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Problem 42 Medium Difficulty

A woman stands on a scale in a moving elevator. Her mass is 60.0 kg, and the combined mass of the elevator and scale is an additional 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9410 N. What does the scale read during the acceleration?

Answer

645 $\mathrm{N}$

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Video Transcript

what the scale reads is these normal force. So the normal forest acting from the woman. Then we have to apply the Newtown second low Toe that woman. Newton's second law tells us that the net force acting on the woman is equals to her mass times. Her acceleration. Let me choose my refereeing show as being such that everything that is pointing up is positive, and everything that is pointing now is negative. Then the net force that is acting on the woman is given by the normal force minors. The weight off that woman. And these is, of course, to the math off the woman times her acceleration, the reform, the reading off the scale is equals to the mass off the woman times. That's relation, plus the weight off the woman. Therefore, the normal force is it goes to 60 times her acceleration plus her weight, which is equals to 60 times acceleration of gravity, which is approximately 9.8 meters per second squared. So the old information that is missing is the acceleration, and how can we calculate acceleration will note that acceleration off the woman is the coast to the acceleration off the elevator So all we have to do is calculate acceleration off the elevator. And how can we do that? We can do it by applying Newton's second law to the elevator. Newton's second law tells us that the Net force acting on the elevator is it close to its mass times acceleration. But don't be fooled by these one. The mass off the elevator is composed of my the mass of the elevator itself, the mass off the scale and the mass off the woman. So the mass we have here is the mass off the woman, plus the mass off the elevator and the scale at times. Next, relation off that them. The Net force that is acting on the elevator is not equals Onley to this weight force, but because these weight force plus the weight off the woman because she's inside elevator so we have that attention is the miners. The weight off the elevator, minus the weight off the woman, is because the combined mass off the world system, which is 60 plus 850 so 875 times acceleration off the system, attention force is equals to 94 10 the weight off the elevator is it goes to the Mass off the elevator. 850 times acceleration off gravity 9.8. The weight off the woman Is it close to her mass. 60 kilograms times acceleration of gravity. 9.8 and there's wolfing is equals to 875 times. Next generation of the system therefore acceleration off the system is equals to 9410 miners 850 times 9.8 miners 60 times 9.8 divided by 875. And this gives us an acceleration off approximately 0.954 meters per second. Squared them. We can go back to the other circulation and finish loading the question. So what? The scale well read is the following 60 times 0.954 plus 60 times 9.8 and this gives us approximately 645 mutants.

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