Originally Posted by

**Bilbo Baggins** I don't know anything about physics; however, I know the math. If the chain is 10 meters long and weighs 20kgs, and we assume the mass to be uniformly distributed, then the mass per linear displacement is 2kgs/meter. Now, let's analyze this problem with Calculus. Essentially, calculus works through taking dynamic relationships down to a level where they are static. At this level, we can construe things as being constant. We evaluate these little pieces and put them together to arrive at an answer for the event as a whole. This, in essence, is the concept of integration.

So, work is force over a distance. Well, the mass of every infinitesimal piece of chain is simply 2dx kgs. What about the distance? If I read your problem correctly, you want to take the point 7 meters from end and lift it so that that point is 15 meters above the ground which means that the bottom of the chain itself is 8 meters above the ground. Each infinitessinal unit of chain is therefore lifted 18-x units in the air. That's the integral. The answer is 161 I didn't take gravity into account. Again, I don't know the physics.