A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 15.0 N. (b) What is the acceleration of either block?

Video transcript

Welcome back everybody. We have a pulley that is positioned at the top of a well and we have a cable that passes over this fully. Now at the bottom of this cable, we have a bucket just sitting there, we are told that a person starts drawing the bucket up and it is going to have a acceleration of 4.0 m per second squared. We're told that the tension of the rope is 20 newtons and we are asked to find what the mass of the bucket is. Well, we know that the sum of all forces is equal to the mass times acceleration according to Newton's second law. But have we accounted for all of our forces? Well, I've actually left this one out which is the weight of the bucket equal to its mass times the acceleration due to gravity. So acting on this bucket, we have both the tension minus the weight of the bucket. I say minus because this is pointing downward. Now this is going to be equal to the mass of our bucket times our acceleration. Right here we're trying to find this mass so we need to isolate that term. So I'm actually gonna add this both sides first. This yields the equation that tension is equal to mass times acceleration plus mass times the acceleration due to gravity. Taking out the mass term. We get on the right hand side. It's mass times acceleration plus the acceleration due to gravity dividing on both sides. Here we get that our mass is equal to the tension in our rope divided by the acceleration of the bucket, Plus the acceleration due to gravity. So let's go ahead and plug in. Those terms of a rope is 20 newtons Divided by the acceleration of our bucket, which is four plus the acceleration due to gravity, which is 9.8, which gives us 1. kg as our mass, giving us our final answer of a thank you guys so much for watching. Hope this video helped. We will see you all in the next one.