www.bpho.org.uk Oxford 24th June 2014      Physics Challenge AS Challenge A2 Challenge Experimental Project BPhO ◦ ◦ ◦ ◦ Round 1 Round 2 Training Camp IPhO “Moreover a physics problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution”. David Hilbert Robin Hughes  King’s College School Wimbledon  British Physics Olympiad  Rutherford Schools Project www.Rutherford-Physics.org.uk  www.BPhO.org.uk [email protected] What makes a student competitive in physics and engineering?  Problems that demand understanding? Linguistically stylised – interpretation & recognition Massless pulleys Infinite planes Inextensible massless string Point particles Zero friction Etc. Superfluous information Occurs in the real world  Transferable skills Clarity of thought Perseverance The buzz of success Confidence Interest Empowering Our people are our greatest asset        Explanations Computations & calculations Estimates & Fermi problems Technique spotting Proofs Bookwork Data analysis Recent research by SEPnet (from ASE EiS April 2011) Employer views of the skills of physics graduates indicated that the three aspects most highly prized were those of  mathematical competence  the ability to use equipment to produce evidence  being good at problem solving. What was disturbing was the view that the only one that employers felt they were getting was the first. • • • • Requires a knowledge of physics ideas Requires a “feel” for some of the ideas Requires putting in numbers Requires a feel for the physics and what seems reasonable 2 501 – 2 499 0. 4 Is it likely that you breathe in a molecule from Caesar's last breath? Estimate the mass of the earth's atmosphere Estimate the temperature of a newly formed star     Any good ideas? Any numbers we know? Is it too hard? Is the hard way the only way?       When a river floods, the debris that is left behind is often seen in the form of large boulders. Most rivers do not flow very much faster when the river floods as the slope of the river bed remains the same. What is the physics? What are the variables? Are they related? What is the result? Is this what we observe?      Mass of the boulder rolled m Speed of the river flow v Density of boulder (and river combined into some density parameter) ρ field strength g Derive a dimensionally homogeneous equation for m in terms of v, ρ and g. 𝑚 = 𝑓(𝑣, ρ, g)    [ M ]  [v ] [  ] [ g ] 1  3  2  [ M ]  [ LT ] [ ML ] [ LT ] equating powers of M , L, T M 1  L 0    3   T 0    2   3  6 Mass of rock swept down by a flooding river: v  M k 3 g 6       What is the (simple) physics? Is it a fundamental physics idea? What are the variables? Are they related? What is the result? Is this what we observe?   An explosion produces a pressure wave and the speed of the wave is determined by the nature of the surrounding medium and the energy of the explosion. Explosions producing pressure waves in the air can be can be caused by atomic bombs, exploding petrol cans, nitroglycerine, etc. R  f ( E, t ,  ) R  R  const E  t or E  2 t 1 5  1 2 5 5 5 E = 1.2 x 4.2 x 1013 J ρair=1.2 kg m-3 1 tonne TNT = 4 x = 5 x 1013 J 109 J = 5 x 1013 / 4 x 109 T TNT = 12 kilo tonne TNT Trinity Atomic Explosion 0.006 ms 53 ms 16 ms 62 ms 25 ms 90 ms R5 / m5 Trinity Explosion R5 = 4.2 x 1013 t2 (+ 6 x 109) R2 = 0.996 4.0E+11 3.5E+11 3.0E+11 2.5E+11 2.0E+11 1.5E+11 1.0E+11 5.0E+10 0.0E+00 0 0.002 0.004 0.006 t 2 / s2 0.008 0.01 Trinity Explosion y = 0.367x + 2.7 R² = 0.997 2.4 Log(R/m) 2.3 2.2 2.1 2 1.9 1.8 -2.4 -2.2 -2 -1.8 -1.6 Log(t/s) -1.4 -1.2 -1     A star of uniform density is formed from a very large cloud of gas The loss of gravitational potential energy appears as thermal energy of the star Average stars radiate due to fusion processes going on internally. But how does this start? Do the “hot” protons get close enough to fuse, and then start the exothermic (nuclear) reaction? Mass dm falls from a great distance to radius r and forms a thin shell of thickness dr Integrate up from 0 to R to determine the total gpe lost. GPE lost in forming a star of mass M, of radius R, and of uniform density ρ is given by 3 GM 2 5 R        For the sun, M = 2 x 1030 kg no. of protons, N (1.2 x 1057 ) Average ke of a proton (3.3 x 10-16 J ≈ 2.2 keV) Temp of star (1.6 x 107 k) Closest approach of protons (3.5 x 1013 m) Range of strong nuclear force ≈ 10-15 m de Broglie wavelength ≈ 6 x 10-13 m      Tea Social event Portfolio of questions Pupils are the key asset Teacher role      Overall winner of the 1988 IPhO Competition Conrad McDonnell (UK) O levels 1986 A levels 1988 Special Paper 1988 Ox Entrance Paper Nov ‘87 Overall winner of the 1988 IPhO Competition; Conrad McDonnell (UK) O levels 1986, A levels 1988, Special Paper 1988, Ox Entrance Paper Nov ‘87 O & C Special Paper 1988 Bathed in the Glow of Success