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Answer :
The largest mass that the fish can have and still be reeled in without breaking the line is approximately 1.291 kg.
To determine the largest mass of the fish, we need to consider the forces acting on the fishing line. The tension in the line is equal to the force required to reel in the fish, while the force exerted by the fish acts in the opposite direction.
First, let's convert the given values to SI units:
Tension (t) = 42.7 N
Force exerted by the fish (f) = 37.9 N
Acceleration (a) = 0.294 m/s^2
Now, let's analyze the forces acting on the fishing line using Newton's second law, F = ma:
t - f = ma
Rearranging the equation, we can find the tension in the line caused by the acceleration:
t = f + ma
Substituting the given values:
42.7 N = 37.9 N + (m)(0.294 m/s^2)
Simplifying the equation:
42.7 N - 37.9 N = 0.294 m/s^2 * m
4.8 N = 0.294 m/s^2 * m
To solve for m, divide both sides of the equation by 0.294 m/s^2:
m ≈ 4.8 N / 0.294 m/s^2
m ≈ 16.327 kg
However, we need to account for the buoyant force canceling out the weight of the fish. Since the weight is canceled out, the tension in the line is solely due to the fish's acceleration. Therefore, we can use the equation for weight, W = mg, to find the mass:
W = t
mg = t
Solving for m:
m = t / g
Substituting the given values:
m ≈ 42.7 N / 9.8 m/s^2
m ≈ 4.358 kg
However, this is the maximum mass the fish can have without breaking the line. To find the largest mass that can still be reeled in with the given acceleration of 0.294 m/s^2, we subtract the force exerted by the fish from the maximum mass:
Max mass = 4.358 kg - 1.291 kg
Max mass ≈ 3.067 kg
Therefore, the largest mass that the fish can have and still be reeled in without breaking the line is approximately 3.067 kg.
Learn more about buoyant force
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