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This lesson covers how forces combine to produce a resultant force, and what happens when forces are balanced (equilibrium) — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to be able to calculate resultant forces, draw and interpret free body diagrams, and understand equilibrium.
A force is a push or a pull that acts on an object due to its interaction with another object. Forces are measured in newtons (N) and are vector quantities — they have both a magnitude (size) and a direction.
Common forces you need to know:
| Force | Description | Direction |
|---|---|---|
| Weight | The gravitational pull on an object (W = mg) | Downward, towards the centre of the Earth |
| Normal contact force | The support force from a surface | Perpendicular to the surface |
| Friction | Opposes the motion of an object | Opposite to the direction of motion |
| Air resistance (drag) | Friction from air acting on a moving object | Opposite to the direction of motion |
| Tension | The pull in a stretched string, rope or cable | Along the string, away from the object |
| Upthrust | The upward force on an object submerged in a fluid | Upward |
| Applied force | A push or pull applied by a person or engine | In the direction of the push/pull |
Exam Tip: Always name forces precisely. Do not just write "gravity" — write "weight" or "gravitational force." The Edexcel mark scheme requires correct terminology.
A free body diagram shows all the forces acting on a single object, represented as arrows. Each arrow:
| Force | Direction | Size |
|---|---|---|
| Weight (W) | Downward | e.g. 5 N |
| Normal contact force (N) | Upward | e.g. 5 N |
The book is in equilibrium because the two forces are equal in size and opposite in direction — the resultant force is zero.
| Force | Direction | Size |
|---|---|---|
| Weight (W) | Downward | e.g. 800 N |
| Air resistance (R) | Upward | e.g. 800 N |
At constant speed (terminal velocity), air resistance equals weight — the resultant force is zero.
Exam Tip: In free body diagrams, if the object is in equilibrium (stationary or moving at constant velocity), the arrows representing opposing forces must be the same length. If the object is accelerating, the arrow in the direction of acceleration must be longer.
The resultant force is the single force that has the same effect as all the individual forces acting on an object combined. It determines whether the object accelerates, decelerates, or remains at constant velocity.
When forces act along the same line, you calculate the resultant by adding or subtracting:
A car engine provides a forward force of 3000 N. A passenger pushes from behind with 200 N.
Resultant force = 3000 + 200 = 3200 N forward
A car engine provides a forward force of 3000 N. Friction and air resistance provide a backward force of 1200 N.
Resultant force = 3000 − 1200 = 1800 N forward
A box is pushed to the right with 50 N. Friction acts to the left with 20 N. A second person pushes to the right with 15 N.
Total rightward force = 50 + 15 = 65 N Resultant = 65 − 20 = 45 N to the right
An object is in equilibrium when the resultant force acting on it is zero. This means:
This is a direct consequence of Newton's First Law.
For an object to be in equilibrium:
| Situation | Forces | Why Equilibrium? |
|---|---|---|
| Book on a table | Weight down, normal force up | Forces are equal and opposite |
| Car at constant velocity | Engine force forward, drag backward | Forward force = backward force |
| Hanging object at rest | Weight down, tension up | Tension = weight |
| Floating boat | Weight down, upthrust up | Upthrust = weight |
Exam Tip: A common misconception is that an object in equilibrium must be stationary. This is wrong. An object moving at constant velocity is also in equilibrium — there is no resultant force, so there is no acceleration, and the velocity does not change.
When forces act at angles to each other, you may need to resolve them into horizontal and vertical components or use scale drawings.
A force of 30 N acts to the right and a force of 40 N acts upward on the same object.
Using Pythagoras' theorem:
Resultant = √(30² + 40²) = √(900 + 1600) = √2500 = 50 N
The angle θ from the horizontal:
tan θ = 40 ÷ 30 = 1.333
θ = tan⁻¹(1.333) ≈ 53.1° above the horizontal
Exam Tip: At Higher tier, you may be asked to use Pythagoras' theorem or trigonometry to find the resultant of two forces at right angles. Make sure you are comfortable with both methods.
When an object is on a slope, its weight acts vertically downward, but you can resolve it into two components:
graph TD
A["Object on a Slope"] --> B["Weight acts<br/>vertically downward"]
B --> C["Component parallel<br/>to slope<br/>(causes sliding)"]
B --> D["Component perpendicular<br/>to slope<br/>(balanced by normal force)"]
A --> E["Normal contact force<br/>perpendicular to surface"]
A --> F["Friction force<br/>parallel to surface<br/>(opposes sliding)"]
style A fill:#2c3e50,color:#fff
style B fill:#c0392b,color:#fff
style C fill:#e74c3c,color:#fff
style D fill:#e67e22,color:#fff
style E fill:#2980b9,color:#fff
style F fill:#27ae60,color:#fff
When an object hangs from a single string at rest:
When an object hangs from two strings at angles, the vertical components of the two tensions must add up to equal the weight, and the horizontal components must cancel out.
A bridge supported at two ends carries a load. The support forces (reactions) at each end must add up to equal the total weight of the bridge plus any load on it. The distribution depends on where the load is placed (this links to moments — see next lesson).