Statics

This lesson covers statics at A-Level — the study of objects in equilibrium under the action of coplanar forces. Statics problems involve finding unknown forces, angles, or distances when a body is not accelerating.

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Conditions for Equilibrium

A body is in equilibrium when:

1. The resultant force is zero: $\sum F_x = 0$∑Fx​=0 and $\sum F_y = 0$∑Fy​=0
2. The resultant moment about any point is zero: $\sum M = 0$∑M=0

For a particle (all forces act at one point), only the force conditions are needed. For a rigid body, both force and moment conditions are needed.

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Resolving Forces

To apply equilibrium conditions, resolve all forces into two perpendicular components (typically horizontal and vertical):

$\text{Horizontal: } \sum F_x = 0$Horizontal: ∑Fx​=0 $\text{Vertical: } \sum F_y = 0$Vertical: ∑Fy​=0

Example: A particle is in equilibrium under three forces: 10 N acting horizontally to the right, a force $P$P at 30 degrees above the horizontal to the left, and a vertical force $Q$Q downwards.

Horizontal: $10 - P\cos 30\degree = 0$10−Pcos30°=0, so $P = \frac{10}{\cos 30\degree} = 11.5$P=cos30°10​=11.5 N