AQA GCSE Combined Science (8464), Higher tier · Physics › Forces › Forces and their interactions
Practise Resultant forces. 14 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
The resultant force is the single force that has the same effect as all the forces acting on an object together. You need to find the resultant of forces along a line, draw free body diagrams, and (Higher) use scale drawings to add two forces at an angle or to resolve one force into two components at right angles.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
Define resultant forceA single force that has the same effect as all the original forces acting together.
4
Find the resultant of forces along a lineAdd forces acting in the same direction; subtract forces acting in opposite directions.
5
Recognise balanced forces (zero resultant)If the resultant force is zero, the object stays at rest or keeps moving at a steady velocity.
6
Draw and use free body diagramsShow every force acting on one object as a labelled arrow drawn from the object.
7
Find a resultant using a scale drawingDraw the two forces tip-to-tail to scale; the resultant is the arrow from the start of the first to the end of the second.
8
Resolve a force into two perpendicular componentsDraw the force to scale and complete a right-angled triangle to measure its horizontal and vertical components.
8
Use vector diagrams for equilibriumIf three forces are in equilibrium, their arrows drawn tip-to-tail form a closed triangle.
Notes
Forces along a line
The forces acting on an object can be replaced by a single resultant force that has the same effect as all of them together.
Forces in the same direction: add them. Forces in opposite directions: subtract, and the resultant acts in the direction of the larger force.
Example: 700 N forwards and 250 N backwards give a resultant force of 450 N forwards.
If the resultant force is zero, the forces are balanced. The object is either stationary or moving at a constant velocity.
Free body diagrams grade 6+
A free body diagram shows one object (often as a box or dot) with every force acting on it drawn as an arrow.
Each arrow starts at the object, points in the direction of the force and is labelled with its name and size.
Longer arrows mean bigger forces. Balanced forces are shown by equal-length arrows in opposite directions.
Only include forces that act on the object, not forces that the object exerts on other things.
Adding two forces at an angle grade 7+
Choose a scale, e.g. 1 cm = 10 N, that makes the drawing as large as possible.
Draw the first force to scale. From its tip, draw the second force to scale in its direction (tip-to-tail).
The resultant is the arrow from the tail of the first force to the tip of the second. Measure its length for the magnitude and its angle with a protractor for the direction.
An object is in equilibrium when the force arrows drawn tip-to-tail make a closed shape: the resultant is zero.
Resolving a force grade 8+
A single force can be resolved into two components acting at right angles to each other. Together, the two components have the same effect as the single force.
Draw the force to scale, then draw horizontal and vertical lines to make a right-angled triangle with the force as the longest side. Measure the other two sides.
Example: a 50 N pull at 37° above the horizontal has a horizontal component of about 40 N and a vertical component of about 30 N.
Cheatsheet
Resultant force = single force with the same effect as all the forces together
Same direction: add; opposite directions: subtract
Balanced forces: resultant = 0 N, so the object is at rest or moves at constant velocity
Free body diagram: all the forces acting ON one object, labelled arrows drawn to scale
Scale drawing: draw the forces tip-to-tail; the resultant goes from the start to the finish grade 7+
A force can be resolved into two perpendicular components that have the same effect grade 8+
Equilibrium: force arrows drawn tip-to-tail make a closed triangle grade 8+
How to answer each type of question
Calculate the resultant of forces along a line
2 marks4
Add up all the forces acting in each direction.
Subtract the smaller total from the larger.
Give the size and the direction of the resultant.
Example. A cyclist has a driving force of 180 N forwards. Air resistance of 60 N and friction of 25 N both act backwards. Calculate the resultant force on the cyclist and give its direction.
Draw one arrow for each force acting on the object, starting on the object.
Label each arrow and make the lengths show the relative sizes.
Use the resultant force to explain the motion.
Example. A lamp hangs at rest from a ceiling on a cable. Describe the free body diagram for the lamp and explain why the lamp stays at rest.
Show the model answer
An arrow downwards from the lamp labelled weight (1). An arrow upwards labelled tension, the same length as the weight arrow (1). The forces are equal and opposite, so the resultant force is zero and the lamp stays at rest (1).
Scale drawing: resultant of two forces at an angle
3 to 4 marks7
Choose and state a scale.
Draw the forces tip-to-tail, accurately, with a ruler and protractor.
Draw the resultant from start to finish.
Measure its length and angle, and convert the length using the scale.
Example. Two tugs pull a ship. Tug A pulls with a force of 30 kN due east. Tug B pulls with a force of 40 kN due north. Use a scale drawing to determine the size and direction of the resultant force on the ship.
Show the model answer
Suitable scale, e.g. 1 cm = 5 kN, with 6.0 cm east then 8.0 cm north drawn tip-to-tail (1) Resultant drawn from the start to the finish (1) Length 10.0 cm, so the resultant = 50 kN (1) Direction about 53° north of east (1)
Scale drawing: resolve a force into components
2 to 3 marks8
Draw the force to scale at the given angle.
