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Solving Physics Problems - University of Oxford · BPhO Round 1 Round 2 Training Camp IPhO Oxford...
Transcript of Solving Physics Problems - University of Oxford · BPhO Round 1 Round 2 Training Camp IPhO Oxford...
Physics Challenge
AS Challenge
A2 Challenge
Experimental Project
BPhO ◦ Round 1
◦ Round 2
◦ Training Camp
◦ IPhO
www.bpho.org.uk Oxford 24th June 2014
Robin Hughes
King’s College School Wimbledon
British Physics Olympiad www.BPhO.org.uk
Rutherford Schools Project www.Rutherford-Physics.org.uk
“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
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
5012 – 4992
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
0. 4
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)
6
3
20
30
1
,,
][][][][
][][][][
231
T
L
M
TLMofpowersequating
LTMLLTM
gvM
3
6
g
vkM
Mass of rock swept down by a flooding river:
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.
2
5
5
2
5
1
5
1
t
REortEconstR
),,( tEfR
E = 1.2 x 4.2 x 1013 J
= 5 x 1013 J
= 5 x 1013 / 4 x 109 T TNT
= 12 kilo tonne TNT
ρair=1.2 kg m-3
1 tonne TNT = 4 x 109 J
0.006 ms 16 ms 25 ms
53 ms 62 ms 90 ms
Trinity Atomic Explosion
R5 = 4.2 x 1013 t2 (+ 6 x 109) R2 = 0.996
0.0E+00
5.0E+10
1.0E+11
1.5E+11
2.0E+11
2.5E+11
3.0E+11
3.5E+11
4.0E+11
0 0.002 0.004 0.006 0.008 0.01
R5 /
m5
t2 / s2
Trinity Explosion
y = 0.367x + 2.7 R² = 0.997
1.8
1.9
2
2.1
2.2
2.3
2.4
-2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1
Lo
g(R
/m)
Log(t/s)
Trinity Explosion
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?
GPE lost in forming a star of mass M, of radius R, and of uniform density ρ is given by
R
GM 2
5
3
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.
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