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David and Goliath: Strength and Power in Sport

David and Goliath: Strength and Power in Sport. John D Barrow. Mass and Weight. Mass = Force/Acceleration m= F/A Weight is a force W = Mg A= M/m  g Expt: (M-m)/(M+m) < 10 -12 Implies m = M exactly (Einstein). accelerate. gravity. M. M. M’. M’. If m  m’. Latitude and Gravity. r.

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David and Goliath: Strength and Power in Sport

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  1. David and Goliath:Strength and Power in Sport John D Barrow

  2. Mass and Weight • Mass = Force/Acceleration m= F/A • Weight is a force W = Mg • A= M/m  g • Expt: (M-m)/(M+m) < 10-12 • Implies m = M exactly (Einstein) accelerate gravity M M M’ M’ If m  m’

  3. Latitude and Gravity r Mr2 Weight of mass M is least at Equator and most at Poles MgEquator < MgPoles 100 Kg weighs 0.5% more at the Poles = 500 gm

  4. Throwing and Jumping Maximum Horizontal Range: V2/2g Maximum vertical height: V2/g

  5. The Best Place to Be a Weightlifter High altitude  greater distance from Earth’s centre  lower g Mg = GMME/R2 Mexico City is the best venue to combine height and latitude gains g = 9.779 m/s² so 100kg weighs 977.9 N A good place to lose weight Some of worst venues are Oslo or Helsinki, where 9.819 m/s² and 100 kg weighs 981.9 N

  6. Leverage rowing press ups Barbell curls Class 1 Class 2 Class 3

  7. Wrestling holds: class 2 > class 3 > class 1 Cael Sanderson 2004 Olympic champion

  8. 6.14m PV 4.5-5m 2m 2.45m HJ

  9. Karate Need 3100 N to split 20x30x1cm pine block 3200 N for same area brick 4cm thick Black belt strikes at V = 7m/s Arm mass is about m = 3.4 kg Momentum of arm is mV = 7 × 3.4 = 24 kg m/s contact time with the target is less than T = 5 millisec Force  m x V/T = 24 ÷ 0.005 = 4800 N [A 70kg person weighs 70 × 9.8 = 686 N] Easy !

  10. The Giant Swing Bangkok 1784-1935 Wat Suthat Temple, 30m high !

  11. 1910 To thank the god Shiva for the annual rice harvest Ceremonies stopped in 1932 due to fatal accidents

  12. How big a force do you feel?

  13. Angular velocity at top = w Centre of gravity 2.5m Angular velocity at bottom = W

  14. w Rotation energy at bottom = Rotation energy at top + Potential Energy lost ½ IW2 = ½ Iw2 + 2Mgh Ang Vely s-1 W Max force on gymnast is at the bottom Maximum force felt by the gymnast = Mg + MhW2 = Mg + 4M2gh2/I I = Mk2 Mh2 Total force felt by the gymnast = Mg(1 + 4h2/k2 +hw2/g) With a typical angular velocity at the top of 2-3 per s and g = 9.8 m/s2 and a typical body size with h = 1.3m, Total force felt by the gymnast  Mg(1 + 4 + 1.2)  6Mg Start from handstand only reduces it by 1g Head spins in circle h approx 1.3m only

  15. Naim Suleymanoglu (b.1967) lifts 3 times his body weight

  16. Strength versus Size Strength is proportional to area  R2 Weight is proportional to volume  R3

  17. Strength and Weight strength  (weight)2/3 Giants eventually break!

  18. World Weightlifting Records (strength)3 (weight)2

  19. Putting The Shot – Two Surprises World record 23.12 metres

  20. Max range isn’t achieved with45 degree launch angle

  21. Launching from above ground level h  2 m

  22. The Second Surprise Top class shot putters use a launch angle of about 37 deg – not 42-43 deg Because… They can’t achieve the same launch speed at all launch angles

  23. A Constrained Optimisation Launch speed falls as angle increases Typically 34-38 degrees is best But is athlete dependent

  24. 21.3 metres (= 70 ft) optimal angle is 42 deg 15.24 metres (=50 ft) ------------------- 41 deg 10.7 metres (= 35 ft) -------------------- 39 deg Rmax = h tan(2max)

  25. Rowing in Numbers How does the speed of the boat depend on the number of rowers? Drag on boat  V2  wetted surface area of boat  V2  L2 Volume of boat  L3  N – the number of crew Drag  V2 N2/3 Crew Power overcoming drag = N  P = V  Drag V3 N2/3 P is the constant power exerted by each (identical rower) V  N1/9 With a cox V  N1/3/[N + 1/3 ]2/9 if cox is third the weight of a rower

  26. Results of 1980 Olympic coxless races (N = 1, 2, 4) + coxed N = 8 Distance is 2000 metres Compare with a cox N = 2, T = 422.5 s N = 4 ,T = 374.5 s (predicted if cox = 1/3 of a rower mass) Better without one! T = (2000) / V  N-0.11 V  N0.11  N1/9

  27. Weight Classes Why do we have them in boxing, wrestling, judo and weightlifting? But not in Shot put, hammer, rowing, …..? Why not height classes in high jump and basketball?

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