Several studies indicate that the elastic properties of tendons can change in re

Question

Several studies indicate that the elastic properties of tendons can change in response to exercise. In one study, guinea fowl were divided into a group that ran for 30 minutes a day on a treadmill, and a control group that was kept in their cages. After 12 weeks, the researchers measured the mechanical properties of the gastrocnemius tendon in each bird. The results for one control bird and one treadmill bird are shown in (Figure 1) .

Part A

Treating the tendon as an ideal spring, what is the force constant for the control bird?

Express your answer to two significant figures and include appropriate units.

Part B

By how much does the control bird’s tendon need to be stretched in order to have the same amount of stored energy as the tendon of the treadmill bird at a deformation of 3.0 mm?

Express your answer to two significant figures and include appropriate units.

Im stuck on B!

Explanation / Answer

B] Force constant for level = 80/1 x 10-3 = 8 x 104 N/m

so, for a deformation of 3 mm, the energy stored will be: E = (1/2)kx2 = (1/2)(8 x 104)(3 x 10-3)2 = 0.36 J

this energy needs to be the same for the control.

kcontrol = 4 x 104 N/m

therefore, 0.36 = (1/2)(4 x 104)x2

=> x = 4.243 x 10-3 m = 4.2 mm.

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