Chapter 7, Problem 32RE

a.

To determine

To Find: The work required to lift the equipment.

Answer to Problem 32RE

  $4000J$ .

Explanation of Solution

Given information:

100N of equipment is to be huled.

Weight of the rope $0.8\text{N/m}$ .

Length of rope beneath him is 40m.

Formula used:

The work to move an object from $x=a$ to $x=b$ is: $W={\displaystyle \underset{a}{\overset{b}{\int }}F(x)dx}$ .

Calculation:

Work done to take the lift,

  $\left(100\text{N}\right)\left(0.8\right)=4000\text{J}$ .

b.

To determine

To Find: The work required to lift the rope.

Answer to Problem 32RE

640J.

Explanation of Solution

Given information:

100N of equipment is to be huled.

Weight of the rope $0.8\text{N/m}$ .

Length of rope beneath him is 40m.

Formula used:

The work to move an object from $x=a$ to $x=b$ is: $W={\displaystyle \underset{a}{\overset{b}{\int }}F(x)dx}$ .

Calculation:

Here $F(y)=32-0.8y;a=0;b=40$ .

If the travelled distance is $y$ then, the weight of the remaining portion is,

  $(40-y)(0.8)=32-0.8y$

The total work to life the rope is,

  $\begin{array}{c}{\displaystyle \underset{0}{\overset{40}{\int }}\left(32-0.8y\right)dy}={\left[32y-0.4y^2\right]}_0^{40}\\ =640\text{J}\end{array}$

c.

To determine

To Find: The work required to lift the rope and equipment together.

Answer to Problem 32RE

4640J.

Explanation of Solution

Given information:

100N of equipment is to be huled.

Weight of the rope $0.8\text{N/m}$ .

Length of rope beneath him is 40m.

Previously calculated, work done to lift the rope is 640J and to lift the equipment that is 4000J.

Formula used:

The work to move an object from $x=a$ to $x=b$ is: $W={\displaystyle \underset{a}{\overset{b}{\int }}F(x)dx}$ .

Calculation:

Total work done is $4000+640=4640\text{J}$ .