Resultant Forces

This lesson covers resultant forces and their effects on objects as required by the AQA GCSE Physics specification (4.5.3). When multiple forces act on an object, you can replace them with a single force that has the same overall effect — this single force is called the resultant force. Understanding resultant forces is essential for predicting whether an object will accelerate, decelerate, change direction, or remain in equilibrium.

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What Is a Resultant Force?

The resultant force is the single force that has the same effect as all the individual forces acting on an object combined. It is sometimes called the net force or unbalanced force.

To find the resultant force, you must consider:

• The magnitude (size) of each force.
• The direction of each force.

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Forces Along the Same Line

When forces act along the same straight line, calculating the resultant is straightforward.

Same Direction

If forces act in the same direction, you add their magnitudes.

Example: A force of 8 N to the right and a force of 5 N to the right.

Resultant = 8 N + 5 N = 13 N to the right

Opposite Directions

If forces act in opposite directions, you subtract the smaller from the larger. The resultant acts in the direction of the larger force.

Example: A force of 12 N to the right and a force of 7 N to the left.

Resultant = 12 N - 7 N = 5 N to the right

Situation	Force 1	Force 2	Resultant Force
Same direction	10 N right	6 N right	16 N right
Opposite directions	15 N right	15 N left	0 N (balanced)
Opposite directions	20 N up	8 N down	12 N up
Opposite directions	5 N left	9 N right	4 N right

Exam Tip: Always state the direction of the resultant force as well as its magnitude. Forgetting the direction is a very common error that will lose you a mark. If the resultant is zero, state "the forces are balanced" or "the resultant force is zero."

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Balanced and Unbalanced Forces

Balanced Forces (Resultant = 0)

When the resultant force on an object is zero, the forces are said to be balanced. A balanced force means:

• If the object is stationary, it remains stationary.
• If the object is moving, it continues to move at the same speed in the same direction (constant velocity).

A resultant force of zero does NOT mean the object is stationary — it means the object's motion does not change.

graph TD
    subgraph "Balanced Forces - Object at Rest"
        N1["Normal force = 50 N (up)"] --> O1["Book on table"]
        O1 --> W1["Weight = 50 N (down)"]
    end

    style O1 fill:#2c3e50,color:#fff
    style N1 fill:#27ae60,color:#fff
    style W1 fill:#e74c3c,color:#fff

Unbalanced Forces (Resultant is not 0)

When the resultant force is not zero, the forces are unbalanced. An unbalanced force causes the object to:

• Accelerate (speed up) if the resultant force is in the direction of motion.
• Decelerate (slow down) if the resultant force is opposite to the direction of motion.
• Change direction if the resultant force acts at an angle to the direction of motion.

Exam Tip: Many students think that a moving object must have a resultant force acting on it. This is wrong. An object moving at constant velocity has a resultant force of ZERO. A resultant force only causes a CHANGE in motion (acceleration or deceleration), not motion itself.

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Newton's First Law and Resultant Forces

Newton's first law states:

An object will remain at rest or continue to move at a constant velocity unless acted upon by a resultant (unbalanced) force.

This means:

• No resultant force = no change in motion (object stays still or moves at constant velocity).
• Resultant force present = the object accelerates (changes speed or direction).

Resultant Force	Effect on Stationary Object	Effect on Moving Object
Zero	Stays stationary	Continues at constant velocity
Non-zero (in direction of motion)	Starts moving	Speeds up (accelerates)
Non-zero (opposite to motion)	N/A	Slows down (decelerates)
Non-zero (at an angle)	Starts moving at an angle	Changes direction

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Examples of Resultant Forces

Example 1: A Car Driving at Constant Speed

A car drives along a straight road at a constant speed of 30 m/s.

Forces acting on the car:

• Driving force (from the engine) = 2000 N forwards
• Friction and air resistance = 2000 N backwards

Resultant force = 2000 N - 2000 N = 0 N

The car continues at constant speed because the resultant force is zero.

Example 2: A Car Accelerating

The driver presses the accelerator, increasing the driving force to 3500 N. Friction and air resistance remain at 2000 N.

Resultant force = 3500 N - 2000 N = 1500 N forwards

The car accelerates because there is an unbalanced force forwards.

Example 3: A Skydiver in Free Fall

Immediately after jumping from a plane:

• Weight = 700 N downwards
• Air resistance = 0 N (initially, speed is very low)

Resultant force = 700 N - 0 N = 700 N downwards

The skydiver accelerates downwards.

As the skydiver speeds up, air resistance increases until:

• Weight = 700 N downwards
• Air resistance = 700 N upwards

Resultant force = 700 N - 700 N = 0 N

The skydiver has reached terminal velocity and falls at a constant speed.

graph TD
    subgraph "Just after jumping"
        A1["Air resistance = 0 N"] --> S1["Skydiver"]
        S1 --> W1["Weight = 700 N"]
        R1["Resultant = 700 N down"]
    end
    subgraph "At terminal velocity"
        A2["Air resistance = 700 N"] --> S2["Skydiver"]
        S2 --> W2["Weight = 700 N"]
        R2["Resultant = 0 N"]
    end

    style S1 fill:#2c3e50,color:#fff
    style S2 fill:#2c3e50,color:#fff
    style R1 fill:#e74c3c,color:#fff
    style R2 fill:#27ae60,color:#fff

Exam Tip: The skydiver question is one of the most commonly asked AQA GCSE questions. You must be able to explain how the forces change during the fall. Remember: (1) initially weight is greater so the skydiver accelerates, (2) as speed increases air resistance increases, (3) when air resistance equals weight the resultant force is zero and the skydiver reaches terminal velocity.

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Equilibrium

An object is in equilibrium when all the forces acting on it are balanced and the resultant force is zero. An object in equilibrium is either: