Chapter 16, Problem 11AAE

(a)

To determine

Show that the work done $\text{Work}=\underset{n\to \infty }{\text{lim}}{\displaystyle \sum _{k=1}^{n}g{x}_k{y}_k{}^2\Delta s_k}={\displaystyle \underset{C}{\int }gx{y}^{2}ds}$ by gravity to move the string straight down to $x\text{-axis}$.

(b)

To determine

Find the total work done by evaluating the line integral ${\displaystyle \underset{C}{\int }gx{y}^{2}ds}$.

(c)

To determine

Verify that the total work done equals to the work required to move the string’s centre of mass $\left(\overline{x},\overline{y}\right)$ straight down to the $x\text{-axis}$.