# Thursday 9 June 2016 Afternoon

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2 2 Answer all the questions. SECTION A 1 Here is a list of physical quantities. acceleration force kinetic energy power work (a) Choose the correct two quantities to complete this equation.... = mass... [1] (b) Which two quantities have the same unit?... and... [1] (c) Which two quantities are vectors?... and... [1] 2 In each of the four equations below, k is a constant. y 2 = kx y = kx y = k x y A B C D Which is the correct equation, A, B, C or D, to represent the relationship between y and x in each of the situations below? (a) y: the probability of a photon arriving at a particular location x: the amplitude of the vector sum for all possible phasor paths (b) y: the energy of a photon of electromagnetic radiation x: the wavelength of that radiation (c) y: the velocity of an object accelerating from rest at a constant rate x: the distance that the object has travelled (d) y: the kinetic energy of a vehicle travelling at a constant speed x: the mass of the vehicle... [1]... [1]... [1]... [1] = k x

3 3 Here is a list of orders of magnitude (a) Choose the value closest to the wavelength, in metres, of microwave radiation.... [1] (b) Choose the value closest to the thickness, in metres, of one page of this examination paper.... [1] Turn over

4 4 4 When parallel waves of wavelength l pass through a gap of width b as shown in Fig. 4.1, they spread out by diffraction. The intensity is a maximum in the forward direction, dropping away to zero intensity at an angle q to the forward direction. Fig. 4.1 shows incident wavefronts on the left of the gap, and the directions of maximum and zero intensity on the right. λ zero intensity b θ θ maximum zero intensity Fig. 4.1 Complete the following two diagrams. No calculations are necessary. (a) Complete the right-hand side of this diagram in a similar way to Fig λ b maximum [1]

5 (b) The width b is reduced. Complete the left-hand side of this diagram in a similar way to Fig zero intensity b θ θ maximum zero intensity [1] Turn over

6 5 An arrow of mass kg leaves a bow at a speed of 60 m s 1. (a) Show that its kinetic energy is about 50 J. 6 (b) The arrow is in contact with the bow-string over a distance of 0.60 m as it is fired. Calculate the average force exerted on the arrow. average force =... N 6 When white light passes through two narrow parallel slits marked on a blackened slide, an interference pattern of fringes is produced on a distant screen. Measurements of the fringe separation can be difficult because the fringes are dim and fuzzy and closely spaced. white light source blackened slide with two slits screen red filter Fig. 6.1 In an attempt to produce clearer fringes, a student puts a red filter between the white light source and the slits as shown in Fig Describe and explain one change in the clarity of the fringes when the red filter is in place.

7 7 In deep water, the waves on the surface of the sea do not all travel at the same speed. Their speed varies with wavelength l and is given by 7 gλ v = + 2π where g is the acceleration due to gravity, and k is a constant of value m 3 s 2. (a) Explain why this equation approximates to k m v = gλ 2π for waves of wavelength longer than about a metre. (b) A storm at sea creates waves of different wavelengths that travel away from it and can be detected a long way from the storm. Use the approximate equation in (a) to describe and explain differences in the time of arrival of these waves coming from the distant storm. Turn over

8 8 SECTION B 8 This question is about the use of diffraction gratings to investigate infrared spectra. Fig. 8.1 shows part of an infrared (IR) spectrometer. diffraction grating IR radiation θ θ 1st order diffraction maximum 1st order diffraction maximum IR detector Fig. 8.1 (a) The diffraction grating in Fig. 8.1 has a grating spacing d of 8.0 mm. (i) Diffraction gratings are labelled with the number of lines per mm rather than the grating spacing. Calculate the number of lines per mm for this diffraction grating. number =... mm 1 (ii) Explain why infrared of wavelength longer than m could not be detected with this diffraction grating.

