Question

2. The tentacle of a squid

By what percentage would a squid tentacle increase in length when a circumferential muscle contracts with a strain of 0.2?

Answer: The final length is 1.56 times the initial length, which is an increase of 56%. But how do I get to this answer? Please show work and formulas used to get the provided answers. Thank you!

Answer 1

we have,

strain ( absolute value os strain ) with which the circumferential muscle contracts ,

The contraction of circumferential muscle means final radius of circumferential cross-section of tentacle after contraction is less than the initial radius before contraction, and since the strain is defined as ,

strain = ( final length - initial length ) / initial length

circumferential muscle strain must have negative sign, so we get,

So, circumferential muscle strain

When the circumferential muscle of tentacle of squid contracts the length of tentacle would increase, the relation between circumferential muscle strain and the strain along the length of the tentacle is given as,

using in above relation we get,

So,

strain along the length of the tentacle ( Expressed in two significant figures )

positive sing indicates the elongation along the length of tentacle.

Since by definition of strain,

we get,

That is the final length is 1.56 times the Initial length corresponding to increase of 56 %,