Final answer:
The mass of a fish that would stretch the spring by 23.0 cm is 18.1 kg. This is found using Hooke's law and the known weight of a fish that stretches the spring by 14.0 cm to calculate the spring constant, and then applying that constant to the new stretch length.
So, the correct answer is D) 18.1 kg.
Step-by-step explanation:
To determine the mass of a fish that would stretch the spring by 23.0 cm, we can use Hooke's law, which relates the force exerted on a spring to the displacement of the spring (F = kx, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position).
First, we find the spring constant using the given data:
108 N = k × 0.14 m (because 14.0 cm is equivalent to 0.14 m)
k = 108 N / 0.14 m
k = 771.43 N/m
Now, using the spring constant, we can find the mass that would stretch the spring 23.0 cm (or 0.23 m):
F = k × x
F = 771.43 N/m × 0.23 m
F = 177.429 N
To find the mass, we use the formula weight (W) = mass (m) × gravitational acceleration (g), where g is approximately 9.81 m/s²:
m = F / g
m = 177.429 N / 9.81 m/s²
m = 18.1 kg
So, the correct answer is D) 18.1 kg.