Chapter 8, Problem 32RE

a.

To determine

To find : the work will take to lift the equipment.

Answer to Problem 32RE

It will take $4000$ J to lift the equipment.

Explanation of Solution

Given information : A rock climber is about to haul up $100$ N of equipment that has been hanging beneath her $40m$ of rope weighing $0.8\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ .

Calculation :

The work will take to lift the equipment:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{40}{\int }}100dx}\\ \Rightarrow 4000J\end{array}$

b.

To determine

To find : the work will take to lift the rope.

Answer to Problem 32RE

It will take $640$ J to lift the rope.

Explanation of Solution

Given information : A rock climber is about to haul up $100$ N of equipment that has been hanging beneath her $40m$ of rope weighing $0.8\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ .

Calculation :

The work will take to lift the rope:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{40}{\int }}0.8xdx}\\ \Rightarrow 640\end{array}$

c.

To determine

To find : the work will take to lift the rope and equipment together.

Answer to Problem 32RE

It will take $4640$ J to lift the rope and equipment together.

Explanation of Solution

Given information : A rock climber is about to haul up $100$ N of equipment that has been hanging beneath her $40m$ of rope weighing $0.8\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ .

Calculation :

The work will take to lift the rope is $640$ J.

The work will take to lift the equipment is $4000J$ .

  $\begin{array}{l}4000+640\\ \Rightarrow 4640\end{array}$