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Problem 102 Hard Difficulty

In a European country a bathroom scale displays its reading in kilograms. When a man stands on this scale, it reads 92.6 $\mathrm{kg}$ . When he pulls- down on a chin-up bar installed over the scale, the reading decreases to 75.1 $\mathrm{kg}$ . What is the magnitude of the force he exerts on the chin-up bar?


172 $\mathrm{N}$


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Video Transcript

the situation here is the following. The man is a standing on a scale which exerts a normal forest on him and at the same time he's exerting a force F downwards on the bar and then the bar. Who he's up. We for force F. They only have to discover what is the magnitude off the force f. In order to do that, we have to use Newton's second law. For that, I would choose the following reference frame a vertical axis pointing upwards a party. Newton's second law in that situation results in the following The net force is equals to the mast. The actor mass off the men Times news acceleration. But the net force is composed by three forces the weight, the normal and the force f Then we have normal force plus f minus the weight forest being equals to zero because the acceleration is the question zero has a man is standing still. So the force F is given by the weight force minus normal force. But we don't know what is the value off the normal force. So how can we calculates the force half without knowing the normal? It happens that we know about is the normal the scale presents and mass that's related to the normal force, not to the weight force. What the scale presence is the normal force divided by the acceleration of gravity. This is what the scale can read. It can't actually read your mass. It can only read the normal force so we can use the fact that the normal force is given by the operator mast times the acceleration of gravity and at the same time the weight force is given by his actor mass times acceleration of gravity. So the force half is given by already factoring the acceleration of gravity. He is actor last minus his apparent mess. So remembering that G is approximately 9.8 meters per second squared, we get 9.8 times 90 true 900.6 minus 75.1, and the results in the force off approximately 172 neutrons. And this is the answer to this question.