Question

1. Sports scientists find that, on average, the knee extensor tendons in sprinters stretch by 44 mm, while those of non-athletes stretch only by 32 mm. The spring constant is the same for both groups, 33 N/mm.

a) How much more energy do those sprinters store than the rest of us at full extension (2 s.f.)?

b) If the efficiency of energy storage of the sprinters' tendons is about 93%, how much kinetic energy does the sprinter recover from a fully stretched knee tendon (2 s.f.)?

c) What happens to the missing 7% of stored energy? Explain why this must be true.

Answer 1

a)

energy stored in sprinter E1 = (1/2)*k*x1^2

k = spring constant = 33 N/mm = 33*10^3 N/m

x1 = stretch in sprinter = 44 mm = 0.044 m

E1 = (1/2)*3*10^3*0.044^2 = 2.904 J

energy stored by rest E2 = (1/2)*k*x2^2

k = spring constant = 33 N/mm = 33*10^3 N/m

x2 = stretch in sprinter = 32 mm = 0.032 m

E2 = (1/2)*3*10^3*0.032^2 = 1.536 J

excess energy store by sprinter = E1 - E2 = 1.368 J

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b)

kinetic energy recovered = 97% of E1

KE = (97/100)*2.904 = 2.82 J

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c)

the missing energy goes in the form of internal energy