Question

A bag with a mass of 2 kg hangs by a chord attached to a wall. The chord is pulled aside with a horizontal force F such that it makes an angle of 30° with the wall.

Determine the tension of the chord and the force pulling on it.

Answer 1

Given,

Mass of the bag $(m)=2kg$

Value of horizontal force F

Angle $(\theta)=30^\circ$

As per the given condition in the question,

Now, applying the force balance,

Force in the vertical direction, $T\sin\theta = 2g...(i)$

Force in the horizontal direction, $T\cos\theta = F... (ii)$

From the equation (i)

$\Rightarrow T = \frac{2g}{\sin 30^\circ}$

$\Rightarrow T= 4g$

now, substituting the value of T in the equation (ii),

$\Rightarrow F=4g\times \cos(30^\circ)$

$\Rightarrow F = 2\sqrt{3}gN$