A 2.9-m nylon fishing line used to hold up a 5.2 kg fish has a diameter of 1.4 mm

How much is the line elongated?

To find the elongation of the fishing line, we can use Hooke's law, which states that the elongation of an object is directly proportional to the force applied to it.

The formula for elongation is given as:

ΔL = (F * L) / (A * E)

Where:
ΔL = elongation of the fishing line
F = force applied to the fishing line (weight of the fish)
L = length of the fishing line
A = cross-sectional area of the fishing line
E = Young's modulus of the fishing line

First, let's calculate the force applied to the fishing line:

F = m * g

Where:
F = force applied to the fishing line
m = mass of the fish
g = acceleration due to gravity (approximately 9.8 m/s²)

Plugging in the values:

F = 5.2 kg * 9.8 m/s²

Calculating:
F = 50.96 N

Next, we need to calculate the cross-sectional area of the nylon fishing line:

A = π * r²

Where:
A = cross-sectional area of the fishing line
r = radius of the fishing line (half of the diameter)

Plugging in the values:

r = 1.4 mm / 2 = 0.7 mm = 0.7 * 10^-3 m

Calculating:
A = π * (0.7 * 10^-3 m)²

Calculating:
A ≈ 1.539 * 10^-6 m²

Now, we need to find the Young's modulus of the nylon fishing line. The Young's modulus for nylon is typically around 2-4 GPa (gigapascals).

For this example, let's use a value of 3 GPa, which is equivalent to 3 * 10^9 Pa.

E = 3 * 10^9 Pa

Now, we can substitute all the values into the elongation formula and calculate the elongation of the fishing line:

ΔL = (F * L) / (A * E)
ΔL = (50.96 N * 2.9 m) / ((1.539 * 10^-6 m²) * (3 * 10^9 Pa))

Calculating:
ΔL ≈ 0.053 m

Therefore, the fishing line would be elongated by approximately 0.053 meters when holding up a 5.2 kg fish.

To determine the amount of elongation in the fishing line, we can use Hooke's Law, which states that the elongation of a material is directly proportional to the force applied to it, as long as the material remains within its elastic limit.

First, let's calculate the force applied to the fishing line using the weight of the fish. The weight of an object can be determined using the formula:

Weight = mass × gravitational acceleration

Given that the mass of the fish is 5.2 kg and the gravitational acceleration is approximately 9.8 m/s², we can calculate the weight:

Weight = 5.2 kg × 9.8 m/s² = 50.96 N

Now, let's calculate the cross-sectional area of the fishing line. The cross-sectional area can be determined using the formula:

Area = π × (radius)²

Given that the diameter of the fishing line is 1.4 mm, we can calculate the radius:

Radius = (1.4 mm) / 2 = 0.7 mm = 0.0007 m

Substituting the radius value into the area formula, we can calculate the cross-sectional area:

Area = π × (0.0007 m)²

Now, let's substitute the values of the force and the cross-sectional area into Hooke's Law equation to calculate the elongation:

Elongation = (Force × Length) / (Young's Modulus × Area)

Young's Modulus is a property of the material of the fishing line and measures its stiffness. For nylon, it typically ranges from 1,000 to 4,000 MPa. Let's assume a value of 2,500 MPa (2.5 × 10⁹ N/m²) for this calculation.

Elongation = (50.96 N × Length) / (2.5 × 10⁹ N/m² × Area)

To determine the length of the fishing line, we need to know how it is secured or attached. Assuming the line is attached at both ends, we can assume a fixed length. If we don't have this information, we won't be able to calculate the elongation accurately.

Once you know the length of the fishing line, you can substitute it into the elongation formula to calculate the amount of elongation.