A 13 cm long animal tendon was found to stretch 3.8 mm by a force of 13.8 N. The tendon was approximately round with an average diameter of 7.0 mm. Calculate the elastic modulus of this tendon.
To calculate the elastic modulus of the tendon, we first need to understand its definition. The elastic modulus (also known as Young's modulus) is a measure of how much a material deforms under stress. It represents the stiffness or rigidity of the material.
The formula to calculate the elastic modulus is as follows:
E = (F * L) / (A * ΔL)
Where:
E is the elastic modulus
F is the force applied to the material
L is the original length of the material
A is the cross-sectional area of the material
ΔL is the change in length of the material
In this case, we are given:
F = 13.8 N
L = 13 cm = 130 mm
ΔL = 3.8 mm
Diameter = 7.0 mm
To calculate the cross-sectional area (A) of a circular tendon, we can use the formula for the area of a circle:
A = π * (D/2)^2
Where:
π is a mathematical constant (approximately 3.14159)
D is the diameter of the tendon
Substituting the given values into the equations, we have:
A = π * (7.0 mm / 2)^2
A = π * (3.5 mm)^2
A = 3.14159 * (12.25 mm)
A = 38.48 mm^2
Now, we can substitute all the values into the elastic modulus formula:
E = (13.8 N * 130 mm) / (38.48 mm^2 * 3.8 mm)
Calculating this expression gives us the value for the elastic modulus of the tendon.