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The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. sports scientists have studied the change in lenght of the knee extensor tendon in sprinters and nonathletes. they find (on average) that the sprinters' tendons stretch 43mm, while nonatheletes' stretch only 30mm. the spring constant for the tendon is the same for both groups, 33 n/mm. what is the difference in maximum stored energy between the sprinters and the nonathletes?

Respuesta :

Use Hooke's law:

[tex]Elastic\,Potential\,Energy: \frac{1}{2}kx^{2} [/tex]
 
[tex]\frac{1}{2}*33*43^{2} - \frac{1}{2}*33*30^{2} = 15658.5 N mm = 15.7J[/tex]

An sprinter's tendon stores about 15.7J more energy as compared to the non-athletes.
Lanuel

The difference in maximum stored energy between the sprinters and the nonathletes is 2.06.

Given the following data:

  • Extension of sprinter = 43 mm
  • Extension of nonathletes = 30 mm
  • Spring constant = 33 n/mm.

To find the difference in maximum stored energy between the sprinters and the nonathletes:

Assuming that the knee extensor tendon obeys Hooke’s Law and stretches in a straight line, we would use this formula:

[tex]U_s = \frac{1}{2} kx^2[/tex]

Where:

  • Us is the elastic energy of a spring.
  • k is the spring constant.
  • x is the extension of a spring.

For the sprinter:

[tex]U_s = \frac{1}{2} \times 33 \times 10^{3} \times [43 \times 10^{-3}]^2\\\\U_s = 16500 \times 1.849 \times 10^{-3}[/tex]

Elastic energy, [tex]U_s[/tex] = 30.51 Joules

For the nonathletes:

[tex]U_s = \frac{1}{2} \times 33 \times 10^{3} \times [30 \times 10^{-3}]^2\\\\U_s = 16500 \times 9 \times 10^{-3}[/tex]

Elastic energy, [tex]U_s[/tex] = 14.85 Joules

[tex]Difference = \frac{30.51}{14.85}[/tex]

Difference = 2.06

Read more: https://brainly.com/question/14621920

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