A fisherman is fishing from a bridge and is using a "43.0-N test line." In other words, the line will sustain a maximum force of 43.0 N without breaking. What is the weight of the heaviest fish that can be pulled up vertically, when the line is reeled in (a) at constant speed and (b) with an acceleration whose magnitude is 2.84 m/s2?
To find the weight of the heaviest fish that can be pulled up vertically, we need to use Newton's second law of motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a).
(a) When the line is reeled in at a constant speed, the acceleration is zero because the speed is not changing. Therefore, the force required to lift the fish is equal to its weight.
To find the weight, we need to convert the given force of 43.0 N to kilograms (kg), which is the SI unit of mass. We divide 43.0 N by the acceleration due to gravity (approximately 9.8 m/s^2) to find the mass in kg:
Weight = Force / Acceleration due to gravity
Weight = 43.0 N / 9.8 m/s^2 ≈ 4.39 kg
So, the weight of the heaviest fish that can be pulled up vertically at a constant speed is approximately 4.39 kg.
(b) When the line is reeled in with an acceleration of magnitude 2.84 m/s^2, there will be an additional force acting on the fish due to this acceleration. We can calculate this force by multiplying the mass of the fish by the acceleration:
Force = mass × acceleration
Force = m × 2.84 m/s^2
To find the weight, we solve this equation for mass:
Weight = Force / Acceleration due to gravity
Weight = (m × 2.84 m/s^2) / 9.8 m/s^2
Now we can substitute the given force of 43.0 N into the equation:
43.0 N = (m × 2.84 m/s^2) / 9.8 m/s^2
To find the mass, we rearrange the equation:
m = (43.0 N × 9.8 m/s^2) / 2.84 m/s^2 ≈ 148.31 kg
So, the weight of the heaviest fish that can be pulled up vertically with an acceleration of magnitude 2.84 m/s^2 is approximately 148.31 kg.