9 9 (b) In most practical spectrometers, the detector shown in Fig. 8.1 does not move. The diffraction grating is rotated. This effectively reduces the grating spacing, as shown in Fig how grating appears, seen from direction of incoming radiation slit view of grating from above d d A A grating at 90 to radiation grating rotated through an angle A Fig. 8.2 When the grating is rotated through an angle A, it produces the same diffraction pattern as a grating of spacing d A. Explain why d A = d cos A. Turn over

10 10 (c) Infrared spectrometers are used to detect a wide range of wavelengths as shown below. Wavelength range / mm near infrared 0.74 to 2.5 mid infrared 2.5 to 25 far infrared 25 to 300 Explain why different diffraction gratings are needed for the different wavelength ranges.

11 11 BLANK PAGE Question 9 begins on page 12 PLEASE DO NOT WRITE ON THIS PAGE Turn over

12 9 This question is about infrared radiation with a wavelength of 1064 nm. (a) Calculate the energy of an infrared photon of wavelength 1064 nm. Give your answer to an appropriate number of significant figures. c = m s 1, h = J s. 12 energy =... J [3] (b) This infrared radiation is emitted in short pulses of energy from a laser. Each pulse has energy 100 mj and duration 10 ns. The energy of each photon is J. (i) Show that the power during a pulse is several kilowatts. [1] (ii) Calculate the number of photons in a single pulse. number =...

13 13 (c) Pulses of light from this laser can be passed through a crystal of lithium triborate which absorbs the infrared radiation and emits monochromatic green light of wavelength 532 nm. (i) The lithium triborate crystal is often called a frequency doubler. Explain why this description is appropriate. (ii) The number of infrared photons absorbed by the frequency doubler crystal is more than the number of green light photons emitted. Explain why this must be so. (iii) This process converts an infrared laser into a green light laser. Suggest one application where a green light laser would be more appropriate than an infrared laser. [1] Turn over

14 10 This question is about a light hollow ball falling from rest through air. The graphs in Fig show the displacement s and velocity v against time t from release s / m and v / m s Key s v t / s Fig (a) Explain in terms of the forces acting why the s-t graph is curved at the start, but straight after about 1 second of fall. (b) Use the v-t graph to confirm the plotted value of displacement s at 0.50 seconds. Show your working. [3]

15 15 (c) Find the acceleration at time t = 0.5 s by drawing a suitable tangent to one of the curves in Fig (d) The light hollow ball is now crushed into a pellet and dropped from rest as before. Compare the v-t graph for this fall with the v-t graph in Fig In your answer, you should link the forces acting on the falling objects with the shape of the graphs. [3] Turn over

16 16 11 This question is about the high jump in athletics. The most successful modern technique involves twisting the body so that the centre of mass of the athlete is as low as possible (Fig. 11.2). position of centre of mass bar old technique modern technique Fig Fig (a) The modern technique requires less gravitational potential energy than the old technique with the bar set at the same height. Calculate the extra gravitational potential energy required to jump over a bar 1.5 m above the ground using the old technique. Make appropriate estimates for quantities that you need. estimates calculation [3]

17 17 (b) A recent world record holder for the men s high jump is nearly 2 m tall. Suggest why it is an advantage for a high jumper to be tall. (c) In one particular high jump, the centre of mass of the athlete rises a height of 1.1 m. [1] (i) Show that the athlete must leave the ground with a vertical component of velocity of more than 4 m s 1. (ii) The athlete runs up to the bar with a horizontal velocity of 8.0 m s 1. When the athlete leaves the ground, his velocity is 6.0 m s 1 at an angle of 53 to the horizontal, as shown in Fig m s 1 before leaving the ground 6.0 m s 1 53 just after leaving the ground Fig Draw a vector diagram to show that the magnitude of the velocity change during the jump is more than 6 m s 1. Turn over

18 (iii) 18 The athlete s jumping foot is in contact with the ground for 180 ms before take-off. Calculate the mean accelerating force exerted by his foot while the velocity is changing. mass of athlete = 82 kg force =... N SECTION C 12 This question is about the article Dot plots. The data in Fig show values of extension obtained when a spring is stretched by a standard laboratory mass of 1 kg extension / cm Fig (a) Find the mean and the spread of the data in Fig Give both your numerical answers to an appropriate number of significant figures. extension =... ±... cm

