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 41 {\rm mm}, while nonathletes' stretch only 33 {\rm 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

26.22J

Step-by-step explanation:

Conversion to metric unit

41 mm = 0.041 m

33 mm = 0.033 m

31 N/mm = 31 (N/mm) * 1000 (mm/m) = 31000 N/m

The elastics energy has the following formula

`E_e = kx^2/2`

Where k = 31000N/m is the spring constant and x is the distance stretched

The elastics energy stored for athlete is

`31000*0.041^2/2 = 26 J`

His maximum energy stored when running is 26 / 35% = 26*100/35 = 74.4 J[/tex]

The elastics energy stored for non-athlete is

`31000*0.033^2/2 = 16.9 J`

His maximum energy stored when running is 16.9 / 35% = 16.9*100/35 = 48.23 J[/tex]

So the difference in maximum energy stored is 74.45 – 48.23 = 26.22 J