Resultant Forces

This lesson covers resultant forces and their effect on objects, as required by AQA GCSE Combined Science Trilogy (8464), section 6.5.1. The resultant force is one of the most important concepts in the entire Forces topic — it determines whether an object accelerates, decelerates, or remains at constant velocity.

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What Is a Resultant Force?

A resultant force is the single force that has the same effect as all the individual forces acting on an object combined. It is the overall (net) force.

• If forces act in the same direction, add them.
• If forces act in opposite directions, subtract the smaller from the larger.
• The resultant acts in the direction of the larger force (when forces are opposite).

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Calculating Resultant Forces Along a Line

Same Direction

Two forces of 6 N and 4 N both act to the right:

Resultant = 6 + 4 = 10 N to the right

Opposite Directions

A force of 12 N acts to the right and 5 N acts to the left:

Resultant = 12 − 5 = 7 N to the right

graph LR
    subgraph "Forces in Same Direction"
        S1["6 N -->"] --- S2["4 N -->"]
        S3["Resultant = 10 N -->"]
    end
    subgraph "Forces in Opposite Directions"
        O1["12 N -->"] --- O2["<-- 5 N"]
        O3["Resultant = 7 N -->"]
    end

    style S3 fill:#27ae60,color:#fff
    style O3 fill:#27ae60,color:#fff

Worked Example

A boat has a driving force of 3000 N forwards and water resistance of 1200 N backwards. Calculate the resultant force.

Solution:

Resultant force = 3000 − 1200 = 1800 N forwards

Because there is a resultant force acting forwards, the boat will accelerate in the forward direction.

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Balanced and Unbalanced Forces

Balanced Forces (Resultant = 0 N)

When all forces cancel out, the resultant force is zero. The object is said to be in equilibrium.

An object with a resultant force of zero will:

• Stay stationary if it is already at rest.
• Continue moving at constant velocity if it is already moving.

Situation	Forces	Result
Book on a table	Weight (down) = Normal force (up)	Stationary — balanced
Car at constant speed	Driving force = Friction + drag	Constant velocity — balanced

Unbalanced Forces (Resultant ≠ 0 N)

When the forces do not cancel out, there is a non-zero resultant force. The object will accelerate in the direction of the resultant force.

Situation	Forces	Result
Rocket launching	Thrust > Weight	Accelerates upwards
Car braking	Braking force > Driving force	Decelerates (slows down)

flowchart TD
    R["Is the resultant force zero?"]
    R -->|Yes| B["Forces are BALANCED"]
    R -->|No| U["Forces are UNBALANCED"]
    B --> BS["Object is stationary OR moving at constant velocity"]
    U --> US["Object ACCELERATES in the direction of the resultant force"]

    style R fill:#f39c12,color:#fff
    style B fill:#27ae60,color:#fff
    style U fill:#e74c3c,color:#fff
    style BS fill:#2ecc71,color:#fff
    style US fill:#c0392b,color:#fff

Exam Tip (AQA 8464): A very common misconception is that "if an object is moving, there must be a force acting on it." This is WRONG. An object moving at constant velocity has a resultant force of zero. Only a change in velocity requires a resultant force.

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Terminal Velocity

When an object falls through a fluid (air or water), the sequence of events is:

1. The object starts to fall — weight is greater than air resistance, so the resultant force is downwards and the object accelerates.
2. As speed increases, air resistance increases (it depends on speed).
3. Eventually air resistance equals weight — the resultant force is zero and the object falls at a constant speed called terminal velocity.

graph TD
    subgraph "Falling Object — Three Stages"
        A["Stage 1: Weight > Air resistance"] --> B["Resultant force downwards — ACCELERATES"]
        C["Stage 2: Weight still > Air resistance, but gap closing"] --> D["Resultant force decreasing — acceleration decreasing"]
        E["Stage 3: Weight = Air resistance"] --> F["Resultant force = 0 — TERMINAL VELOCITY"]
    end

    style B fill:#e74c3c,color:#fff
    style D fill:#f39c12,color:#fff
    style F fill:#27ae60,color:#fff

Worked Example

A skydiver of weight 800 N jumps from a plane.

(a) At the moment they jump, what is the air resistance? What is the resultant force?

Solution: Air resistance = 0 N (they have just started falling). Resultant force = 800 − 0 = 800 N downwards.

(b) After some time, the air resistance has increased to 500 N. What is the resultant force?

Solution: Resultant force = 800 − 500 = 300 N downwards. The skydiver is still accelerating, but at a lower rate.

(c) The skydiver reaches terminal velocity. What is the air resistance now?

Solution: At terminal velocity, air resistance = weight = 800 N. Resultant force = 0 N.

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Free Body Diagrams and Resultant Forces

In the exam, you may be given a free body diagram and asked to find the resultant force. Follow these steps:

1. Identify all forces and their directions.
2. Choose a positive direction (e.g. right or up).
3. Add forces in the positive direction and subtract forces in the negative direction.
4. State the magnitude and direction of the resultant.

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Common Mistakes

• Believing that a resultant force of zero means "no forces are acting" — it means the forces are balanced, not absent.
• Thinking a moving object must have a resultant force — a constant velocity requires zero resultant force.
• Forgetting to state the direction of the resultant force.
• Confusing terminal velocity with zero velocity — at terminal velocity the object is still moving, just at a constant speed.
• Adding forces when they should be subtracted (opposite directions).

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Summary