Chapter 9, Problem 23P

To determine

The tension in the clothesline on either side of the sheet. The reason the tension is so much greater than the weight of the sheet.

Answer to Problem 23P

Solution:

Tension in the clothesline is $\text{6}0.\text{2 N}$ . The tension is a lot greater than the weight of the sheet because the angle with the vertical is very small.

Explanation of Solution

Given:

Mass of the sheet, $m=0.75\text{ kg}$

The angle that the sheet makes $\theta ={3.5}^o$

Formula used:

For equilibrium:

  ${\displaystyle \sum F=ma=0}$

Here, m is the mass and a is the acceleration.

Calculation:

  $\begin{array}{l}{\displaystyle \sum F_y=0}\\ T\sin 3.5°+T\sin 3.5°-mg=0\\ 2T\sin 3.5=mg\\ T=\frac{mg}{2\sin 3.5°}\\ T=\frac{0.75(9.8)}{2\sin 3.5°}\\ T=60.2\text{N}\end{array}$

The tension is a lot greater than the weight of the sheet because the vertical components of the sheet only support the weight of the sheet. The angle with vertical is very small, so the tension has to be very large to have large enough vertical components to balance the weight of the sheet.

Conclusion:

Tension in the clothesline is $\text{6}0.\text{2 N}$ . The tension isa lot greater than the weight of the sheet because the angle with the vertical is very small. So the vertical components of the tension supporting the the sheet are large enough to support its weight.