Chapter 8.5, Problem 11E

To determine

To find the work will it take if the rope weights 0.624 N/m.

Answer to Problem 11E

780J work will it take if the rope weights 0.624 N/m.

Explanation of Solution

Given information: A mountain climber is about to haul up a 50-m length of hanging rope.

Calculation:

The function for the force can br determined by the weight of the rope times the length of the rope that is still hanging, i.e. $F\left(x\right)=0.624\left(50-x\right)$ .

Therefore, the work is given by the integral,

  $\begin{array}{l}{\displaystyle {\int }_0^{50}0.624\left(50-x\right)}dx\\ =780\end{array}$

Hence, 780J work will it take if the rope weights 0.624 N/m.