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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 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 Mr2 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
Throwing and Jumping Maximum Horizontal Range: V2/2g Maximum vertical height: V2/g
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
Leverage rowing press ups Barbell curls Class 1 Class 2 Class 3
Wrestling holds: class 2 > class 3 > class 1 Cael Sanderson 2004 Olympic champion
6.14m PV 4.5-5m 2m 2.45m HJ
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 !
The Giant Swing Bangkok 1784-1935 Wat Suthat Temple, 30m high !
1910 To thank the god Shiva for the annual rice harvest Ceremonies stopped in 1932 due to fatal accidents
Angular velocity at top = w Centre of gravity 2.5m Angular velocity at bottom = W
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
Strength versus Size Strength is proportional to area R2 Weight is proportional to volume R3
Strength and Weight strength (weight)2/3 Giants eventually break!
World Weightlifting Records (strength)3 (weight)2
Putting The Shot – Two Surprises World record 23.12 metres
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
A Constrained Optimisation Launch speed falls as angle increases Typically 34-38 degrees is best But is athlete dependent
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(2max)
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
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
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?