Chapter 8.5, Problem 6E

To determine

To find the work done lifting the water.

Answer to Problem 6E

4900J work was done to lifting the water to a point 20 meters above the ground.

Explanation of Solution

Given information: The Bucket in Exercise 5 is hauled up more quickly so that there is still 10L (98N) of water when the bucket reaches the top.

Calculation:

You know from the previous problem that at 0 meters the bucket is 490N and that from problem 6 the bucket at 20 meters it has 98N. So the coordinates of the points are (0,490) and (20,98) and if you do a rough sketch of the points and find the equation the line it turns out to be $f\left(x\right)=490-19.6x$ . 490 being the y-intercept and 19.6 being the slope of the line.

  $\begin{array}{l}{\displaystyle {\int }_0^{20}490-19.6}dx\\ =5800\end{array}$

Hence, 5800J work was done lifting the water.