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Problem 72 Medium Difficulty

A fisherman is fishing from a bridge and is using a “45-N test line.” In other words, the line will sustain a maximum force of 45 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 a constant speed and (b) with an acceleration whose magnitude is 2.0 $\mathrm{m} / \mathrm{s}^{2} ?$

Answer

45 $\mathrm{N}$
37$\mathrm{N}$

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Video Transcript

to solve this question, we can apply Newton's second law on the vertical access. I would choose that everything that is pointing up its positive on everything that is pointing down as negative as a consequence. Then Newton Cycle Low tells us that the net force that acts on the fish is it close to the mass off the fish times its acceleration. If the fish is being pulled up with a constant velocity, its acceleration is because 20 then the net force that acts on the fish is of course, zero. But the net force is composed by true forces attention force that is pointing up miners the weight force that is pointing down. Then the tension force should be you close to the weight off the fish. But the maximum tension that the line can sustain is 45 Newtons. Therefore, for the maximum tension we have 45 Newtons equals to the weight off the heaviest fish that can be fish it under this conditions. On the next item, we have an acceleration. So the net force that acts on the fish is it goes to the mass off the fish times its acceleration, which is equals to two meters per second squared in the second situation. Now the net force is again composed by two forces. That tension forced miners the weight force and these is of course to the mass times acceleration. Therefore, by solving this equation for the weight, we get the following the tension minus two times the mass off the fish. Is it close to the weight off the heaviest fish that can be fissured Under these conditions, the tension is equals to 45 new terms on extremo situation. So this miners two times the mass off the heaviest fish should be equal to the weight off that fish. But the weight is given by the mass off the heaviest fish times. The acceleration of gravity, which is approximately 9.8 meters per second squared then is equals true am times 9.8. So now we can solve this equation for the mass and then calculate what is the weight? Then we got the following 45 is he goes to 9.8 times the mass plus true plans. The mass 45 then is equals to 11.8 times the mass. So the mass off the heaviest fish is 45 divided by 11.8, then the weight off The heaviest speech is the coast to 45 divided by 11.8 times 9.8 meters per second squared on these results in approximately 37 Newtons.