Question

The elastic energy stored in your tendons can contribute up to 35% of your energy need when running. During a race, sprinters will use shoes with nearly no padding because their body returns more energy without it. Find the energy stored in an athlete's quadriceps tendon with length 42.0 mm and diameter 8.00 mm when the tendon is strained by 11%. The Young's modulus of the tendon is 236 MPa.

Answer 1

Answer 2

The elastic potential energy stored in a tendon is given by:

$U = \frac{1}{2}kx^2$

where $k$ is the spring constant and $x$ is the amount of deformation.

The spring constant for a cylindrical tendon can be calculated using the equation:

$k = \frac{\pi d^4 E}{64L^3}$

where $d$ is the diameter of the tendon, $E$ is the Young's modulus, and $L$ is the length of the tendon.

Substituting the given values, we get:

$k = \frac{\pi (8.00 \times 10^{-3} \text{ m})^4 (236 \text{ MPa})}{64 (42.0 \times 10^{-3} \text{ m})^3}$

$k = 8.94 \times 10^6 \text{ N/m}$

The amount of deformation is given as 11% of the original length:

$x = 0.11(42.0 \times 10^{-3} \text{ m})$

$x = 4.62 \times 10^{-3} \text{ m}$

Substituting these values into the expression for elastic potential energy, we get:

$U = \frac{1}{2}(8.94 \times 10^6 \text{ N/m})(4.62 \times 10^{-3} \text{ m})^2$

$U = \boxed{94.6 \text{ J}}$