Sports scientists find that, on average, the knee extensor tendons in sprinters

Question

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.

Explanation / Answer

Energy Stored across the Sping is Elastic Potential energy

given by U = 0.5 kx^2

for Sprinters ,

K = 33 N/mm=   33*10^3 N/m

x = 44 mm   or 0.044 m

so

Us = 0.5 * 33*10^3 * 0.044^2

Us = 31.944 J

for NOn athlets, x = 32 mm or 0.032 m

so

Ua = 0.5 * 33*10^3 * 0.032^2

Ua = 16.896 Joules

So diff on eenrgy Between sprinters and Non athlets is

U = 31.944 - 16.896 = 15.048 Joules

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part B:

Kinetic energy recoverd = 93% of Sprinters Eergy

KE = 93/100 * 0.5 * 33*10^3 * 0.044^2

KE = 29.707 J

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part C:

remaining 7% of energy is wasted or liberated out in the form of swwaet and heat.

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