A fisherman yanks a fish vertically out of the water with an a...

Question

A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s² using very light fishing line that has a breaking strength of 183 N (≈ 4lb) . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

Accepted Answer

Welcome back. Everyone in this problem. An angler pulls a troll directly upward from the water at an acceleration of 3.5 m per second squared with a thin rope capable of withstanding up to 22.5 newtons, which is about five points. If the rope breaks the throat escapes, what does the rope breaking indicate about the throat's mass? A? It means that the mass is greater than 1.7 kg B that it's greater than 3.6 kg C that it's less than 6.3 kg and D that it's greater than 7.1 kg. Now, to figure this out, let's first draw our diagram here. So let's say that this is our throat. OK. This is our throat. I hope this looks like a throat. And for the throat, we have a thin rope that's pulling the throat up. Let's say that the tension of that rope is ft. And then we have the mass of the throat acting downwards. Let's call its weight, sorry, it's weight acting downwards. Let's call that MG. OK. And we know that our angler is pulling the throat up directly from the water at an acceleration of 3.5 m per second. So we know what that acceleration is. Now in this problem, we want to figure out what the rope breaking means about the trots mass. In other words, we want to find some relationship between the mass of the trot and a scenario where the rope breaks. Now here, let's assume that G is the acceleration or G or acceleration due to gravity is 9.8 m per second squared. OK. So if we think about this for our problem, we know that acceleration due to gravity is 9.8 m per second squared, we also are assuming that the, the, the, the wit, OK? Or the force or the thin rope, the tension in the rope is 22.5 newtons because that's up to the point that the rope can withstand. OK. And we also know that there is an acceleration of 3.5 m per second squared. But we don't know the mass of the troll because the mass is what is going to decide whether the rope breaks or not? No, let's ask ourselves, what do we know about our forces related to any of these variables here? Well, we can recall Newton's second law of motion and that law tells us that force force is directly proportional to acceleration by the formula that says the net force is equal to the mass multiplied by the acceleration. OK. Now, if we apply Newton's law in the vertical direction considering opus positive. Then that means our formula OK? Is now going to become FT or upward force minus the weight MG or downward force being equal to M multiplied by A OK. Where FT is the tension in the rope? MG is the weight of the trot and ma is the force needed to accelerate the trot upwards at a meters per second. Now remember we're trying to figure out the tension in the rope before the rope breaks. So we want to sulfur FT. OK. OK. And now if we rearrange for FT, we get FT to be equal to MGK plus MA. This equation shows that the tension is equal to the mass of the throat times the sum of gravity and the specified acceleration because we could factor out M here to get M multiplied by G A. So since we know the tension in the rope already the maximum tension, then we can figure out what the mass is because no, OK. That means our mass is going to be equal to our tension FT divided by acceleration due to gravity plus A. So we know all these values we can substitute. The maximum tension is 22.5 Newton acceleration due to gravity is 9.8 m per second squared and the acceleration to move the throat upwards. OK. We found that to be, remember earlier, we said that it was 3.5 m per second. Squared. OK. So no, we can figure out what that must would be, what, what's the must at that breaking point? Well, no, if we put this expression into our calculator, we get our mass to be equal to 1.69 kg, which if we round it to the nearest 10th of a kilogram will be 1.7 kg. Thus the mass of the throat that the sorry, the throat mass of 1.7 kg is the maximum that the rope can support given the specified acceleration without breaking. Since the rope broke, it implies the throat. Actual mass exceeded 1.7 kg leading to the rope's failure. Because if the mass is more than 1.7 kg, it's heavier and thus has a greater downward force. Therefore, that means that the mass would have to be greater than 1.7 kg for the rope to break. A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s² using very light fishing line that has a breaking strength of 183 N (≈ 4lb) . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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