Question

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 length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch 43 mm , while nonathletes' stretch only 32 mm .What is the difference in maximum stored energy between the sprinters and the nonathlethes?

Answer 1

Complete Question:

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 length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters' tendons stretch 43 mm , while nonathletes' stretch only 32 mm . The spring constant for the tendon is the same for both groups,
`31 {\rm {N}/{mm}}`. What is the difference in maximum stored energy between the sprinters and the nonathlethes?

Answer:

`\triangle E = 12.79 J`

Step-by-step explanation:

Sprinters' tendons stretch,
`x_s = 43 mm = 0.043 m`

Non athletes' stretch,
`x_n = 32 mm = 0.032 m`

Spring constant for the two groups, k = 31 N/mm = 3100 N/m

Maximum Energy stored in the sprinter,
`E_s = 0.5kx_s^2`

Maximum energy stored in the non athletes,
`E_m = 0.5kx_n^2`

Difference in maximum stored energy between the sprinters and the non-athlethes:

`\triangle E = E_s - E_n = 0.5k(x_s^2 - x_n^2)\\\triangle E = 0.5*3100* (0.043^2 - 0.032^2)\\\triangle E = 0.5*31000*0.000825\\\triangle E = 12.79 J`