Calculate the resultant of two forces acting in a straight line.
BEEZYREVISOR
GCSE Physics Revision
Learn it. Recall it. Revise it.
GCSE Physics revision
Resultant forces
Forces and their interactions
Your specification
AQA student objectives
Learning pathway
All Ā· Most Ā· Some
Apply the principle of resultant force to calculate the combined effect of forces acting along a straight line.
Analyse a situation involving several forces and justify the direction and magnitude of the resultant.
Revision summary
Key knowledge
Read on screen, then print for Cornell-style active revision.
What Are Free Body Diagrams?
- A free body diagram is a simple diagram that shows all the forces acting on a particular object using force arrows.
- Each force arrow must show both a direction (which way the arrow points) and a magnitude (represented by the length of the arrow).
- Forces are labelled in Newtons (N) because all forces are vector quantities, meaning they have both size and direction.
Forces on a Flying Plane
- A plane in flight has four main forces acting on it: thrust (forwards), drag/air resistance (backwards), weight (downwards), and lift (upwards).
- By drawing these forces as arrows on a free body diagram, we can clearly see which forces oppose each other.
- Opposing forces can cancel each other out, so it is important to consider forces acting along the same line separately.
Calculating the Resultant Force
- The resultant force is the overall, single force that represents the combined effect of all forces acting on an object.
- It is easiest to calculate the resultant force by splitting forces into their horizontal and vertical components and dealing with each direction separately.
- For the vertical component, if lift = 80,000 N upwards and weight = 80,000 N downwards, the vertical resultant force = 80,000 ā 80,000 = 0 N.
- For the horizontal component, if thrust = 120,000 N and drag = 90,000 N, the resultant force = 120,000 ā 90,000 = 30,000 N to the right.
Equilibrium
- An object is said to be in equilibrium when all forces are perfectly balanced, resulting in a resultant force of zero.
- In equilibrium, both the horizontal and vertical components of the resultant force must equal zero ā not just one of them.
- For example, if air resistance increased to 120,000 N, the horizontal resultant would become 120,000 ā 120,000 = 0 N, meaning the plane is in equilibrium.
- An object in equilibrium will either remain stationary or continue moving at a constant velocity, as there is no net force to change its motion.
Key Terminology to Remember
- Thrust is the forward-driving force produced by an engine, whilst drag (air resistance) is the opposing force acting backwards.
- Weight is the downward force due to gravity acting on an object's mass, whilst lift is the upward force generated by a plane's wings.
- Resultant force is the single force that has the same effect as all the individual forces combined, found by adding or subtracting forces acting along the same line.
Resultant Force
- When several forces act on an object, they can be replaced by a single equivalent force called the resultant force.
- For forces acting along the same straight line, the resultant is found by subtracting the smaller force from the larger force if they act in opposite directions.
- For example, a car with 30 N forwards and 10 N backwards has a resultant force of 30 - 10 = 20 N forwards, causing acceleration.
- If the resultant force on an object is zero, the forces are described as balanced and the object moves at constant velocity or remains stationary.
Balanced Forces & Terminal Velocity
- A parachutist falling at constant velocity (terminal velocity) experiences balanced forces: weight of 800 N downwards and air resistance of 800 N upwards.
- Balanced forces mean there is no resultant force, so there is no change in the object's velocity ā it continues at a steady speed.
- Terminal velocity is reached when the upward air resistance equals the downward weight, resulting in zero resultant force.
Free Body Diagrams
- A free body diagram represents an object as a single point with arrows showing all the forces acting on it.
- Each arrow starts at the point representing the object, with its length indicating the magnitude of the force and its direction showing which way the force acts.
- For an aeroplane at constant velocity and constant altitude, thrust equals drag (horizontally) and lift equals weight (vertically), so all forces are balanced.
- Free body diagrams are a useful tool for visualising and analysing the forces on an object without drawing the object itself.
Scale (Vector) Diagrams
- Scale vector diagrams are used to find the resultant force when two or more forces act at an angle to each other.
- To draw a scale diagram: draw the force arrows at the correct angles and to scale, then complete a parallelogram using those arrows as two sides.
- The resultant force is represented by the diagonal of the parallelogram, measured from the starting point to the opposite corner.
- A suitable scale must be chosen (e.g.
- 1 cm = 1 N) so that the length of the diagonal can be converted into the actual magnitude of the resultant force.
Worked Example: Vector Diagram
- A runner exerts a force of 10 N forwards while wind pushes her with a force of 8 N at 30Ā° to her direction of motion.
- Using a scale of 1 cm = 1 N, the two forces are drawn at the correct angle and a parallelogram is completed.
- The diagonal of the parallelogram is measured (e.g.
- 17 cm), giving a resultant force of 17 N using the chosen scale.
- This method allows the resultant force to be determined accurately even when forces do not act along the same straight line.