A house painter uses the chair-and-pulley arrangement of FIGURE P7.45 to lift himself up the side of a house. The painter's mass is 70 kg and the chair's mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at 0.20 m/s².

Video transcript

Hey, everyone. This problem is working with tension forces. Let's see what we're looking at. We have a well fitted with a pulley. A bucket hangs from the pulley using a flexible cable. A person uses the pulley to get themselves into and out of the well, the bucket has a mass of 15 kg and the person's mass is 62 kg. How hard should the person pull on the cable to create an upward acceleration of 0.45 m per second squared? Our answer choices here are a 17.3 newtons. B 745 newtons, C 395 newtons or D newtons. So the way that we're going to tackle this problem is to recall that Newton's second law is F equals M A. So that some of the forces are going to equal the mass, the total mass of the system times the acceleration of the system. So here we know that the total mass from the problem, it's gonna be the mass of the bucket plus the mass of the person. So that was 15 kg plus 62 kg equals 77 kg. We also know from the problem of the acceleration. What we're shooting for here is 0.45 m/s squared. And they're asking us to solve for this force. So the next step is going to be to draw a free body diagram so that we can see the forces that are acting in this system. So we have our pulley comes down to our bucket. So the forces acting on the bucket, you have the weight and then we have the tension force in the pulley On both sides. So tension Times two, since acting on, on both ends of the cable, so when we go to some, our forces will have to T minus weight, right? T it's positive, it's in the positive Y direction. Weight is gonna be in the negative Y direction. So that's negative. So to T minus W equals mass times acceleration. So our tension, we can simplify this a little bit more. So to t wait, we can recall is mass times gravity. So we've got mass times acceleration plus mass times gravity. And then we can just, we can just divide that out by two. So we have mass times acceleration plus gravity over to it's equal to our attention. That's the force that the person is going to be using to pull on the cable. So from here it's just a plug and chug. So mass we've determined is 77 kg. Our acceleration from the problem is 0.45 m/s squared. Our gravity constant we can recall is 9.8 m/s squared. All of that divided by two Plug that in and we get 395 mutants. So that is the answer to this problem. And that aligns with answer choice C that's all we have for this one. We'll see you in the next video.