Resultant Force & Equilibrium

When several forces act on one object, they can be replaced by a single resultant. Same direction means the resultant is the sum; opposite directions leave the difference, toward the larger force. Equal magnitudes in opposite directions give zero resultant, so the object stays at rest or in uniform straight motion. Use the sliders to change F₁ and F₂ and watch same-direction, opposite-direction, and book-on-desk equilibrium.

Two Forces in the Same Direction

F₁5 N

F₂3 N

💡 What is a Resultant Force?

①When two forces act in the same direction, resultant = their sum

②In tug of war, teammates combine their pulls

③The resultant has the same direction as the original forces

④A resultant force replaces multiple forces with one

Two Forces in Opposite Directions

→ Force6 N

← Force6 N

🔍 Resultant of Opposite Forces

①Opposite directions: resultant = larger − smaller

②The direction of the resultant matches the larger force

③If both forces are equal, resultant = 0 → Equilibrium!

④In tug of war, equal pulls mean no motion

Force Equilibrium

Equilibrium Condition

Resultant = 0 (equal magnitudes, opposite directions)

Equilibrium: the object stays at rest or moves with constant velocity

Same-Direction Resultant

F_total = F₁ + F₂

Two forces in the same direction add up

Opposite-Direction Resultant

F_total = |F₁ − F₂|

Two opposite forces leave their difference as the resultant

Exam Key Points

Core Summary

Resultant = 0 → Equilibrium → Rest or uniform straight motion

When two forces are equal in magnitude and opposite in direction, the motion state does not change

🎯 Exam Key Points

①Resultant: a single force replacing several

②Same-direction resultant = F₁ + F₂

③Opposite-direction resultant = |F₁ − F₂|, direction of the larger force

④Equilibrium: resultant = 0, equal magnitude and opposite direction

⑤In equilibrium: object is at rest or in uniform straight motion

Examples and Unit Test

Example 1

A 5 N force to the right and a 3 N force to the left act on one object at the same time. What is the size and direction of the resultant force?

For two forces in opposite directions, the resultant is the larger force minus the smaller, in the direction of the larger force.

5 N - 3 N = 2 N, and the direction is to the right, the larger force.

▸ 2 N, to the right

Opposite-direction resultant = |F1 - F2|, in the direction of the larger force.

Example 2

A book resting on a desk has 8 N of gravity acting on it. When the book is at rest, what is the size of the normal force the desk pushes up with?

When the book is at rest, the forces are in equilibrium, so the resultant is 0.

Gravity (down) and the normal force (up) must be equal in size and opposite, so the normal force = gravity = 8 N.

▸ 8 N (upward)

In equilibrium the resultant is 0; the book stays still because gravity = normal force.

Unit-test style

Which statement about resultant force and equilibrium is correct?

①The resultant of two forces in the same direction is their difference

②When forces are in equilibrium, the resultant is 0

③An object in equilibrium must be at rest

④The resultant of two opposite forces points toward the smaller force

⑤If the resultant is 0, the motion of the object keeps changing

▸ ② When forces are in equilibrium, the resultant is 0

Equilibrium is the state where the resultant force is 0, so ② is correct.

A same-direction resultant is the sum of the forces (①), equilibrium includes both rest and constant-velocity motion (③), an opposite-direction resultant points toward the larger force (④), and if the resultant is 0 the motion does not change (⑤).

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