A particle P of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point O - Edexcel - A-Level Maths Mechanics - Question 3 - 2013 - Paper 1

To find the value of the force $F$, we can use the equilibrium conditions of forces acting on the particle P.

First, we consider the vertical components of the forces. The tension in the string $T$ can be resolved vertically:

$T \cos(30°) + F \cos(60°) = 2g$

Where $g = 9.8 \, \text{m/s}^2$, giving us:

1. Substitute $g$: $T \cos(30°) + F \cos(60°) = 2 \times 9.8$ $T \cos(30°) + F \cdot 0.5 = 19.6$

Next, horizontally, the only horizontal component is due to the force $F$:

2. Setting horizontal components: $T \cos(30°) - F \cos(30°) = 0$ Rearranging gives us: $T \cos(30°) = F \cos(30°)$ Thus, we have: $F = T$

Next, we can substitute this back into the first equation to solve for $F$. By combining these equations, we can isolate $F$.