Final answer:
To find the mass of a fish that would stretch the spring by 23.0 cm, we can use Hooke's Law. The mass is approximately 18.41 kg.
Step-by-step explanation:
To find the mass of a fish that would stretch the spring by 23.0 cm, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position.
The formula for Hooke's Law is F = kx, where F is the force, k is the spring constant, and x is the displacement.
Given that the weight of the fish is 108 N and it stretches the spring by 14.0 cm, we can determine the spring constant by dividing the weight by the displacement: k = F / x.
So, the spring constant is 108 N / 14.0 cm = 7.71 N/cm.
To find the mass of a fish that would stretch the spring by 23.0 cm, we can rearrange the formula and solve for the mass:
F = kx = mg
m = F / g
Using the given equation and substituting the values, we get:
m = (7.71 N/cm)(23.0 cm) / 9.8 m/s^2 = 18.41 kg
Therefore, the mass of a fish that would stretch the spring by 23.0 cm is approximately 18.41 kg.