AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER
Resultant forces
Forces · Lesson 3 of 20
Teacher copy - includes the notes for whoever is teaching from it.
Warm-up
Answer each one, then check.
1. What is a force measured in?
Newtons
2. What does balanced mean?
Equal and opposite
3. Is force a vector?
Yes
4. What does a resultant force of zero mean for motion?
No change in velocity
5. Add 40 N and 15 N.
55 N
Learning Objectives
1. Define a resultant force.
2. Calculate the resultant of two forces acting in a straight line.
3. Describe the forces on an isolated object using a free body diagram (Higher tier).
4. Use scale drawings to find the resultant of two forces, and resolve a force into components (Higher tier).
Resultant Force
A number of forces acting on an object may be replaced by a single force that has the same effect: the resultant force.
Forces in the same direction are added. Forces in opposite directions are subtracted. If the resultant is zero the forces are balanced.
Finding the Resultant
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Add same-direction forces; subtract opposite ones. |
Three examples of finding a resultant: opposite forces subtracted, same direction added and equal opposite forces giving zero.
Forces in a Straight Line
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A car's engine produces a driving force of 1800 N. Friction and air resistance give 1200 N in the opposite direction. Find the resultant force. |
1. Opposite directions
Subtract
2. Calculate
1800 − 1200 = 600 N
Answer: 600 N in the direction of the driving force.
Free Body Diagram (Higher)
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Draw a free body diagram for a book at rest on a table. |
1. Isolate the book
Draw the book as a box on its own
2. Weight
An arrow down from the centre of the box
3. Normal contact force
An arrow up of equal length
4. Resultant
Zero, so the forces are balanced
Answer: Equal arrows up and down: the resultant force is zero, so the book stays at rest.
Scale Drawing (Higher)
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Two forces of 3.0 N (east) and 4.0 N (north) act on an object. Find the resultant using a scale drawing. |
1. Scale
1 cm = 1 N
2. Draw
3 cm east, then 4 cm north from the end of the first arrow
3. Join start to finish
The arrow is 5.0 cm
4. Direction
Measure the angle: about 53° north of east
Answer: Resultant 5.0 N at about 53° north of east.
Resolving a Force (Higher)
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A force of 10 N acts at 30° above the horizontal. Find the horizontal and vertical components using a scale drawing. |
1. Scale
1 cm = 1 N
2. Draw
A 10 cm line at 30° to a horizontal line
3. Drop a perpendicular
Make a right-angled triangle
4. Measure
Horizontal about 8.7 cm and vertical 5.0 cm
Answer: Components: about 8.7 N horizontally and 5.0 N vertically.
Key Points
Remember in an exam.
▸ Direction. Give the direction of the resultant.
▸ Balanced. Zero resultant means constant velocity (Newton's first law).
▸ Free body diagram. Show only the forces on the object, as arrows from its centre.
▸ Units. Forces in newtons.
Key Terms
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Resultant force A single force with the same effect as all the forces on an object. |
Balanced forces Forces that are equal and opposite. |
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Free body diagram A diagram showing all forces acting on an isolated object. |
Component One of two perpendicular forces that together have the same effect as one force. |
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Resolve Split a force into two components at right angles. |
Equilibrium When the forces on an object are balanced. |
Your Task: Find the Resultant
10 minutes
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Find the resultant force: (a) 50 N right and 20 N left (b) 30 N up and 30 N down (c) 12 N right and 8 N right. 1. Same direction: add. 2. Opposite: subtract. |
A good answer shows: (a) 30 N right (b) 0 N (c) 20 N right.
Note: Ask what each resultant means for motion.
Can I...?
☐ Define a resultant.
☐ Add forces in the same direction.
☐ Subtract opposite forces.
☐ Recognise balanced forces.
☐ Draw a free body diagram.
☐ Use a scale drawing.
☐ Resolve a force.
☐ Give direction.
Summary
✓ Resultant: same direction add, opposite subtract.
✓ Zero resultant: balanced.
✓ Higher: free body diagrams and scale drawings.
✓ Resolve into perpendicular components.
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EXAM FOCUS A driving force of 1800 N and a resistive force of 1200 N act on a car. Calculate the resultant force. (2 marks) Subtract the smaller from the larger and give the direction. |
Exam Practice: Resultant forces
Answer all questions. Use the mark allocation as a guide to how much to write. · 14 minutes
▸ Question 1 · 2 marks · Calculate. A car engine produces a driving force of 1800 N. The total resistive force is 1200 N. Calculate the resultant force on the car and state…
▸ Question 2 · 2 marks · Use the diagram. The diagram shows the forces acting on a box. Calculate the resultant force.
▸ Question 3 · 2 marks · Explain. A skydiver has a weight of 800 N and air resistance of 500 N. Calculate the resultant force and state its direction.
▸ Question 4 · 3 marks · Draw. Draw a free body diagram for a stationary book on a table. Label the forces.
▸ Question 5 · 4 marks · Determine. Two forces act on an object at right angles to each other: 3.0 N east and 4.0 N north. Use a scale drawing to find the magnitude and…
Question 1 · 2 marks · Calculate
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“A car engine produces a driving force of 1800 N. The total resistive force is 1200 N. Calculate the resultant force on the car and state its direction.” |
HOW TO ANSWER IT Command word: Calculate. Worth 2 marks, so plan before writing.
Question 1 · mark scheme
2 marks available. Award a mark for each point made.
▸ 600 N. 1 mark
▸ In the direction of the driving force. 1 mark
▸ Model answer. 1800 − 1200 = 600 N in the direction of the driving force (forwards).
Question 2 · 2 marks · Use the diagram
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The diagram shows the forces acting on a box. Calculate the resultant force. (2 marks) |
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Question 2 · mark scheme
2 marks available. Award a mark for each point made.
▸ Subtracts 15 from 40. 1 mark
▸ 25 N to the right. 1 mark
▸ Model answer. 40 − 15 = 25 N to the right.
Question 3 · 2 marks · Explain
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“A skydiver has a weight of 800 N and air resistance of 500 N. Calculate the resultant force and state its direction.” |
HOW TO ANSWER IT Command word: Explain. Worth 2 marks, so plan before writing.
Question 3 · mark scheme
2 marks available. Award a mark for each point made.
▸ 300 N. 1 mark
▸ Downwards. 1 mark
▸ Model answer. 800 − 500 = 300 N downwards.
Question 4 · 3 marks · Draw
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“Draw a free body diagram for a stationary book on a table. Label the forces.” |
HOW TO ANSWER IT Command word: Draw. Worth 3 marks, so plan before writing.
Question 4 · mark scheme
3 marks available. Award a mark for each point made.
▸ Downward arrow labelled weight. 1 mark
▸ Upward arrow labelled normal contact force. 1 mark
▸ Arrows equal in length. 1 mark
▸ Model answer. A box with a downward arrow labelled weight and an upward arrow labelled normal contact force, of equal length.
Question 5 · 4 marks · Determine
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“Two forces act on an object at right angles to each other: 3.0 N east and 4.0 N north. Use a scale drawing to find the magnitude and direction of the resultant force.” |
HOW TO ANSWER IT Command word: Determine. Worth 4 marks, so plan before writing.
Question 5 · mark scheme
4 marks available. Award a mark for each point made.
▸ Correct scale chosen. 1 mark
▸ Right-angled triangle drawn accurately. 1 mark
▸ 5.0 N. 1 mark
▸ Direction about 53° north of east. 1 mark
▸ Model answer. A scale drawing (for example 1 cm = 1 N) gives a resultant of 5.0 N at about 53° north of east (accept 51° to 55°).