doing physics with superman jean-baptiste boin. hi everyone and welcome ! talk inspired by roland...
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Doing physics with Superman
Jean-Baptiste Boin
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Hi everyone and welcome !
• Talk inspired by Roland Lehoucq, a French astrophysicist (and a great teacher !)
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1938 – A new hero
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Impressive powers
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Impressive powers
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Super-strength : First argument
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Super-strength : First argument
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Quick aside…
Countries officially not using the metric system
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Quick aside…
« Specifically, the flight system software on the Mars Climate Orbiter was written to take thrust instructions using the metric unit newtons (N), while the software on the ground that generated those instructions used the Imperial measure pound-force (lbf). This error has since been known as the "metric mixup" and has been carefully avoided in all missions since by NASA. »
Mars Climate Orbiter
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Super-strength : First argument
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Super-strength : First argument
60 m(200 ft)
200 m (660 ft)
gKrypton ≈ 30 gEarth !
Radius of Krypton ≈ 30 Radius of EarthMKrypton ≈ 303 MEarth = 27,000 MEarth
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Super-strength : First argument
• MEarth ≈ 6 x 1024 kg
• MSun ≈ 2 x 1030 kg
• Mkrypton ≈ 2 x 1029 kg
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Super-strength : First argument
Krypton
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Super-strength : Second argument
Weight : 10 mg Can carry up to 1 g
X 100 !
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Super-strength : Second argument
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Super-strength : Second argument
Can an elephant carry 100 elephants ?
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The square-cube law
1 cm 2 cm
Area ?
Volume ?
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The square-cube law
1 cm 2 cm
Area of a face : 1 cm2
Volume : 1 cm3
Area of a face : 4 cm2
Volume : 8 cm3
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The square-cube law
1 cm 2 cm
Area of a face : 1 cm2
Volume : 1 cm3
Area of a face : 4 cm2
Volume : 8 cm3
X 4
X 8
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The square-cube law
1 cm L cm
Area of a face : 1 cm2
Volume : 1 cm3
Area of a face : L2 cm2
Volume : L3 cm3
x L2
x L3
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The square-cube law - strength
Power developed by a muscle : proportional toa surface (L2)
Mass : proportional to a volume (L3)
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The square-cube law - strength
M1 M2
• M2/M1 = (L2/L1)3 L⇒ 2/L1 = (M2/M1)1/3
• P2/P1 = (L2/L1)2 = (M2/M1)2/3
• Strength is proportional to mass2/3 !
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The square-cube law - strength
Mass of the athlete (kg)M
ass
lifted
/ M
ass
of a
thle
te2/
3
Mass of the athlete (kg)
Mas
s lift
ed (k
g) Clean-and-jerk
Snatch
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The square-cube law - strength
• Man (75 kg) can lift ≈ his weight• Ant ?
• An ant is not that impressive finally…
Mliftedant = Mliftedman (Mant/Mman)2/3
≈ 1.9 g
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Strength isn’t all…
200T 200T
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Strength isn’t all…
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Run, Superman, run !
• Speed : 30 times faster than a human• 300 m/s (1080 km/h = 670 mile/h) = bullet• Problem : friction, proportional to v2
• Max speed : only 3 times faster than a human
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Another superhero : (Gi)Ant-man !
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Another superhero : Ant-man !
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Another superhero : Ant-man !
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The square-cube law - stress
Stress at the bottom of the cube : s = F/A = Mg/A
Much higher for larger structures !
Multiplied by L
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The square-cube law - stress
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The square-cube law - stress
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The square-cube law - stress
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The square-cube law - stress
Bad news for Giant-man !
(but also for King Kong and Godzilla)
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Ant-man’s daily problems
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The square-cube law - temperature
• Energy (heat) produced : proportional to a volume
• Energy (heat) dissipated : proportional to a surface
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It’s a bird ! It’s a plane !
• Necessary speed : 70 km/h (100 mph)• Power needed to overcome drag : 2,000,000 W
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• 480 kcal per second• Efficiency of 25%• … equivalent of 2 lunches
consumed per second
Food for thought
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• Telescopic vision• Night/infrared vision• Heat vision• X-ray vision• Super-hearing• Freeze breath• …
Other (cool?) superpowers
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Jean-Baptiste Boin
Thanks ! Questions ?