(III) A scallop forces open its shell with an elastic material called abductin, whose Young's modulus is about 2.0 x 106 N/m2. If this piece of abductin is 3.0 mm thick and has a cross-sectional area of 0.50 cm2, how much potential energy does it store when compressed 1.0 mm?

Step-by-step solution

Step 1 of 3 ^

E=2x106N/m2 (young`s modulus)

L0=3mm=0.003m=3x10-3m (the thickness of the anductin)

ΔL=1mm=0.001m=1x10-3m (change in length of the abductin under compression)

A=0.5cm2=0.5x10-4 m2 (the cross-section area of the abductin)

The abduction length decreases under the effect of compression like a spring. If the object is like a spring we can find the spring constant k of the abduction.

k=? (spring constant of the abduction)

If the abduction extend or compress like a spring. It stores elastic potential energy like a spring.

U=? (elastic potential energy of the abduction)

Step 2 of 3 ^

If the abductin is treated like a spring, the formula above gives the hooks law.

So