Answer:
Approximately 0.024 kg
Step-by-step explanation:
We can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be written as:
F = -kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. The negative sign indicates that the force is in the opposite direction of the displacement.
We can use the given information to find the spring constant:
k = F/x = 175 N / 0.13 m = 1346.15 N/m
The fish is oscillating vertically, which means that the force of gravity is acting on it. The weight of the fish can be calculated as:
W = mg
where W is the weight, m is the mass, and g is the acceleration due to gravity (9.81 m/s^2).
The oscillation frequency of the fish can be related to its mass and the spring constant using the formula:
f = 1/2π * sqrt(k/m)
where f is the frequency of oscillation, π is a constant (approximately 3.14), and sqrt is the square root function.
We can rearrange this equation to solve for the mass of the fish:
m = k/(4π^2 * f^2)
Substituting the given values, we get:
m = 1346.15 N/m / (4 * 3.14^2 * (2.35 Hz)^2) ≈ 0.024 kg
Therefore, the mass of the fish is approximately 0.024 kg.