Beijing Olympics: The Mechanics of the Tyson Bolt 100m Race
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A) By studying video footage, it can be seen that Bolt took 41 strides in total over the 100 m. 29 strides were taken in the last 80 m, and 18 strides were taken during the second 50 m of the race. Calculate the average length of his stride over 100 m, 80 m and 50 m respectively.
B) Using the data given in Table 1, and given that Bolt's mass is 95 kg and his height is 1.95 m, calculate the length and mass of one of his legs. Repeat the calculation for the athlete who took silver, Tyson Gay, whose mass is 75 kg and height 1.8 m.
C)For the purposes of this question, it can be assumed that a sprinter's leg can be idealised as a uniform rod pivoted at the hip.
If the moment of inertia of a rod pivoted at one end is given by: I=(mL^2/3) where m is the mass and L is the length, calculate the moment of inertia of one of Bolt's legs and one of Gay's legs.
D) How much more torque would Bolt need in order to rotate his leg at the same angular acceleration as Gay's leg? Express your answer as a percentage. T=Ia (where T is the torque, I is the moment of inertia, and a is the angular acceleration).
E) The power exerted by the athletes is proportional to the product of the torque and angular velocity of their legs (i.e. the number of cycles per second).
In the race, Tyson Gay took 45 steps in 9.71 seconds compared to Bolt's 41 steps in 9.58 seconds.
Compare quantitatively the power exerted by Bolt with the power exerted by Gay. State any assumptions you have made in your derivation.
Using the expression from part (d), calculate the difference in average power of the two athletes. Express the answer as a percentage.
F) Based on these calculations, briefly discuss the reasons why Bolt was able to run the 100 metres in a time 0.13 seconds faster than Gay.
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Solution Summary
Examining the Bio Mechanics of the Tyson Bolt 100m Race at the Beijing Olympics including comparison of the power generated during the race by the Athletes Usain Bolt and Tyson Gay.
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