelengths increase. (v) The yellow line emitted by a helium discharge tube in the laboratory has a wavelength of 587 nm as shown in the diagram. The same yellow line in the helium spectrum of a star has a measured wavelength of 590 nm. What can you deduce about the motion of the star? The star is moving away from earth (vi) Calculate the speed of the moving star. Substitution: c = 3 × 108, f = 5.11073 × 1014 and f’ = 5.08475 × 1014 Answer: u = 1.5333 × 106 m s-1 (vii) Give another application of the Doppler effect. Radar, medical imaging, blood flow measurement (echocardiogram), temperature measurement, (underwater) acoustics, etc. uc fcf + =′ 8 [2010] A hair dryer with a plastic casing uses a coiled wire as a heat source. When an electric current flows through the coiled wire, the air around it heats up and a motorised fan blows the hot air out. (i) What is an electric current? An electric current is a flow of charge (ii) Heating is one effect of an electric current. Give two other effects of an electric current. Magnetic and chemical (iii) The diagram shows a basic electrical circuit for a hair dryer. Describe what happens when switch A is closed and the rheostat is adjusted The fan operates and its speed of rotation changes. (iv) Describe what happens when switch A and switch B are closed. Current flows through coil and the coil gets hot. The fan blows hot air (vi) Calculate the current that flows through the coil when the dryer is turned on. P = VI I = P/V = 2000/230 I = 8.7 A (v) The maximum power generated in the heating coil is 2 kW. What is the initial resistance of the coil? V = RI R = 230/8.7 = 26.4 Ω (vii) A length of nichrome wire of diameter 0.17 mm is used for the coil. Calculate the length of the coil of wire. A = πr2 A = (3.14)(0.085 × 10-3)2 A = 2.27 × 10-8 m2 ƿ = RA/l l = RA/ ƿ l = (26.4)( 2.27 × 10-8)/(1.1 × 10-6) l = 0.545 m (viii) Explain why the current through the coil would decrease if the fan developed a fault and stopped working. The coil gets hot therefore its resistance increases (or any correct statement explaining why Rcct or Rcoil has increased) 10 (b) [2010] (i) Distinguish between intrinsic conduction and extrinsic conduction in a semiconductor. Intrinsic conduction occurs in a pure semiconductor and involves an equal number of electrons and (positive) holes. Extrinsic conduction occurs in a doped semiconductor where either the electrons or the positive holes are the majority charge carriers. (ii) The circuit shows four light-emitting diodes connected to a resistor R and a 6 V a.c. supply of frequency 1 Hz. What is observed when the circuit is operating? During one second/cycle D1 and D4 flash (together during one half cycle) followed by D2 and D3. (iii) Explain what is observed by referring to the circuit. When D1 and D4 are forward biased (and so they will conduct) D2 and D3 are reverse biased (iv) What is observed when the frequency of the a.c. supply is increased to 50 Hz? The diodes flash so fast that the leds appear to light continuously (v) Give two functions of the resistor R. It protects the leds from over-load and also limits the current (acts as a load resistor). (vi) How was the output voltage displayed? Using a cathode ray oscilloscope or datalogger. (vii) Draw graphs to show the differences between the input voltage and the output voltage. There is an a.c input and an in phase fully rectified output. (viii) It is noticed that the output voltage is lower than the input voltage. Explain why. There is a voltage drop across a led ( ≈1.6 V). 11 [2010] Read the following passage and answer the accompanying questions. A person’s exposure to radiation when using a mobile phone is measured in terms of the Specific Absorption Rate (SAR). This is a measure of the rate at which radio frequency energy is absorbed by a person’s body during a phone call and is expressed in watts per kilogram. A radio frequency wave penetrates the body to a depth that depends on its frequency. At mobile phone frequencies the wave energy is absorbed by about one centimetre of body tissue. The energy absorbed is converted into heat and is carried away by the body. Any adverse health effects from radio frequency waves are due to heating. Current scientific evidence indicates that exposure to radiation from mobile phones is unlikely to induce cancer. (Adapted from a Dept. of Communications, Energy and Natural Resources Press Release of 22 March 2007.) (i) Give two properties of radio waves. They travel at speed of light, electromagnetic radiation, travel through vacuum, can be reflected, refracted, polarized etc. (ii) In a three-minute phone call, 10 g of head tissue absorbs 0.36 J of radio frequency energy. Calculate the SAR value. Power = Energy/time = 0.36 / (3 × 60) = 0.002 W SAR = Power/mass = 0.36/(3 × 60)(10 ×10-3) = 0.20 W kg-1 (iii) What happens to the radio frequency energy absorbed by the body? It is converted into heat in the body. (iv) Why are radio frequency waves not very penetrating? They have a low frequency / long wavelength / low energy. (v) A mobile phone converts the received radio frequency waves to sound waves. What are the audible frequency limits for sound waves? 20 Hz to 20 000 Hz (vi) Give two safety precautions you should take when using a mobile phone. Keep phone at distance, use loudspeaker function, ‘no hands, brief calls only, direct antenna away from your head etc. (vii) A mobile phone transmits at 1200 MHz from its antenna. Calculate the length of its antenna, which is one quarter of the wavelength that it transmits. λ = c/f λ = (3 × 108)/(1.2 × 109) λ = 0.25 m Length of antenna = 0.25/4 = 0.0625 m. (viii) Name an electromagnetic wave which may induce cancer. Justify your answer. Gamma rays / X-rays / UV - they can all cause ionization of body cells. 12 (a) [2010] (i) A student holds a motion sensor attached to a data-logger and its calculator. List the instructions you should give the student so that the calculator will display the graph shown in Fig 1. Stand 1 m from wall (and select START) Stationary for 5 s Move back to 3 m (from wall) in 6 s / accept specific velocity and time/distance Stationary for 7 s Approach to 1 m in 4 s (ii) The graph in Figure 2 represents the motion of a cyclist on a journey. Using the graph, calculate the distance travelled by the cyclist and the average speed for the journey. Distance travelled = area under the graph 18 km h-1 = 18000/60 m s-1 = 300 m min-1 S1 = 150 × 6 = 900 m S2 = 300 × 8 = 2400 m S3 = 150 × 5 = 750 m Total distance = 4050 m Average speed = total distance divided by total time = 4050/19 = 213.2 m min-1 = 3.55 m s-1