(b) How much force does the astronaut exert on his chair while accelerating straight up at 10 m/s^2?

Video transcript

Hey, everyone. So this problem is working with Newton's second law and Newton's third law. Let's see what they're asking us. An ill person lies on a stretcher inside an elevator. We are asked to determine the absolute value of the force that that person of mass kg exerts on the stretcher when accelerating vertically upwards at 7.5 m per second squared. Our multiple choice answers here are a 4.88 times 10 to the two Newtons. B 6.37 times 10 to the two Newtons C 1.12 times 10 to the three Newtons or D 1.50 times 10 to the two mutants. All right. So the first thing we're going to do here is recall that because of Newton's third law, the force that the person exerts on the structure and the force that the structure exerts on the person are equal in magnitude. And so when we paired that knowledge with Newton's second law, which is F equals ma. As we recall, we can surmise that F and some of the forces is equal to the mass of the person times the acceleration. And So when we look at the structure as a particle, we have weight acting in the negative direction and the force that the person exerts acting in the positive direction. So we'll send that, we'll say F S minus W equals MP A. From here, we can recall that weight is equal to mass times gravity. So we will add weight to the other side of the equation. And that will look like M PM M sub P A plus M sub P G. And from here, we can plug in our known values to solve for this F sub S. So from the problem, we are told that mass is 65 kg multiplied by the acceleration given in the problem 7.5 m per second squared. We will add that to again the mass of the person kg times gravity. Our known constant that we can recall is 9.8 m/s squared. And when we plug that into our calculators, we are left with 1.12 times 10 to the three newtons. And so that is our answer for this problem. It aligns with answer choice C. So that's all we have for this one. We'll see you in the next video.