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Problem 82 Hard Difficulty

To hoist himself into a tree, a 72.0-kg man ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. He then pulls downward on the free end of the rope with a force of 358 N. Neglect any friction between the rope and the branch, and determine the man’s upward acceleration.

Answer

0.14 $\mathrm{m} / \mathrm{s}^{2}$

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Video Transcript

for these question. You choose the falling reference frame, my vertical access, we try to call the Y. Access will point upwards, and this is all they have to do with respect to the reference frame. Now the situation is the following. There is a man that's trying to pull himself up this tree through this nylon cable, and to do that, he persists one end off the nylon cable, and by doing that, he produces attention. And this tension should be bigger than his weight so that he can pull himself up to calculate his acceleration. We should write Newton's second law, as this is the only equation we ever know that relates forces with accelerations, then applying Newton's second law to the Y direction. We guess that the net force in that direction is equal to the mass off the man times thes acceleration. The net force that has been exerted on the man is composed by three forces. He's weight force, the tension force that acts on his waist and detention force that acts near his hands. Then Newton's second law tells us that two times the tension force minus the weight forces because of the mass off the men times he's acceleration, then these acceleration Is it close to two times detention force minus the weight forced, divided by his mass. One question that might arise now is why haven't I considered the forced F on this equation and the reasons they're following? I'm applying Newton's second law on the men's. Therefore, we should consider only forces that are being exerted on the men. This force F is being exerted by the men on the rope, so we shouldn't consider it when dealing with the man itself. Then Now all we have to do is carefully for is the value off the tension force? But this is not difficult to do. Newton's third law predict that this force, after that the men exerts on their hope, is equals to the force that they hope exerts on the man. So one of the tension t is it goes to the force half on the other. Intention is also equal to the force f the reform. The tension is because they apply it force so effectively. This log is multiplying. They apply it forced by true then his accelerations given by true times the applied force minus wait force, which is his mass times. The gravity acceleration. If I don't buy his mass, then blocking devices that were given by the problem we get two times 358 minus 72 times 9.8. Remember G is approximately 9.8 meters percent on square near the surface of the earth, and this is divided by his mast 72. These results in an acceleration off approximately 0.14 meters per second squared.