Question

A particle of mass 10 kg is attached to one end of a light inextensible string whose other end is fixed. The particle is pulled aside by a horizontal force until the string is at 60° to the vertical. Find the magnitude of the horizontal force and the tension in the string.

Answer 1

The sum of forces' vectors is $\overrightarrow{0}$ : $\overrightarrow{R} = m\overrightarrow{a} = \overrightarrow{F} + \overrightarrow{T} + m\overrightarrow{g} = \overrightarrow{0}$

Horizontal direction: $F = T \cdot sin60^\circ;$

Vertical direction: $T \cdot cos 60^\circ = mg;$

Then $T = \dfrac{mg}{cos60^\circ} = \dfrac{mg}{1/2} = 2mg;$ $F = T \cdot sin60^\circ = 2mg \cdot \dfrac{\sqrt{3}}{2} = \sqrt{3}mg$

m is known from the task and g you should take with the necessary accuracy.