Question

Any physics expert online? See the attachment below.

Answer 1

There is missing information in the question about quantitative physical properties of tendons.

We have two ways to make an assessment about elongation of tendons under stress.

1. Modulus of elasticity.
   A thin rod of length `L_0` having area of cross section `A` is stretched through length `\Delta L` when a force `F` (tension) is applied parallel to its length.
   We know that modulus of elasticity `Y` is given within elastic limits as

   `Y=F/A L_0/(Delta L)`
   There is not information about `Y and A` of tendon.

2. Hook's Law: For for small deformations, the size of the deformation is proportional to the force. Mathematically,

   `F=-kDelta L`
   where `k` is characteristic of object. In the question there is no information about `k`

We know that most materials return to their original lengths if the deformation is less than about `0.1%` However, wrist tendons are known to stretch to about `2.4%` and Achilles tendon is known to stretch to about `6.2%`. Using this information let us find `DeltaL`

Inserting given value we get for

1. Most materials
   `(DeltaL)/L_0=1/1000xx100=0.1\ mm`
2. Wrist tendon
   `DeltaL=170xx2.4/100=4.08\ mm`, (Actual `L=17\ cm`)
3. Achilles tendon
   `DeltaL=290xx6.2/100=17.98\ mm`, (Actual `L=29\ cm`)
   We also know that wrist tendons are capable of taking forces of the order of `50\ N`, whereas Achilles tendon can absorb forces as high as about `5\ kN`.

Keeping this view I would like to choose answer as `3.4\ mm` for a tendon of given length of `10\ cm` which has same order of magnitude of other tendons as above.