How Much Elastic Energy Is Stored in the Achilles Tendon?

[dvolpe]

Homework Statement

If the maximum tension in the Achilles tendon when the foot is sent down is 4.5 kN and the tendon's spring constant is 360 kN/M, calculate how much elastic energy is stored in it.

Homework Equations

F = kx
Hookes Law: Energy = 1/2*k*x squared

The Attempt at a Solution

Got x from F = kx x = 0.0125 m this is correct per submission.
Then substituted all values into Hookes law and got energy = .0281 J This was wrong according to submission.

If the elastic energy is a measure of the potential energy, how do I find that?

 

[rock.freak667]

Your formula for energy should work. Did you properly convert the units?

 

[dvolpe]

Yes I converted th distance x of 1.25 cm to .0125 m. The constant is 360 kN/m . Wait..do I need to convert the constant to N/m?
Which then makes the answer -.0281 KJ or -28.1 joules, correct?

 

[rock.freak667]

Yes I converted th distance x of 1.25 cm to .0125 m. The constant is 360 kN/m . Wait..do I need to convert the constant to N/m?
Which then makes the answer -.0281 KJ or -28.1 joules, correct?

Yes. However your answer would be positive and not negative.

 

[rwisz]

To find the elastic potential energy stored in the tendon, you can use the formula:

Elastic potential energy = 1/2 * k * x^2

Where k is the spring constant and x is the displacement of the tendon. In this case, the displacement would be 0.0125 m, as you correctly calculated.

So, the elastic potential energy stored in the tendon would be:

Elastic potential energy = 1/2 * 360 kN/m * (0.0125 m)^2 = 0.0281 kN*m = 28.1 J

This is the same value you calculated, so it is likely that your submission was incorrect for another reason. Double check your calculations and units to make sure they are correct.