# THIS IS A NEW SPECIFICATION

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2 2 Answer all the questions. Section A 1 Here is a list of units. J s 1 N kg 1 J m 1 N m J s Choose the correct unit for (a) power (b) acceleration.... [1]... [1] 2 y y y y x 0 x 0 x 0 A B C D x Fig 2.1 Which graph, A, B, C or D in Fig. 2.1, is obtained when the y and x axes represent the two quantities given in each case below? (a) y-axis: the potential energy gained when an object is lifted x-axis: the vertical height through which it is lifted (b) y-axis: the kinetic energy of a moving object x-axis: the speed of the object (c) y-axis: the energy of a photon of electromagnetic radiation x-axis: the wavelength of the radiation... [1]... [1]... [1]

3 3 X-rays have a wavelength of m. Calculate the energy of one X-ray photon. c = m s 1 h = J s 3 energy =... J [3] 4 When a beam of light is incident on two slits, an interference pattern is seen on a screen. max min max not to scale beam of light two slits screen min max min max min max Here are some statements about what happens at the screen. Put a tick ( ) next to each correct statement. A minimum occurs where photons have passed through only one slit. A maximum occurs where phasors for each path line up. Slits closer together would give a bigger separation of maxima and minima. The photons arrive at the screen at a rate proportional to the resultant phasor amplitude. Turn over

4 5 Phil creates standing waves on a rope by shaking one end of it vertically. The other end of the rope is fixed to a wall. 4 wall rope (a) Write the letter A on the diagram at the position of one antinode. [1] (b) The distance from Phil s hand to the wall is 2.4 m. Phil is shaking the rope end with a time period of 0.4 s. Calculate the wavelength and frequency of the waves travelling along the rope. wavelength λ =... m frequency f =... Hz

5 5 6 A high-performance car has an acceleration of 0.86 g. (a) Calculate the time it takes to reach a velocity of 27 m s 1 (60 miles hour 1 ). g = 9.8 m s 2 (b) The car can brake from 27 m s 1 to rest in a distance of 35 m. Calculate the mean force exerted by the brakes. mass of car = 1600 kg time =... s mean force =... N Turn over

6 6 7 When heavy barrels are unloaded off a lorry, they are dropped onto a thick mat to stop them breaking open when hitting the ground. The mat compresses from a thickness of 30 cm to a thickness of 6.0 cm. This decelerates the barrel. barrel 1.2 m mat 30 cm 6.0 cm before after (a) Show that the work that must be done to decelerate a barrel to rest after it has fallen 1.2 m is about 1.3 kj. mass of barrel = 110 kg g = 9.8 m s 2 (b) Calculate the mean force exerted by the mat to decelerate the barrel to rest. Assume that no energy is lost before the barrel hits the mat. mean force =... N [Section A Total: 21]

7 7 Section B 8 This question is about forces on a helium party balloon. A helium balloon rising in the air has more than one force acting on it. Besides weight, there is upthrust. The upthrust is equal in magnitude to the weight of the air which would have occupied the volume taken up by the balloon. When the balloon is moving there is also air resistance. (a) Fig. 8.1 shows a helium party balloon. Fig. 8.1 On Fig. 8.1, draw three arrows, labelled W, U and AR, to show the directions of the weight, the upthrust and the air resistance acting on this balloon as it rises through the air. [1] (b) The balloon is released at time t = 0. (i) Explain why the air resistance force AR is zero at time t = 0. [1] Turn over

8 (ii) 8 Use the data below to show that the resultant force acting on the balloon at time t = 0 is about 0.02 N. Show your working clearly. mass of rubber and helium = kg mass of air taking up the same volume = kg g = 9.8 m s 2 (c) Air resistance forces increase as the balloon accelerates. In a mathematical model to analyse the motion of the balloon, the air resistance force F AR is given by F AR = kv where v is the velocity of the balloon and k is a constant. (i) Suggest and explain one change to the balloon which would make the value of k smaller. In your answer you should use technical terms, spelled correctly.

9 9 Using the mathematical model F AR = kv with one particular value of k gives the graph in Fig v / ms t / s 1.8 Fig. 8.2 (ii) Explain why the graph becomes less steep, and eventually horizontal, as time increases. (iii) Fig. 8.2 shows that the velocity reaches a maximum of 1.5 m s 1. Show that this is consistent with a value of k = N s m 1. [Total: 10] Turn over

10 10 9 This question is about the colours seen in light reflected from DVDs. The surface of a DVD contains a regular array of closely spaced tracks which acts like a reflection diffraction grating. The first order of diffraction is at the same angle θ for a reflection grating and a transmission grating with the same grating spacing, as shown in Fig incident beam first order first order incident beam reflection grating transmission grating Fig. 9.1 The similarity shown in Fig. 9.1 means that the equation nλ = d sin θ can be used for a reflection grating as well as for a transmission grating. (a) The distance between tracks (the grating spacing) on a DVD is m. (i) Show that the angle θ is about 30 for the first order of incident red light of wavelength 700 nm. (ii) Without calculation, state and explain the difference you would observe when the red light is incident on a CD where the distance between tracks is slightly larger than on a DVD.

