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 40 mm , while nonathletes' stretch only 33 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 nonathletes?

Express your answer using two significant figures in J.

Answer 1

Answer:7.92 J

Step-by-step explanation:

Given

`x_1=40 mm`

`x_2=33 mm`

spring constant of tendons
`k=31 N/mm\approx 31* 10^3 N`

Energy stored in athletes tendon
`=(kx_1^2)/(2)=(31* 10^3* (40* 10^(-3))^2)/(2)`

Energy stored in athletes tendon
`=(kx_2^2)/(2)=(31* 10^3* (33* 10^(-3))^2)/(2)`

Difference in maximum stored energy
`=(k)/(2)(x_1^2-x_2^2)`

`=(31* 10^3)/(2)(1600-1089)* 10^(-6)`

`=7.92 J`