Final answer:
The problem is a physics question where the work done to raise one end of a chain against gravity is calculated using integration, accounting for the changing weight of the chain as it is lifted.
Step-by-step explanation:
The question asks about the work required to raise one end of a chain to a certain height. This is a physics problem that involves calculating work done against gravity. Work is defined as the product of the force and the displacement in the direction of the force. Here, as we lift one end of the chain, we must consider that the force (which is the weight of the portion of the chain being lifted) changes continuously from 0 to the full weight of the chain at the highest point. Therefore, we integrate the weight per unit length of the chain over the height to which it is raised.
To solve the problem, we first find the weight per foot of the chain (which is 80 lbs divided by 11 feet). Then we set up an integral from 0 to 8 feet of the product of the height and the incremental weight being lifted as we go up. This calculation gives us the total work done in foot-pounds.