Figure 1 (A420U10-1) SECTION B 7. Read through the following article carefully. Cool Physics for Smart Phones by Justino Luis Moreno Some meters can be expensive to buy but if you’ve got a smart phone it’s surprising just how many meters it can be employed as, if you get hold of the right apps. Right now on my iphone I’ve got a seismometer, magnetometer, accelerometer, tiltometer, protractor, light meter, ruler, decibel meter, oscilloscope and frequency meter. In the hands of a physicist your smart phone is transformed into a whole lot of experimental fun. Experiment 1 - Measuring the speed of sound All you need is a hollow cardboard tube of length between 1 and 3 metres. You’ll also need a frequency meter app (mine’s part of a free guitar tuner) and somebody who can make didgeridoo noises into the cardboard tube. Anyone can make these noises after a bit of practice and you should even be able to play the two lowest notes. The cardboard tube didgeridoo can be classed as a pipe that is closed at one end. There is a node of air displacement at the closed end, and an antinode at the open end. The second lowest note is called the third harmonic because it has a frequency of 3 times the lowest (or ‘fundamental’ or ‘first harmonic’). When carrying out this experiment with a hollow tube of length 1.800 m, the fundamental note had a frequency of 47 Hz. This gave a value of the speed of sound of around 340 m s–1 which is not bad with a piece of throw-away cardboard and a free guitar tuning app. Experiment 2 - Investigating polarisation of light Unfortunately, light meter software tends to use a unit called ‘lux,’ but as long as we don’t change light source mid-experiment the lux is proportional to the intensity. We shall concentrate on an experiment to do with polarisation - the variation of transmitted intensity through a polaroid with angle of the polaroid relative to the polarised light. The set-up is shown below. 16 © WJEC CBAC Ltd. The polariser provides the polarised light, the analyser is rotated in steps through 180° and the intensity of light is recorded using the smart phone. You can measure the angle (θ ) with a plastic protractor but there is a smarter way. You can tape the analyser over the smart phone camera and have 2 apps running simultaneously – a light meter to measure the light intensity and a tiltometer to measure the angle of the analyser. Unpolarised light Polariser Polarised light Transmission axis Analyser smart phone θ E0 Figure 2 1 2 3 4 Paragraph Turn over. 17 (A420U10-1) These were the results obtained: © WJEC CBAC Ltd. 0 0 100 200 40 80 120 160 20 60 100 140 180 0 300 40 80 120 160 20 60 100 140 180 These results are in excellent agreement with Malus’s Law – that the intensity, I, of light is given by: I = I0 cos2 θ where θ is the angle of the analyser relative to the polariser. Experiment 3 - Measuring the coefficient of friction There is a simple rule of friction that states: F = μR Light intensity / arbitrary units Figure 3 Figure 4 θ / ° where F is the maximum frictional force, R is the normal contact force and μ is the coefficient of friction. Basically, μ is a dimensionless constant that tells you how slippery the contact is between two smooth surfaces. The greater the value of μ the greater the frictional force (for a given value of R). One of the easiest methods of obtaining values of the coefficient of friction is to place a block on a slope and tilt the slope until the block slips. When the block slips it’s easy to show that the coefficient of friction is given by: μ = tanθ R F 5 6 7 Paragraph Figure 5 36.5° θ (A420U10-1) 18 © WJEC CBAC Ltd. Table 1 The angle can be measured easily with an uncertainty of less than 1° using a smart phone with a tiltometer placed on the slope. Here are some results obtained for rubber on tarmac. Surface Mean slide angle (degrees) Mean coefficient of friction smooth rubber on tarmac 44.4 0.98 rubber with treads on tarmac 40.4 0.85 Experiment 4 - Investigating magnetic field strengths The phone was used as a magnetometer to take readings of the magnetic field strength, B, at two distances, r, from the centre of a small bar magnet (with the magnet end-on to the magnetometer). The results are shown in Table 2. r / cm B / mT 8.0 9.8 12.0 2.9 These results suggest that B depends on r according to an inverse cube law, that is a law of the form: where K is a constant. B K r3 = 8 9 10 11 Table 2 Experiment 5 - Investigating the acceleration of a car All sorts of investigations can be done with a mobile phone used as an accelerometer. Oscillations particularly lend themselves to this method. As an even simpler case, though, here is a (tidied up) acceleration-time graph, based on accelerometer readings for a car starting from rest at time t = 0 and going along a straight road. 0 0.2 0.4 0 0.1 0.3 0.5 0.6 10 20 30 40 50 a / m s–2 Figure 6 Paragraph t / s Turn over. 19 (A420U10-1) Examiner only © WJEC CBAC Ltd. Answer all questions. Answer the following questions in your own words. Direct quotes from the original article will not be awarded marks. (a) Experiment 1 - Draw diagrams showing the stationary wave patterns for the lowest frequency (first harmonic) and the next lowest frequency (third harmonic) in the hollow cardboard tube (Paragraph 2). [2] (b) Experiment 1 - Calculate the frequency and wavelength for the third harmonic in the 1.800 m tube (Paragraph 2). [2] (c) Experiment 2 - Explain qualitatively why the variation in light intensity detected by the smart phone is as shown in Figure 3 (see Paragraphs 4 & 5 and Figure 2 also). Do not refer to Malus’s law or the cos2 θ  dependency. [4] (A420U10-1) 20 Examiner only © WJEC CBAC Ltd. (d) Experiment 2 - In paragraph 5 it is claimed that the results plotted in Figure 3 are in excellent agreement with the law I = I0 cos2θ . (i) Show clearly that for these results, using the arbitrary units of the graph scale, I0 = 340. [1] (ii) Check whether or not the point plotted in Figure 3 for θ = 140° is in agreement with the law I = I0 cos2θ. Show all steps in your working. [2] (e) Experiment 3 - Some textbooks claim that “rubber tyres have patterns of grooves or tread: these patterns increase the roughness and give better grip.” Evaluate whether the data in Table 1 (Paragraph 8) disproves this theory or whether this result is due to experimental uncertainty. [3] (f) Experiment 4 - According to the writer, the results in Table 2 (Paragraph 9) suggest that B depends on r according to an inverse cube law, that is a law of the form: (Paragraph 10) Justify this statement. [2] B K r3 = (A420U10-1) 21 Examiner only (g) Experiment 5 (i) For the car, starting from rest, whose acceleration-time graph is given in Figure 6, calculate the velocity at t = 25 s. [1] (ii) Sketch a velocity-time graph for the car, on the blank grid below. Put a scale on the vertical axis. (A copy of Figure 6 is provided so that you can refer to it easily.) [3] © WJEC CBAC Ltd. 0 0.2 0.4 0 0.1 0.3 0.5 0.6 10 20 30 40 50 0 0 10 20 30 40 50 a / m s–2 v / m s–1 t / s t / s END OF PAPER 20 Turn over. BLANK PAGE (A420U10-1) 22 © WJEC CBAC Ltd. 23 Examiner only © WJEC CBAC Ltd. For continuation only. (A420U10-1) BLANK PAGE (A420U10-1) 24 © WJEC CBAC Ltd.