Resultant forces — AQA GCSE Combined Science
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Resultant forces explained
When several forces act on an object, their combined effect is represented by a single resultant force.
Read the full explanation
This has the same effect as all original forces acting together. To find it, add forces acting in the same direction and subtract those in opposite directions. For example, if a box is pushed right with 10 N and left with 4 N, the resultant is 6 N to the right. If forces are balanced, the resultant is zero and the object remains at rest or moves at constant velocity. If unbalanced, the resultant causes acceleration. For forces at an angle, a scale diagram can be used to find the resultant (HT only). Understanding resultant force is essential for explaining motion.
Students should be able to calculate the resultant of two forces that act in a straight line.
A resultant force is the single force that has the same effect as all the forces acting on an object combined. When exactly two forces act along the same straight line, they may point in the same direction or in opposite directions. If they act in the same direction, add their magnitudes: 30 N right plus 20 N right gives 50 N right. If they act in opposite directions, subtract the smaller magnitude from the larger: 30 N right plus 20 N left gives 10 N right. The resultant always takes the direction of the larger force. A resultant of zero means the forces are balanced, so the object's motion does not change. Draw a free-body diagram, choose a positive direction, then combine the two values with correct signs before stating magnitude and direction.
describe examples of the forces acting on an isolated object or system
The published AQA 8464 Combined Science specification places this outcome beneath its '(HT only) Students should be able to:' marker. An isolated object or system is one considered on its own, allowing you to describe the external forces acting upon it. These forces can be balanced or unbalanced; an isolated object can have a resultant force and accelerate. For a single object, identify every force by its type and direction: a book resting on a table has weight acting downwards and a normal contact force acting upwards. For a moving car, list the driving force forwards, drag backwards, weight downwards and normal contact force upwards. State the direction and whether each force is a push or a pull. Describing means naming the forces and giving their directions, using free-body diagrams to model the forces acting on the isolated object.
use free body diagrams to describe qualitatively examples where several forces lead to a resultant force on an object, including balanced forces when the resultant force is zero.
A free body diagram shows one chosen object as a dot or box with arrows for every force acting on it from its surroundings. Arrow length represents magnitude and the arrowhead gives direction. To describe the motion qualitatively, compare the forces along each line: if the forward and backward arrows are equal, the resultant force is zero and the object stays at rest or moves at constant velocity; if one arrow is longer, there is a resultant force in that direction and the object accelerates, slows or changes direction. For example, a skydiver with weight 700 N down and drag 500 N up has a resultant force of 200 N downwards, so they accelerate downwards. Only forces on the chosen object are drawn, never forces it exerts on other things.
(HT only) A single force can be resolved into two components acting at right angles to each other. The two component forces together have the same effect as the single force.
This Higher Tier only statement requires resolving a single force into two perpendicular components using scale drawings, not trigonometry. Any single force can be replaced by two components at right angles that together produce the same effect. To resolve a force, draw it to scale at the correct angle (e.g., 1 cm = 10 N). Draw a rectangle around it so the force is the diagonal. The sides represent the horizontal and vertical components. For example, to resolve a 50 N force at 30°, draw a 5 cm diagonal at 30°, complete the rectangle, and measure the sides. A 4.3 cm horizontal side means a 43 N component, and a 2.5 cm vertical side means a 25 N component. The components are a mathematical replacement simplifying analysis.
(HT only) Students should be able to use vector diagrams to illustrate resolution of forces, equilibrium situations and determine the resultant of two forces, to include both magnitude and direction (scale drawings only).
Vector diagrams show forces as arrows whose length represents magnitude and whose direction represents the force direction. Choose a scale such as 1 cm = 10 N. To find the resultant of two forces, draw them tip-to-tail; the resultant is the arrow from the start of the first to the tip of the second. Measure its length and convert using the scale, then measure its angle with a protractor to give direction. For equilibrium, the forces form a closed triangle: the resultant is zero. To illustrate resolution, draw the single force and construct perpendicular components that meet at right angles, then measure or calculate their magnitudes. Always state the scale and measure angles from a stated reference direction.
Your focus
- Define resultant force as a single force that replaces multiple forces with the same overall effect.
