A 2.7-m nylon fishing line used to hold up a 7.1-kg fish has a diameter of 1.8mm .
Part A
How much is the line elongated?
To calculate the elongation of the fishing line, we need to use Hooke's Law, which states that the elongation of a spring-like material is directly proportional to the force applied.
The formula for elongation is given by:
Δl = (F ⨉ L) / (π ⨉ r² ⨉ E)
Where:
Δl = Elongation
F = Force applied
L = Length of the material
π = Pi (approximately 3.14159)
r = Radius of the material
E = Young's modulus of the material
In this case, we are given the force (weight of the fish), the length of the line, and the radius. However, we don't have the Young's modulus for nylon.
Without the Young's modulus, we cannot calculate the exact elongation. The Young's modulus is a measure of the stiffness of the material and is necessary to determine the exact elongation.
So, unfortunately, we cannot calculate the line's elongation without the Young's modulus.
To calculate the amount of elongation in the fishing line, you can use Hooke's law, which states that the amount of elongation (ΔL) is directly proportional to the force applied (F) and inversely proportional to the cross-sectional area of the material (A) and its modulus of elasticity (E).
The formula to calculate elongation using Hooke's law is:
ΔL = (F * L) / (A * E)
Where:
ΔL = Amount of elongation
F = Force applied
L = Original length of the material
A = Cross-sectional area of the material
E = Modulus of elasticity of the material
In this case, the fishing line is made of nylon. The modulus of elasticity for nylon is approximately 2.5 GPa (gigapascals) or 2.5 × 10^9 Pa.
The force applied is the weight of the fish, which can be calculated using the equation:
F = m * g
Where:
F = Force applied (weight of the fish)
m = Mass of the fish
g = Acceleration due to gravity (approximately 9.8 m/s^2)
Given:
Mass of the fish (m) = 7.1 kg
Diameter of the fishing line (d) = 1.8 mm (which can be converted to meters by dividing it by 1000: d = 1.8 × 10^-3 m)
To calculate the original length (L) of the line, we need to know the relationship between its diameter and its original length. Unfortunately, the information provided in the question doesn't give us enough details to determine the original length.