Question

If this piece of abductin is 3.1 mm thick and has a cross-sectional area of 0.49 cm2 , how much potential energy does it store when compressed 1.5 mm ?

Answer 1

Complete question:

A scallop forces open its shell with an elastic material called abductin, whose Young's modulus is about 2.0×10⁶ N/m2 .

If this piece of abductin is 3.1 mm thick and has a cross-sectional area of 0.49 cm2 , how much potential energy does it store when compressed 1.5 mm ?

Answer:

The elastic potential energy of the material is 0.036 J

Step-by-step explanation:

Given;

Young's modulus, E = 2.0×10⁶ N/m²

Thickness of the abductin, l = 3.1 mm = 0.0031 m

compression of the abductin, x = 1.5 mm = 0.0015 m

area, A = 0.49 cm² = 0.49 x 10⁻⁴ m²

Young's modulus for elastic material is given by;

`E = (stress)/(strain) = (Fl)/(Ax) \\\\ E = (F)/(x)*(l)/(A)\\\\ E = k*(l)/(A)\\\\k = (AE)/(l)\\\\k = ((0.49 x10^(-4))(2*10^6))/(0.0031)\\\\ k = 31,612.9 \ N/m`

The elastic potential energy of the material is given by;

U = ¹/₂kx²

U = ¹/₂(31,612.9)(0.0015)²

U = 0.036 J

Therefore, the elastic potential energy of the material is 0.036 J