4.2.1 Translational Equilibrium

A body can remain at its current position only if all the external forces acting on it sum up to zero. For a body to be in translational equilibrium, it is necessary that

$\displaystyle \sum{F}=0$

Example

When a 20 N weight is hung on a clothes line, the line sags as shown in diagram. Determine the tension in the clothes line.

Solution

Method 1

Consider the equilibrium of the section of the rope where the mass is hung.

Horizontally, SF_x= 0: $\displaystyle \begin{aligned}{{T}_{1}}\sin 75{}^\circ &={{T}_{2}}\sin 55{}^\circ \\{{T}_{1}}&=0.8480{{T}_{2}}\end{aligned}$

Vertically, SF_y= 0: $\displaystyle \begin{aligned}{{T}_{1}}\cos 75{}^\circ +{{T}_{2}}\cos 55{}^\circ &=20\\(0.8480{{T}_{2}})\cos 75{}^\circ +{{T}_{2}}\cos 55{}^\circ &=20\\{{T}_{2}}&=25.2\text{ N}\end{aligned}$