A fishermen 's spring scale is extended to a total length of 0.18m when 0.12 kg fish is suspended from it .If the spring constant is 100N/ m ; what is the total length of the spring when 11.4 kg fish is suspended from it
15.5 m
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Given information:
- Length of the spring when a 0.12 kg fish is suspended, L₁ = 0.18 m
- Mass of the fish, m₁ = 0.12 kg
- Spring constant, k = 100 N/m
- Mass of the fish to be suspended, m₂ = 11.4 kg
Using Hooke's Law, we can calculate the force exerted by the spring when the 0.12 kg fish is suspended:
F₁ = k * L₁
F₁ = 100 N/m * 0.18 m
F₁ = 18 N
The force exerted by the spring when the 11.4 kg fish is suspended will be equal to the force exerted when the 0.12 kg fish is suspended:
F₂ = F₁
F₂ = 18 N
Using Newton's second law (F = m * g), we can calculate the weight of the 11.4 kg fish:
W₂ = m₂ * g
W₂ = 11.4 kg * 9.8 m/s²
W₂ ≈ 111.72 N
Now, we can find the displacement of the spring when the 11.4 kg fish is suspended:
F₂ = k * L₂
L₂ = F₂ / k
L₂ ≈ 111.72 N / 100 N/m
L₂ = 1.1172 m
Therefore, the total length of the spring when the 11.4 kg fish is suspended is approximately equal to 1.1172 meters.
To solve this problem, we'll use Hooke's law, which states that the force exerted by a spring is proportional to the extension or compression of the spring. Mathematically, it can be expressed as:
F = k * x
Where:
F is the force applied on the spring (in newtons),
k is the spring constant (in newtons per meter), and
x is the extension or compression of the spring (in meters).
In this case, we are given the force, mass, and spring constant, and we need to find the extension (x). First, we'll find the force applied on the spring using the mass and gravitational acceleration:
F = m * g
Where:
m is the mass (in kilograms) and
g is the acceleration due to gravity (approximately 9.8 m/s²).
Now, we can solve for the extension using Hooke's law:
F = k * x
Rearranging the equation, we get:
x = F / k
Now, let's plug in the values:
m = 11.4 kg (mass of the fish)
k = 100 N/m (spring constant)
F = m * g = 11.4 kg * 9.8 m/s² = 111.72 N
x = F / k = 111.72 N / 100 N/m = 1.1172 m
Therefore, the total length of the spring when a 11.4 kg fish is suspended from it is 1.1172 meters.