A fisherman is fishing from a bridge and is using a "42.0-N test line." In other words, the line will sustain a maximum force of 42.0 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 1.41 m/s2?

(a) 42 N

(b) 36.7 N

Explanation:

Nomenclature

F = force test line (N)

W : fish weight (N)

Problem development

(a) Calculating of weight of the heaviest fish that can be pulled up vertically, when the line is reeled in at constant speed

We apply Newton's first law of equlibrio because the system moves at constant speed:

∑Fy = 0

F-W = 0

42N - W = 0

W = 42N

(b) Calculating of weight of the heaviest fish that can be pulled up vertically, when the line is reeled with an acceleration whose magnitude is 1.41 m/s²

We apply Newton's second law because the system moves at constant acceleration:

m = W/g, m = W/9.8, m:fish mass, W: fish weight g:acceleration due to gravity

∑Fy = m*a

m = W/g, m = W/9.8, m:fish mass, W: fish weight g:acceleration due to gravity

F-W = (W/9.8) * a

42-W = (W/9.8) * 1.41

42 = W+0.1439W

42=1.1439W

W = 42/1.1439

W = 36.7 N