Question

Hi, I am doing exercise 4J-1 of problem set 6 and am stuck with the reasoning behind the energy formula. The problem states that it requires k units of energy to lift 1 cubic meter of water 1 meter. The solution then explains that energy required is volume times k times yi (i is an index). I am having a hard time correlating the initial statement with the solution.

Answer 1

k Energy to lift 1unit of water a distance of 1 meter. So it takes V*k Energy to lift V units of water a distance of 1 meter (V would be the volume in cubic meters). So to lift that amount 2 meters, it would be Vk for the first meter, and Vk for the second (Vk+Vk)=2Vk. For 3 meters, 3Vk; for a distance of d meters (or y_i meters), dVk.