Chapter 4, Problem 23P

A window washer pulls herself upward using the bucket-pulley apparatus shown in Fig.4-48. (a) How hard must she pull downward to raise herself slowly at constant speed? (b) if she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucker is 72 kg.

To determine

Force applied by window washer to pull herself up with constant speed.

Answer to Problem 23P

Solution:The force applied is $705.6\text{ N}$ .

Explanation of Solution

Given:

  $m=72\text{ kg}$ .............................................................................. (Mass of bucket and person)

  $a=0{\text{m/s}}^{\text{2}}$ ........................................................ (Acceleration is 0 when speed is constant)

To find:

  $T=?$ .................................................................................................. (Tension in the rope)

Formula:

From Newton’s second law of motion:

  ${\displaystyle \sum F}=ma$

Where, m is mass and a is acceleration.

Calculation:

There is no mass on the side where force is applied.

Thus, all the force applied by window washer appears in the form of Tension in the rope.

Hence force applied = T

Using Newton’s second law

  

  $\begin{array}{l}{\displaystyle \sum F=ma}\\ T–mg=ma\\ T–\left(72\right)\left(9.8\right)=m\left(0\right)\\ T=705.6\text{ N}\end{array}$

Conclusion: To rise up with constant speed, window washer must pull herself with the force of $705.6\text{ N}$ .

To determine

The acceleration produced when window washer pulls herself with constant force.

Answer to Problem 23P

Solution:

The acceleration of washer in bucket is $1.47{\text{ m/s}}^{\text{2}}$ .

Explanation of Solution

Given:

  $m=72\text{ kg}$ ............................................................................... (Mass of bucket and person)

  $T=705.6\text{ N}$ ................................................ (Tension in the rope when speed is constant)

  $F=0.15T+T=811.44\text{N}$ ................................................. (New Force applied by washer)

To find:

  $a=?$ ..................................................................(Acceleration when new force is applied)

Formula:

Newton’s second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is mass and a is acceleration.

Calculation:

Using Newton’s second law:

  

  $\begin{array}{l}{\displaystyle \sum F=ma}\\ F–mg=ma\\ 811.44–\left(72\right)\left(9.8\right)=72a\\ a=1.47{\text{ m/s}}^{\text{2}}\end{array}$

Conclusion:When force is increased by 15%, the washer in bucket moves with acceleration of $1.47{\text{ m/s}}^{\text{2}}$ .