Human feet and legs store elastic energy when walking or running. They are not nearly as efficient at doing so as kangaroo legs, but the effect is significant nonetheless. If not for the storage of elastic energy, a 70.0-kg man running at 4.00 m/s would lose about 100 J of mechanical energy each time he sets down a foot. Some of this energy is stored as elastic energy in the Achilles tendon and in the arch of the foot; the elastic energy is then converted back into the kinetic and gravitational potential energy of the leg, reducing the expenditure of metabolic energy. If the maximum tension in the Achilles tendon when the foot is set down is 4.38 kN and the tendon's spring constant is 321 kN/m, calculate how far the tendon stretches. Now calculate how much elastic energy is stored in it.

To find the distance the Achilles tendon stretches, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched.

Hooke's Law equation:
F = k * x

Where:
F = Force exerted by the spring (tension in the Achilles tendon)
k = Spring constant
x = Distance the tendon stretches

Rearranging the equation to solve for x:
x = F / k

Substituting the given values:
F = 4.38 kN = 4.38 * 10^3 N (since 1 kN = 10^3 N)
k = 321 kN/m = 321 * 10^3 N/m (since 1 kN/m = 10^3 N/m)

x = (4.38 * 10^3 N) / (321 * 10^3 N/m)
x ≈ 0.0136 m

Therefore, the Achilles tendon stretches approximately 0.0136 meters.

To calculate the elastic energy stored in the tendon, we can use the elastic potential energy formula.

Elastic potential energy equation:
E = (1/2) * k * x^2

Where:
E = Elastic potential energy
k = Spring constant
x = Distance the tendon stretches

Substituting the given values:
k = 321 kN/m = 321 * 10^3 N/m
x ≈ 0.0136 m

E = (1/2) * (321 *​ 10^3 N/m) * (0.0136 m)^2
E ≈ 29.8 J

Therefore, the elastic energy stored in the Achilles tendon is approximately 29.8 Joules.