Complete the right-angled triangle with horizontal and vertical sides.
Measure the side you need and convert it with the scale.
Example. A child pulls a sledge with a force of 60 N along a rope at 30° above the horizontal. Use a scale drawing to determine the horizontal component of the force.
Show the model answer
Force drawn to scale at 30° to the horizontal, e.g. 6.0 cm with 1 cm = 10 N (1) Right-angled triangle completed with horizontal and vertical sides (1) Horizontal side about 5.2 cm, so the horizontal component ≈ 52 N (1)
Shortcuts and memory tricks
Tip-to-tail: draw the arrows like a line of elephants, nose to tail. The resultant runs from the very first tail to the very last tip.
For two forces at right angles, check your drawing with Pythagoras: 30 kN and 40 kN give 50 kN (a 3-4-5 triangle).
Balanced does not mean stopped. A zero resultant means no change in velocity: still, or steady speed in a straight line.
Along a line, the resultant always acts in the direction of the bigger force.
Where marks are lost
Giving a resultant force without a direction. A force is a vector.
Adding forces that act in opposite directions instead of subtracting them.
Thinking a moving object must have a resultant force on it. At constant velocity the resultant force is zero.
Drawing both forces from the same point and joining their tips. That line is not the resultant.
Making scale drawings too small, which makes the measured values inaccurate.
Including forces that the object exerts on something else in a free body diagram.
Exam technique
Always give the size and the direction of a resultant force.
In scale drawings, write your scale on the diagram and give the angle from a stated direction (e.g. '53° north of east').
Examiners allow a small tolerance on measured values, so use a sharp pencil, a ruler and a protractor.
Link the resultant to the motion: zero resultant means constant velocity or at rest; a non-zero resultant means acceleration in its direction.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Name the two other forces acting on the balloon as it rises.
Weight and air resistance.
The tension in the cable is increased to 3900 N. Calculate the resultant force on the crate and give its direction.
300 N upwards N
State what it means for an object when the resultant force acting on it is zero.
It stays at rest or moves at constant velocity (it is in equilibrium).
What word describes an object when the resultant force acting on it is zero?
Equilibrium.
A tractor pulls a trailer using a chain, which exerts a forward force of 2400 N on the trailer. Resistive forces (friction and air resistance) on the trailer total 2400 N. The trailer is already moving forward. Calculate the resultant force on the trailer.
0 N
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
(a) Which of these is the correct definition of the resultant force on an object? Tick (✓) one box.[1]
The largest of the forces acting on the object
The single force that has the same effect as all the forces acting on the object together
The force needed to keep the object still
The force that always acts against the object’s motion
(b) State what it means for an object when the resultant force acting on it is zero.[1]
(c) A stationary crate is pushed with a force of 90 N to the right. Friction of 90 N acts to the left. Calculate the resultant force on the crate.[2]
Show the answer and mark scheme
(a)Answer: The single force that has the same effect as all the forces acting on the object together
(b)Answer: It stays at rest or moves at constant velocity (it is in equilibrium).
the object stays at rest, or continues to move at a constant velocity (it is in equilibrium)
(c)Answer: 0 N
90 − 90
0 (N)
Question 2Medium6 marks
A crane lifts a crate using a vertical steel cable. The weight of the crate is 3600 N. Ignore air resistance.
(a) The crate hangs at rest just above the ground. What is the tension in the cable?[1]
(b) The tension in the cable is increased to 3900 N. Calculate the resultant force on the crate and give its direction.[2]
(c) Describe the motion of the crate while the tension is 3900 N.[1]
(d) Later, the crate moves upwards at a constant speed. Give the tension in the cable. Explain your answer.[2]
Show the answer and mark scheme
(a)Answer: 3600 N
3600 (N)
(b)Answer: 300 N upwards N
300 (N)
upwards
(c)Answer: It accelerates upwards.
accelerates upwards / speeds up (moving upwards)
(d)Answer: 3600 N, because the resultant force is zero at constant speed.
3600 (N)
(constant speed so) the resultant force is zero / the forces are balanced, so the tension equals the weight
Question 3Hard6 marks
A crane lifts a heavy load at a constant speed, using a vertical cable.
Using ideas about resultant force and equilibrium, explain how the crane can lift the load at a constant speed. Then explain what would happen to the load’s motion immediately if the tension in the cable suddenly increased, or if it suddenly decreased.[6]
Show the answer and mark scheme
at a constant speed the load is in equilibrium, so the resultant force on it is zero
this means the tension in the cable must be equal in size to the weight of the load, and act in the opposite direction
if the tension suddenly increases above the weight, there is a resultant force upwards, so the load accelerates upwards (speeds up while moving up)
if the tension suddenly decreases below the weight, there is a resultant force downwards, so the load decelerates while moving up (or accelerates downwards)
the direction of the load’s acceleration is always the same as the direction of the resultant force
at the very start of the lift, from rest, the tension must be greater than the weight, so that the load accelerates upwards from rest in the first place
Marked with levels of response: the full level descriptors are in the app.