- Calculate the resultant force for forces acting along the same line, including opposite directions.
- Explain the effect of a zero resultant force and a non-zero resultant force on an object's motion.
Show all 19 objectives
- Determine the resultant of two forces at an angle using a scale diagram (HT only).
- Identify two forces acting along the same straight line and state their directions.
- Calculate the resultant of two forces acting in the same direction by adding their magnitudes.
- Calculate the resultant of two forces acting in opposite directions by subtracting magnitudes and stating the direction of the larger force.
- Name the external forces acting on a given isolated object or system.
- State the direction and source of each named force.
- Describe how multiple forces act on an isolated object, whether balanced or unbalanced.
- Draw a free body diagram showing the forces acting on a single object.
- Compare forces on a free body diagram to decide whether the resultant force is zero.
- Describe how a zero or non-zero resultant force affects the motion of the object.
- Resolve a single force into two perpendicular components using a scale drawing.
- Explain why the two components together have the same effect as the original force.
- Determine the magnitude of component forces by measuring a scale diagram.
- Construct scale vector diagrams to find the resultant of two forces, including magnitude and direction.
- Use vector diagrams to represent equilibrium situations where the resultant force is zero.
- Illustrate the resolution of a single force into two perpendicular components on a vector diagram.
Resultant forces exam tips
Marking Points
- The resultant force is a single force that has the same effect as all the original forces acting together.
- Forces acting in the same direction are added; forces acting in opposite directions are subtracted.
- The direction of the resultant force is the direction of the larger force when two forces act along the same line.
- If the resultant force is zero, the forces are balanced and the object's motion does not change (it stays at rest or moves at constant velocity).
- If the resultant force is not zero, the object accelerates in the direction of the resultant force.
- For forces at an angle, the resultant can be found using a scale diagram (HT only).
- The resultant force is a vector quantity, having both magnitude and direction.
- Identify the two forces and their directions from the diagram or description before doing any arithmetic.
- Choose a positive direction and assign each force a sign, for example right positive and left negative.
- For forces in the same direction, add the magnitudes and keep that common direction.
- For forces in opposite directions, subtract the smaller magnitude from the larger and give the direction of the larger force.
- State the resultant as a magnitude with a direction, such as 10 N to the left, not just 10 N.
- Recognise that a resultant of 0 N means the two forces are balanced and the object's motion is unchanged.
- Names each external force acting on the isolated object or system, such as weight, normal contact force, friction, drag or tension.
- States the direction of each force, for example weight acts vertically downwards and the normal contact force acts vertically upwards.
- Identifies the object or part of the system that exerts each force, such as the table pushing up on the book.
- Recognises that an isolated object can have unbalanced external forces leading to a resultant force and acceleration.
- Uses correct force vocabulary rather than everyday words, for example drag instead of air resistance where appropriate.
- Draws only the forces acting on the chosen object, with each arrow starting at the object.
- Uses arrow length to represent the relative magnitude of each force and arrowhead to show direction.
- Compares opposing forces to decide whether the resultant force is zero or non-zero.
- States the direction of the resultant force when the forces are unbalanced.
- Links a zero resultant force to constant velocity or rest, and a non-zero resultant force to a change in speed or direction.
- Describes the example qualitatively in words rather than calculating a numerical resultant.
- States that a single force can be resolved into two components acting at right angles to each other.
- Explains that the two component forces together have the exact same effect as the original single force.
- Uses a scale drawing to resolve a force, drawing the original force to scale at the given angle.
- Constructs a rectangle or right-angled triangle to find the perpendicular components graphically.
- Measures the lengths of the component arrows on the scale drawing and converts them back to force values using the scale.
- Selects and states a sensible scale that makes the diagram large enough for accurate measurement.
- Draws force arrows with correct length and direction, using a ruler and protractor.
- For two forces, arranges them tip-to-tail and draws the resultant from the start of the first to the tip of the second.
- Measures the resultant length and converts it to newtons using the stated scale.
- Measures the direction of the resultant as an angle from a clearly stated reference direction.
- For equilibrium, shows that the vector triangle closes so the resultant is zero.
- For resolution, constructs two perpendicular components whose combined effect equals the single force.
