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# Solution - Experimental Competition Solutions Page 1/11...

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Experimental Competition / Solutions Page 1/11 Solutions PART-A Product of the mass and the position of the ball ( m × l ) (4.0 points) 1. Suggest and justify, by using equations, a method allowing to obtain m × l . (2.0 points) m × l = ( M + m ) × l cm (Explanation) The lever rule is applied to the Mechanical “Black Box”, shown in Fig. A-1, once the position of the center of mass of the whole system is found. Fig. A-1 Experimental setup 2. Experimentally determine the value of m × l . (2.0 points) m × l = 2.96 × 10 -3 kg m (Explanation) The measured quantities are M + m = (1.411 ± 0.0005) × 10 -1 kg and l cm = (2.1 ± 0.06) × 10 -2 m or 21 ± 0.6 mm. Therefore m × l = ( M + m ) × l cm = (1.411 ± 0.0005) × 10 -1 kg × (2.1 ± 0.06) × 10 -2 m = (2.96 ± 0.08) × 10 -3 kg m

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Experimental Competition / Solutions Page 2/11 PART-B The mass m of the ball (10.0 points) 1. Measure v for various values of h . Plot the data on a graph paper in a form that is suitable to find the value of m . Identify the slow rotation region and the fast rotation region on the graph. (4.0 points) 2. Show from your measurements that h = C v 2 in the slow rotation region, and h = Av 2 +B in the fast rotation region. (1.0 points) 0 200 400 600 800 0 10 20 30 40 50 v 2 Fig. B-1 Experimental data (Explanation) The measured data are h 1 ( × 10 - 2 m) a) t (ms) h ( × 10 - 2 m) b) v ( × 10 - 2 m/s) c) v 2 ( × 10 - 4 m 2 /s 2 ) 1 25.5 ± 0.1 269.4 ± 0.05 1.8 ± 0.1 8.75 ± 0.02 76.6 ± 0.2 2 26.5 ± 0.1 235.7 ± 0.05 2.8 ± 0.1 11.12 ± 0.02 123.7 ± 0.3 3 27.5 ± 0.1 197.9 ± 0.05 3.8 ± 0.1 13.24 ± 0.03 175.3 ± 0.6 4 28.5 ± 0.1 176.0 ± 0.05 4.8 ± 0.1 14.89 ± 0.03 221.7 ± 0.6 5 29.5 ± 0.1 161.8 ± 0.05 5.8 ± 0.1 16.19 ± 0.03 262.1 ± 0.7 6 30.5 ± 0.1 151.4 ± 0.05 6.8 ± 0.1 17.31 ± 0.03 299.6 ± 0.7 7 31.5 ± 0.1 141.8 ± 0.05 7.8 ± 0.1 18.48 ± 0.04 342 ± 1 8 32.5 ± 0.1 142.9 ± 0.05 8.8 ± 0.1 18.33 ± 0.04 336 ± 1 fast ( × 10 - 4 m 2 /s 2 ) h ( × 10 -2 m )
Experimental Competition / Solutions Page 3/11 9 33.5 ± 0.1 141.4 ± 0.05 9.8 ± 0.1 18.53 ± 0.04 343 ± 1 10 34.5 ± 0.1 142.2 ± 0.05 10.8 ± 0.1 18.42 ± 0.04 339 ± 1 11 35.5 ± 0.1 145.4 ± 0.05 11.8 ± 0.1 18.02 ± 0.04 325 ± 1 12 36.5 ± 0.1 147.8 ± 0.05 12.8 ± 0.1 17.73 ± 0.04 314 ± 1 13 37.5 ± 0.1 148.3 ± 0.05 13.8 ± 0.1 17.67 ± 0.04 312 ± 1 14 38.5 ± 0.1 148.0 ± 0.05 14.8 ± 0.1 17.70 ± 0.04 313 ± 1 15 39.5 ± 0.1 143.9 ± 0.05 15.8 ± 0.1 18.21 ± 0.04 332 ± 1 16 40.5 ± 0.1 141.9 ± 0.05 16.8 ± 0.1 18.46 ± 0.04 341 ± 1 17 41.5 ± 0.1 142.9 ± 0.05 17.8 ± 0.1 18.33 ± 0.04 336 ± 1 18 42.5 ± 0.1 141.9 ± 0.05 18.8 ± 0.1 18.46 ± 0.04 341 ± 1 19 43.5 ± 0.1 142.8 ± 0.05 19.8 ± 0.1 18.35 ± 0.04 337 ± 1 20 44.5 ± 0.1 144.3 ± 0.05 20.8 ± 0.1 18.16 ± 0.04 330 ± 1 21 45.5 ± 0.1 142.2 ± 0.05 21.8 ± 0.1 18.42 ± 0.04 339 ± 1 22 46.5 ± 0.1 139.8 ± 0.05 22.8 ± 0.1 18.74 ± 0.04 351 ± 1 23 47.5 ± 0.1 136.7 ± 0.05 23.8 ± 0.1 19.17 ± 0.04 368 ± 1 24 48.5 ± 0.1 133.0 ± 0.05 24.8 ± 0.1 19.70 ± 0.04 388 ± 1 25 49.5 ± 0.1 129.5 ± 0.05 25.8 ± 0.1 20.23 ± 0.04 409 ± 1 26 50.5 ± 0.1 125.7 ± 0.05 26.8 ± 0.1 20.84 ± 0.04 434 ± 1 27 51.5 ± 0.1 124.3 ± 0.05 27.8 ± 0.1 21.08 ± 0.04 444 ± 1 28 52.5 ± 0.1 123.4 ± 0.05 28.8 ± 0.1 21.23 ± 0.04 451 ± 1 29 53.5 ± 0.1 120.9 ± 0.05 29.8 ± 0.1 21.67 ± 0.04 470 ± 1 30 54.5 ± 0.1 117.5 ± 0.05 30.8 ± 0.1 22.30 ± 0.04 497 ± 1 31 55.5 ± 0.1 114.0 ± 0.05 31.8 ± 0.1 22.98 ± 0.04 528 ± 1 32 56.5 ± 0.1 111.2 ± 0.05 32.8 ± 0.1 23.56 ± 0.05 555 ± 2 33 57.5 ± 0.1 110.5 ± 0.05 33.8 ± 0.1 23.71 ± 0.05 562 ± 2 34 58.5 ± 0.1 108.1 ± 0.05 34.8 ± 0.1 24.24 ± 0.05 588 ± 2 35 59.5 ± 0.1 107.1 ± 0.05 35.8 ± 0.1 24.46 ± 0.05 598 ± 2 36 60.5 ± 0.1 104.6 ± 0.05 36.8 ± 0.1 25.05 ± 0.05 628 ± 2 37 61.5 ± 0.1 102.1 ± 0.05 37.8 ± 0.1 25.66 ± 0.05 658 ± 2 38 62.5 ± 0.1 100.1 ± 0.05 38.8

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