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Physics

Equilibrium of Forces

The condition where the net force acting on an object is zero, resulting in no acceleration.

\sum F = 0

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Source & review

Difficulty

Beginner

Read time

5 min

Prerequisites

Vectors, Basic Physics

Review statusNeeds review

Source

FormuLab initial formula library

Initial content draft pending verification against authoritative course or textbook sources.

Definition

Understanding the core concept

Imagine a tug-of-war where both teams pull with exactly the same strength; the rope doesn't move. Equilibrium of forces is like that: all forces acting on an object perfectly balance each other out. This means the object will either stay still or continue moving at a constant velocity, never speeding up, slowing down, or changing direction.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$F$	Force (vector quantity)	$N$
$\sum$	Summation (indicates summing all forces)	$unitless$
$F_{x}$	Component of net force along the x-axis	$N$
$F_{y}$	Component of net force along the y-axis	$N$

Real-World Applications

Where this formula is used in practice

Structural Engineering

Engineers use equilibrium principles to design stable bridges, buildings, and other structures, ensuring they can withstand loads without collapsing.

Static Analysis of Objects

Used to determine the forces within stationary objects, like the forces in the legs of a table supporting a weight or the tension in cables supporting a suspended object.

Vehicle Design

Important in designing suspension systems and body frames for cars and aircraft, ensuring stability and load distribution when the vehicle is at rest or moving at a constant velocity.

Biomechanics

Analysts study the forces acting on the human body, such as muscle forces required to maintain posture or the forces on joints during static holds.

Worked Example

Step-by-step calculation with real numbers

Problem

A traffic light with a mass of 15 kg is suspended by two cables. Cable 1 makes an angle of 30° with the horizontal, and Cable 2 makes an angle of 60° with the horizontal. Assuming the system is in static equilibrium, find the tension in each cable.

Given

m = 15 kg

θ_{1} = 3 0^{\circ}

θ_{2} = 6 0^{\circ}

g = 9.81 m/s^{2}

Solution

W = m g = 15 \times 9.81 = 147.15 N

For equilibrium: \sum F_{x} = 0 and \sum F_{y} = 0

\sum F_{x} : T_{2} cos (6 0^{\circ}) - T_{1} cos (3 0^{\circ}) = 0

T_{2} (0.5) - T_{1} (\frac{3}{2}) = 0

T_{2} = T_{1} 3

\sum F_{y} : T_{1} sin (3 0^{\circ}) + T_{2} sin (6 0^{\circ}) - W = 0

T_{1} (0.5) + T_{2} (\frac{3}{2}) = 147.15

Substitute T_{2} = T_{1} 3 :

T_{1} (0.5) + T_{1} 3 (\frac{3}{2}) = 147.15

T_{1} (0.5 + 1.5) = 147.15

T_{1} = \frac{147.15}{2} = 73.6 N

T_{2} = 73.6 3 = 127.4 N

Final Answer

T_{1} = 73.6 N, T_{2} = 127.4 N

Formula Guide

Info

DifficultyBeginner

Read Time5 min

PrerequisitesVectors, Basic Physics

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

FormuLab initial formula library

Initial content draft pending verification against authoritative course or textbook sources.

Assumptions

• Use SI units unless the formula or course context states otherwise.
• Check notation, sign conventions, and applicability against your course material.
• Confirm variables and assumptions before using the formula in graded or professional work.