Chapter 10.1, Problem 3PP

a.

To determine

Work done by climber on the backpack.

Answer to Problem 3PP

Work done by climber on the backpack is $602.7\text{J}$ .

Explanation of Solution

Given:

Mass of backpack is $m=7.5\text{kg}$ .

Time is $t=30\text{min}$ .

Distance climbed is $d=8.2\text{m}$ .

Formula used:

Work done can be obtained by:

  $W=Fd$   

Calculation:

As, $F=mg$ (weight)

So, $W=mgd$

Substitute the values and solve:

  $\begin{array}{l}W=7.5\times 9.8\times 8.2\\ =602.7\text{J}\end{array}$

Conclusion:

Work done by climber on the backpack is $602.7\text{J}$ .

b.

To determine

Work done by climber lifting herself and the backpack.

Answer to Problem 3PP

Work done by climber lifting herself and the backpack is $\simeq 5.9\text{kJ}$ .

Explanation of Solution

Given:

Weight of climber is $W=F_g=645\text{N}$

Mass of backpack is $m=7.5\text{kg}$

Time is $t=90\text{min}$

Distance climbed is $d=8.2\text{m}$

Formula used:

Work done can be obtained by:

  $W=F_{g}d+\text{work done on backpack}$  

Calculation:

From (2)

  $W=F_{g}d+602.7\text{J}$

Putting the values

  $\begin{array}{c}W=645\times 8.2+602.7\text{J}\\ =5891.7\text{J}\\ \simeq 5.9\text{kJ}\end{array}$

Conclusion:

Work done by climber lifting herself and the backpack is $\simeq 5.9\text{kJ}$ .