1. A 77 kg athlete is sprinting at 9.3 m/s. During ground contact of one stride

Question

1. A 77 kg athlete is sprinting at 9.3 m/s. During ground contact of one stride the athlete’s Achilles tendon stretches 9 mm. How much strain energy is stored in the tendon if it has a spring constant of 320 kN/m?

2. A 62 kg pole vaulter falls from a peak height of 6.25 m and lands on a thick mat. At first contact with the mat, his center of gravity is only 1.30 m high. During impact the mat compresses to 0.65 m high. What average force was exerted by the mat on the pole vaulter during impact? NOTE: Ignore the change in strain energy (?SE=0) during the impact.

Explanation / Answer

1. Strain energy = k x^2 / 2

= (320 x 10^3)(0.009^2)/2

= 12.96 J

2.Applying energy conservation,

PEi + KEi = PEf + KEf

m g (6.25) + 0 = m g (1.30) + m v^2 /2

v = sqrt(2 x 9.8 x (6.25 - 1.30)) = 9.85 m/s

- F (0.65) + (62 x 9.8 x 0.65) = (62 )(0^2 - 9.85^2)/2

F = 5235 N

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