Question

The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 42 mm while those of nonathletes stretch only 35 mm . The spring constant of the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathlethes?

Answer 1

To develop this problem we will apply the concepts of conservation of energy, specifically the change in elastic potential energy that exists between bodies. Since the model is close to that of a spring, we will look for the amount of potential energy stored for both athletes and sprinters and finally we will calculate the difference between them,

`PE_(elastic) = (1)/(2) kx^2`

Here,

k = Constant Spring

x = Displacement

Our values are given as,

`k = 33N/mm ((1000mm)/(1m))`

`k = 33000N/m`

Displacement non-athletes

`x_1 = 35mm = 0.035m`

Displacement Sprinter

`x_2 = 42mm = 0.042m`

For Sprinter

`PE_(2) = (1)/(2)kx_2^2`

`PE_(2) = (1)/(2)(33000)(0.042)^2`

`PE_(2) = 29.106J`

For non-athletes

`PE_(1) = (1)/(2)kx_1^2`

`PE_(1) = (1)/(2)(33000)(0.035)^2`

`PE_(1) = 20.21J`

Now the total change in Potential Energy is

`\Delta PE = PE_2-PE_1`

`\Delta PE = 29.10-20.21`

`\Delta PE = 8.89J`

Therefore the difference in maximum stored energy between the sprinters and the non-athlethes is 8.89J