A 550-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is 850 kg. As the elevator starts moving, the scale reads 450 N. (a) Find the acceleration of the elevator (magnitude and direction).

Video transcript

welcome back everybody. We are looking at an elevator but we are looking at an elevator at two different periods of time. In one of these states, we are looking at the elevator when the elevator is at rest and in another state we are looking at the elevator when the elevator is moving. Now keep in mind this is the same elevator. We are told that inside this elevator there's a spring scale that is attached to a bag of tomatoes. I'm actually gonna draw a little free body diagram off to the side here on both sides to represent the tomatoes and we've got a couple of forces acting on them, first and foremost for each of these tomatoes, we actually have a tension that is present in the spring scale. And then we also have the weight of the tomatoes. I'm just gonna know Tate with W. And this is equal to the mass times the habitation, gravitational pole or the acceleration due to gravity. Now we are asked to find what the acceleration of the elevator is when the elevator is moving. So we know from Newton's second law that the summation of all forces is equal to mass times acceleration. So, looking at the left hand side here, This tells us that our tension one plus our weight, but in this case our weight is negative since it's pointing downward is going to be equal to zero. That tells us that when at rest the weight of our tomatoes is equal to the tension. Now our weight is going to stay constant on both sides and that will come into effect later on. Here's what I'm gonna do. We know that our tension is equal to our mass times acceleration by this equation right here. So I'm actually going to divide both sides by the gravitational acceleration and we are going to figure out the mass of the tomatoes. This tells us that our mass is equal to our attention. One divided by gravity Which is equal to 40, divided by 9.8, 1 equal to 4.08 telegrams. Now that we have our mass, let's actually look at this right side here. We're gonna have that our attention to plus our weight, which is negative in this case is going to be equal to a mass of our tomatoes. Times the acceleration that we're looking for. If I actually divide both sides by our mass, we are going to find and isolate our acceleration. So let's go ahead and plug in some values here, acceleration is equal to well, we are told that our tension When the elevator's moving is 48.1 newtons and our weight stays the same of the bag of tomatoes. That is still 40 and dividing by the mass. We just found a 4.8. We get that our acceleration of the elevator is equal to 2.0 m per second squared corresponding to our answer. Choice of c. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.