19 (b) The spring constant k for the spring can be found using the equation F = kx. 19 (i) Explain why the uncertainty in the mass can be ignored in this calculation. [1] (ii) Use the data to calculate the spring constant k in N cm 1. g = 9.8 N kg 1 k =... ±... N cm 1 [3] (c) A different spring has a spring constant of k = 3.2 ± 0.6 N cm 1. This spring becomes over-stretched when the extension exceeds 9.0 cm. Taking into account the uncertainty in k, explain whether or not a force of 24 N will damage this second spring. Turn over

20 20 13 This question is about the article Systematic errors. (a) (i) State and explain the difference between systematic errors and random uncertainties. (ii) Explain why systematic errors cannot be reduced by increasing the number of repeat readings taken. (b) The stretched measuring tape described in the article is used to measure the distance in an experiment to determine the speed of someone running. State and explain the effect this would have on the final value of the speed. [1]

21 21 (c) The results from a simple experiment to show that p.d. is directly proportional to current in a resistor are recorded and a straight line graph drawn. The ammeter used is the one described in the article. Sketch the graph you would expect to see and explain what feature would indicate the systematic error. current p.d. Turn over

22 14 This question is about the article Measuring the speed of sound. 22 (a) The experiment as described in the article is dependent on the use of the wave equation v = f l. (i) Show that the units of f l can be written as m s 1. [1] (ii) Sound waves from the loudspeaker set up standing waves in the tube. Draw the standing waves in the tubes shown in Fig which correspond to the equations L 1 + c = 1 4 l and L 2 + c = 3 l. 4 Label all displacement nodes (N) and antinodes (A) on both diagrams. c c L 1 L 2 tube tube water water Fig [3]

23 (iii) 23 Explain how standing waves are formed in the tube. In your answer, you should use appropriate technical terms, spelled correctly. [3] (b) (i) Show how the two equations L 2 + c = 3 4 l and L 1 + c = 1 l can be combined to give 4 L 2 L 1 = 1 2 l. [1] (ii) Combining the two equations eliminates the systematic error of the end correction. State the assumption that must be made for this to be valid. [1] Turn over

24 24 (c) A student does a preliminary experiment to measure the two resonant lengths L 1 and L 2 for two different frequencies. The data are shown in Tables 1 and 2 below. first resonant length second resonant length frequency / Hz L 1 / cm DL 1 / cm frequency / Hz L 2 / cm DL 2 / cm ± ± ± ±1 Table 1 Table 2 The uncertainties DL 1 and DL 2 are estimated from the ranges of lengths over which the note emitted by the tube is much louder than the note from the loudspeaker alone. (i) Suggest and explain one reason why DL 2 > DL 1 for each frequency. (ii) The uncertainties DL 1 and DL 2 for f = 600 Hz are both less than for f = 200 Hz. However, calculation of the speed of sound using L 2 L 1 = 1 2 l and v = f l gives greater uncertainty in the final value of v when the values for L 1 and L 2 for 600 Hz are used rather than those for 200 Hz. Explain why.

25 (iii) 25 The student obtains data for a range of frequencies and plots an appropriate graph instead of calculating the speed of sound directly from the values in Tables 1 and 2. Suggest and explain reasons why the graphical method is better. Turn over for part (d) Turn over

26 26 (d) Fig shows a graph that has been plotted with data from one such experiment using a range of frequencies from 200 Hz to 550 Hz (L 2 L 1 ) / m / ms f Fig (i) Explain why a graph of (L 2 L 1 ) plotted against 1 v f which passes through the origin. 2 should give a straight line of gradient

27 (ii) 27 Draw a best-fit line and calculate a value for v, the speed of sound. v =... m s 1 [3] (iii) Use data from Fig to estimate the uncertainty Dv in the value of the speed of sound calculated in (d)(ii). Assume that the uncertainty in frequency measurement is negligible. Dv = ±... m s 1 [3] Turn over

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### Tuesday 28 June 2016 Morning

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### Monday 10 June 2013 Morning

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### Wednesday 30 May 2012 Afternoon

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### Candidate number. Centre number

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### Wednesday 3 June 2015 Morning

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### Monday 24 June 2013 Morning

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### Thursday 12 January 2012 Afternoon

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