11 (b) (i) 11 Calculate the wavelength of light which gives a second-order (n = 2) angle of 90 when reflected from the DVD. wavelength λ =... m (ii) Explain why there is no second-order for light of wavelength 700 nm. (c) The DVD reflection grating is now illuminated with white light containing all wavelengths between 400 nm and 700 nm. For red light of wavelength 700 nm there is only one order r 1. However, for violet light of wavelength 400 nm, there are three orders v 1, v 2 and v 3. These are shown in Fig For clarity, orders are shown only on one side of the incident beam. incident beam v 1 r 1 v2 v 3 Fig. 9.2 Explain why no light is seen in the region between the angles of the first-order red r 1 and the second-order violet v 2. [Total: 10] Turn over

12 10 This question is about earthquake waves. 12 (a) When earthquakes occur longitudinal P-waves and transverse S-waves spread out in all directions. Explain clearly the difference between transverse and longitudinal waves. (b) Seismometers measure the displacement of the ground as a function of time, and record the results on graphs as shown in Fig t = 0 is set at the time of arrival of the P-waves. P-wave S-wave time / s displacement / mm Fig (i) Show that the time delay Δt between the arrival of P-waves and S-waves from an earthquake a distance D from the seismograph is given by Δt = D 1 1 v S where v S and v P are the velocities of S-waves and P-waves respectively. v P

13 13 (ii) Use data from Fig to calculate the distance D. v S = 3500 m s 1 v P = 8000 m s 1 D =... m [3] (c) Given that the power delivered by a wave is proportional to (amplitude) 2, use data from Fig to calculate the ratio maximum power delivered by S-waves maximum power delivered by P-waves. (d) The Richter scale for measuring the magnitude M of earthquakes where they happen is given by the equation M = log(a) + (factor depending on distance from earthquake) where A is the maximum amplitude of the strongest waves received by the seismometer. Suggest one advantage of having a logarithmic scale for earthquake magnitudes. [1] [Total: 10] Turn over

14 14 11 This question is about a sport called kitesurfing (Fig. 11.1). kite sea board Fig The kitesurfer stands on the board, and is pulled along the surface of the sea by the lines attached to the kite. The kitesurfer, lines and board are modelled in the diagram in Fig kitesurfer kite lines board Fig (a) The total tension in the kite lines is 1000 N. By scale drawing or calculation, show that, when the angle θ = 30, the horizontal force pulling the kitesurfer is about 900 N. [3]

15 (b) (i) 15 Explain why the kitesurfer in this situation needs to have a mass of more than 51 kg. Your answer should refer to the components of forces. g = 9.8 m s 2 (ii) A kitesurfer usually takes a selection of kites of different sizes to the water. Suggest and explain the reason for this. (c) The kitesurfer is pulled along horizontally at a steady speed by the force described in part (a). State what this tells you about the forces between the board and the water. You should refer to components of forces in your answer. [Total: 9] [Section B Total: 39] Turn over

16 16 Section C 12 This question is based on the article Uncertainty in a calculated result. Students in a class measured the force needed to break 29 samples of copper wire from the same reel. Their results are shown in the chart in Fig frequency breaking force / N Fig (a) (i) Explain why the single value at 5.5 N needs to be considered to be a possible outlier. (ii) Suggest what may have happened to the wire to give the much smaller breaking force of 5.5 N. (b) A student calculates the mean value of the remaining 28 values as N. Use the bar chart to write down the best estimate and uncertainty of the breaking force of the copper, using an appropriate number of significant figures. [1] breaking force = ± N

17 17 (c) The diameter of the wire used is measured at several points along its length with a micrometer. The reading is 0.38 ± mm each time. (i) Calculate the percentage uncertainty in the diameter measurement. Give your answer to an appropriate number of significant figures. uncertainty = ± % (ii) Explain why the uncertainty in the diameter measurement can be ignored when calculating the breaking stress of copper. (d) Use the answer to (b) to calculate the mean breaking stress of copper and to estimate the uncertainty in this value. cross-sectional area of copper wire = m 2 [1] breaking stress = ± Pa [3] [Total: 11] Turn over

18 18 13 This question is based on the article Water rockets. (a) The graph in Fig shows the way in which the mean height of the water rocket varies with time. 30 height / m time / s Fig (i) Draw a best-fit curve through the points and use the graph to obtain a value for the maximum height reached by the water rocket. maximum height =... m [1] (ii) Use the graph to show that the initial velocity of the rocket is about 25 m s 1.

19 (iii) 19 Explain how the graph shows that the rocket has an acceleration downwards for its entire flight. (b) (i) Use the equations for uniformly accelerated motion to show that a maximum height of about 30 m can be reached by an object projected vertically with an initial vertical velocity of 25 m s 1. g = 9.8 m s 2 [3] (ii) Suggest and explain one reason why the rocket did not reach the maximum height calculated in (b)(i). Turn over

20 20 (c) This question refers to the second set of results where the students experiment was affected by a horizontal wind. (i) Explain why the height reached by the water rocket was not affected by the wind. (ii) Use data from the graph of Fig to estimate the speed of the wind which resulted in the rocket landing 37 m from its launch position. [Total: 14]

22 14 This question is based on the article Robert Millikan and the Planck constant. 22 (a) In his measurements, Millikan found the stopping p.d. by extrapolating the current curves to zero current. (i) Draw a best-fit curve to find the stopping p.d. for the data in the graph in Fig. 14.1, for sodium metal illuminated with light of wavelength nm. Use your value to complete the table underneath. 90 current / arbitrary units p.d. / V Fig wavelength, λ / nm frequency, f / Hz stopping p.d. / V

23 (ii) 23 Use the table to complete the graph of Fig and determine the gradient of the best-fit straight line through the data. Show your working clearly. p.d. / V frequency / Hz Fig (iii) The gradient of the graph of Fig is h e. Calculate the Planck constant, h. e = C gradient of best-fit line =... V Hz 1 [5] h =... J s [1] (b) (i) Millikan s published value of the Planck constant was J s with an uncertainty of ± 0.5%. Calculate the maximum likely value of h using this information. maximum h =... J s

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