When several forces act on an object at once, their combined effect can be replaced by a single force, called the resultant force.
If two forces point the same way, the resultant is their sum; if they point opposite ways, it is the larger minus the smaller and points the same way as the larger force.
When two equal forces act in opposite directions, the resultant is 0 and the two forces are said to be balanced.
An object under balanced forces that is at rest stays at rest, and one that is moving keeps moving in a straight line at the same speed.
Two forces in the same direction
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Two forces F₁ and F₂ acting the same way, and the resultant made by joining their lengths
5 N
3 N
💡 What a resultant force is
①The single force that has the same effect as several forces together is the resultant force.
②If two forces point the same way, the resultant is the sum of their sizes.
③The resultant points the same way as the two forces.
④It is like two people on the same side of a tug of war pulling together: their forces add.
Two forces in opposite directions
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Two forces acting in opposite directions and the resultant pointing towards the larger one
6 N
6 N
🔍 Resultant of opposite forces
①If two forces point in opposite directions, the size of the resultant is the larger minus the smaller.
②The resultant points in the direction of the larger force.
③If the two forces are equal, the resultant is 0.
④In a tug of war, if both teams pull equally hard, the rope does not move either way.
Balanced forces
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Gravity and the normal force balancing on a book lying on a desk
Condition for balanced forces
resultant = 0 (equal sizes, opposite directions)
An object under balanced forces is at rest or moving in a straight line at a steady speed.
Resultant in the same direction
F = F₁ + F₂
Two forces in the same direction add.
Resultant in opposite directions
F = |F₁ − F₂|
For two opposite forces, the difference in size is the size of the resultant.
Exam checklist
Key summary
resultant = 0 → balanced → motion does not change
When two equal and opposite forces act, the object's state of motion does not change.
🎯 Exam points
①The resultant is the single force that combines several forces.
②The resultant of two forces in the same direction is F₁ + F₂.
③The resultant of two opposite forces is |F₁ − F₂|, towards the larger force.
④Balanced forces mean the resultant is 0: equal sizes, opposite directions.
⑤An object under balanced forces is at rest or moves straight at a steady speed.
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?
1
For two opposite forces, the resultant is the larger minus the smaller, pointing towards the larger.
2
5 N − 3 N = 2 N, pointing right, the direction of the larger force.
▸ 2 N, to the right
The size of the resultant of opposite forces is |F₁ − F₂|, pointing towards 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?
1
The book is at rest, so the forces on it are balanced and the resultant is 0.
2
The downward gravity and the upward normal force must be equal, so the normal force is 8 N.
▸ 8 N (upward)
On a book at rest, gravity and the normal force balance each other.
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
1
Equilibrium is the state where the resultant force is 0, so ② is correct.
2
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).