A 50 kg box hangs from a rope. What is the tension in the rope if: (c) The box has vy = 5.0 m/s and is speeding up at 5.0 m/s^2

Video transcript

Hey, everyone. This problem is working with tension forces. Let's see what they're asking us, determine the tension in a string. When the string holds up a 60 kg box, the box's velocity in the Y direction is eight m per second and its acceleration is eight m per second squared. Our multiple choice answers are a Newtons. B 1220 Newtons, C 1008 Newtons or D 1068 Newtons. So the first thing we're going to do here is draw a free body diagram. So we have the box draw that as a particle, we have the tension and the string acting in an upward direction. And then we have the weight of the box acting in a downward direction or a negative Y direction. So from Newton's second law, we can recall that the sum of the forces is equal to mass multiplied by acceleration. In this case, we're looking at the forces in the y direction. So we have tension minus weight is equal to mass times acceleration. We can recall that weight is given by mass times gravity. So we'll rewrite that here. Mass multiplied by gravity. So tension minus mass multiplied by gravity is equal to mass multiplied by acceleration. And so we're gonna solve four tension, sorry we are going to solve for tension. And so we will move the mass multiplied by gravity term to the other side of the equation. So we will have mass multiplied by acceleration plus mass multiplied by gravity. And from there, we can just plug in our known values. So mass we were told in the problem is 60 kg multiplied by acceleration, which was given to us in the problem as eight m per second squared plus mass. Again, 60 kg multiplied by gravity which is a constant. We can recall 9.8 m per second squared. When we plug that into our calculator, we get 1,068 newtons. And that is the answer to this problem that aligns with answer choice D. So that's all we have for this one. And we'll see you in the next video.