Examiner Tips
- 💡When calculating resultant force, draw a free-body diagram to visualise the forces and their directions.
- 💡If forces are at an angle, use a carefully drawn scale diagram to find the magnitude and direction of the resultant force (HT only).
- 💡For multiple forces along a line, choose a positive direction and assign signs to each force before adding.
- 💡Always check whether the question asks for magnitude only or magnitude and direction.
- 💡Sketch the two forces as arrows on a straight line and mark one direction as positive before calculating.
- 💡Show the signed addition or subtraction in your working so the examiner can follow your reasoning.
- 💡Finish with a full sentence giving magnitude and direction, and check whether the answer is sensible for the sizes given.
- 💡Name the object first, then list each force with its direction and the body that exerts it.
- 💡Use a labelled free-body diagram to support your written description, ensuring arrows start from the object.
- 💡Label every arrow with the force name and, if given, its value in newtons.
- 💡State clearly whether the resultant force is zero or non-zero before describing the motion.
- 💡Use the phrase resultant force in the direction of the longer arrow to make the direction explicit.
- 💡Keep the diagram simple: one dot or box for the object and straight arrows for the forces.
- 💡Always state your scale clearly (e.g., 1 cm = 10 N) and use a protractor to measure angles accurately.
- 💡Draw the original force first, then use a set square or protractor to draw the perpendicular components forming a rectangle.
- 💡Use a sharp pencil, a ruler and a protractor; freehand sketches are not accurate enough for scale-drawing questions.
- 💡Label each arrow with its force and write the scale prominently so the examiner can follow your method.
- 💡For equilibrium, check that the arrows form a closed triangle; if they do not, the object is not in equilibrium.
- 💡Note that scale vector diagrams and resolution of forces are Higher Tier only topics.
Common Mistakes
- Adding all forces together regardless of direction: forces in opposite directions must be subtracted. Correction: assign positive and negative directions before adding.
- Forgetting to state the direction of the resultant force. Correction: always include the direction (e.g., 'to the right' or 'upwards').
- Assuming that if forces are balanced, the object must be stationary: it could be moving at constant velocity. Correction: balanced forces mean no change in motion, not necessarily no motion.
- Confusing resultant force with the sum of all forces without considering direction. Correction: treat forces as vectors.
- Adding the magnitudes of forces that act in opposite directions: correct this by subtracting the smaller from the larger and keeping the direction of the larger force.
- Giving a bare number such as 10 N without a direction: correct this by naming the direction, for example 10 N to the right.
- Treating a resultant of 0 N as 'no forces': correct this by explaining that two equal and opposite forces still act but cancel, so the object's motion does not change.
- Assuming an isolated object must have balanced forces: correct this by recognising that isolated objects can experience a resultant force and accelerate.
- Labelling weight and mass as the same quantity: correct this by stating that weight is a force in newtons acting downwards while mass is in kilograms.
- Omitting the normal contact force on an object resting on a surface: correct this by including the upward contact force from the surface.
- Drawing forces that the object exerts on other bodies; the correction is that a free body diagram shows only forces acting on the chosen object.
- Treating a longer arrow as a larger mass; the correction is that arrow length represents force magnitude, not mass.
- Assuming a moving object must have a resultant force; the correction is that constant velocity means the resultant force is zero.
- Adding forces in different directions as if they were in the same line; the correction is that only forces along the same line are combined directly.
- Using trigonometry (sine and cosine) to resolve forces: correct this by using scale drawings, as trigonometry for force resolution is not required at GCSE.
- Treating the components as additional forces that change the overall effect: correct by stressing that the components replace the single force and are equivalent to it.
- Drawing the components shorter or longer than the rectangle's sides: correct this by ensuring the original force forms the exact diagonal of the rectangle.
- Drawing arrows not to scale or not stating the scale. Correct by choosing a scale, writing it on the diagram and using a ruler for every arrow.
- Joining the two force arrows tail-to-tail and measuring between them, which gives the wrong resultant. Correct by placing the second force at the tip of the first.
- Forgetting to convert a measured length back to newtons, or measuring the angle from an unstated direction. Correct by applying the scale and labelling the reference direction.