A 50 kg box hangs from a rope. What is the tension in the rope if: (b) The box moves up at a steady 5.0 m/s?

Question

Accepted Answer

Hey, everyone. So this problem is working with tension. Let's see what they're asking us. We have a string used to suspend a bucket, bind the tension in the spring. If the bucket rises at a constant speed of 8m/s, the mass of the bucket is 25 kg. Our multiple choice answers here are a 385 newtons. B 165 newtons C 255 newtons or D newtons. So let's draw our free body diagram where we have the bucket. The string used to suspend the bucket is gonna have a tension force acting in the positive Y direction on the bucket. And then the weight of the bucket is going to be acting in the negative Y direction. From Newton's second law, we can recall that the sum of the forces is equal to mass multiplied by acceleration. And in this case, we're working with forces in the Y direction. So the sum of our forces, it's going to be tension in the uh positive because it's in the positive Y direction minus weight is equal to Mass multiplied by our acceleration. Now, the problem gives us a constant speed of 8m/s. It doesn't give us an acceleration. But we can recall that if the speed is constant, our acceleration is zero. So this side of the equation goes to zero. So now we just have our tension is equal to our weight. And we can recall that weight is equal to mass multiplied by gravity From there. We can plug in the mass from the problem which was kg and gravity we can recall is constant 9.8 m/s squared. We plug that into our calculators and we get 245 newtons. So that is the answer to this one and to this problem and that aligns with answer choice D that's all we have for this problem. We'll see you in the next video.

A 50 kg box hangs from a rope. What is the tension in the rope if: (b) The box moves up at a steady 5.0 m/s?

Verified Solution

Key Concepts

Tension in a Rope

Weight of an Object

Uniform Motion