Answer to Question #89953 in Mechanics | Relativity for E

Question

https://isaacphysics.org/questions/towel_washing_line_num

Answer 1

Consider the strings attached to the washing poles. There's vertical force of gravity of towel acting on it and tensions $T_1$ and $T_2$.

According to Newton's second law for the state of equilibrium:

$$Ox:\space T_2-T_1\text{cos}\alpha=0,\\ Oy:\space T_1\text{sin}\alpha-mg=0.$$

Re-write this:

$$Ox:\space T_2=T_1\text{cos}\alpha,\\ Oy:\space mg=T_1\text{sin}\alpha.$$

Divide the lower equation by the upper one:

$$\frac{mg}{T_2}=\text{tan}\alpha,$$

$$T_2=\frac{mg}{\text{tan}\alpha}.$$

Find the angle $\alpha$. From the figure we see:

$$4b=a\text{cos}\alpha+2a+a\text{cos}\alpha,$$

$$\alpha=\text{cos}^{-1}\Big(2\frac{b}{a}-1\Big).$$

Substitute the angle to the equation for tension:

$$T_2=\frac{mg}{\text{tan}\Big[\text{cos}^{-1}\Big(2\frac{b}{a}-1\Big)\Big]}.$$

For the values in the problem we get

$$T_2=1.47\text{ N}.$$