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(II) A fisherman yanks a fish vertically out of the water withan acceleration of 2.5 $\mathrm{m} / \mathrm{s}^{2}$ using very light fishing line thathas a breaking strength of 18 $\mathrm{N}(\approx 4$ lb). The fishermanunfortunately loses the fish as the line snaps. What can yousay about the mass of the fish?

the mass of the fish is $[m>1.5 \mathrm{kg}$

Physics 101 Mechanics

Chapter 4

Dynamics: Newton's Laws of Motion

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

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Hope College

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so we can draw the free body diagram for the fish. This box represents the fish going up would be the force. Tension in the fishing line and then going down would of course, be the weight of the fish. Weaken, right. Newton's second law for the vertical direction we're gonna stay upwards is positive. And we know that the tension is at its maximum. So we can say that Sigma afternoon our direction would equal for his tension minus entry equal the mass times acceleration of the fish. Ah, we can solve for the mass where, uh here we could say forced tension would equal m m a m a rather plus mg and then we're going to divide by. We can factor out m rather and then the divide by the sum of the accelerations. So mass is gonna be equal to the maximum force Tension divided by the acceleration of the fish, plus the acceleration due to gravity on earth. And this is gonna give us 18. Newton's divided by 2.50 plus 9.80 units here would be forced the meters per second squared, and we have that the mass of the fish is 1.5 kilograms. Therefore, this is the maximum mass that the fish line can support. Given this given this acceleration. So Ah, we can say that since the line broke, we can say that the mass of the fish would be greater than 1.5 kilograms again. Ah, this is this is specific to the acceleration so potentially if the, um if Thea acceleration was decreased. So if you were to perhaps a really in slowly ah, little bit more slowly than 2.50 meters per second squared. You may be able to catch this fish without the line breaking, but of course, given this acceleration and given that the line broke again, the mass of the fish must be creator than 1.5 kilograms. That is the end of the solution. Thank you for watching

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