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AQA GCSE Physics · Topic 4.5 Forces · Combined and Triple · Higher tier
Vector Diagrams of Forces: Scale Drawings and Components
In this lesson you'll learn to: use a scale drawing to find the resultant of two forces at an angle,
giving its size and its direction as a three-figure bearing; and split one force at an angle into two
components at right angles, then pick out the one that matters, like the pull along the ground or the push down a slope.
Higher tier only Scale drawings of forces are only on the Higher
papers. Foundation students: you can skip to the next lesson.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. Change the thrust and the wind on the boat and watch the parallelogram, the resultant and its bearing change. Then switch tabs, pull a suitcase and tilt a slope to see a single force split into two parts.
Method:
The two forces · scale 1 cm = 5 kN
The resultant force
Situation:
The components
Scale drawing: draw each force as an arrow, length to scale, at the right angle. Two forces → one: complete the parallelogram (or draw them tip to tail); the diagonal is the resultant. Measure its length and convert with the scale; give the direction as a three-figure bearing, clockwise from North. One force → two: draw it to scale and make a right-angled triangle; the two sides are its components.
Physics With Kate · physicswithkate.com — AQA GCSE Physics 4.5.1.4 · Higher tier
Use Next step to build each drawing one line at a time, the way you'd draw it in the exam.
Forces at an angle don't just add up
Two forces → draw a parallelogram and measure the diagonal. One force → draw a right-angled triangle and measure the sides. The notes show you how to set it out for the marks.
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Revision notes
Why you need a scale drawing
Forces are vectors: they have a size and a direction. When two forces act along the same line you just add or subtract them. When they act at an angle to each other, you can't. A thrust of 20 kN and a wind of 15 kN at right angles do not give 35 kN. At GCSE you find the answer with an accurate scale drawing (a vector diagram).
⭐ Learn this
A scale drawing shows each force as an arrow: the length to scale for its size, drawn in its real direction.
The resultant force is the single force with the same effect as all the forces together. A force can also be resolved into two components at right angles, which together have the same effect as the original force.
Two forces → the resultant (parallelogram method)
1
Choose a scale
Use the one in the question, e.g. 1 cm = 5 kN. Write it on your drawing.
2
Draw both forces
From the same point, with a ruler and protractor: 20 kN → 4 cm north, 15 kN → 3 cm east.
3
Complete the parallelogram
Draw a line parallel to each force from the tip of the other.
4
Draw the diagonal
From the start point to the far corner: that's the resultant. Measure it: 5 cm × 5 = 25 kN.
5
Measure the bearing
Protractor on the start point, zero on North, measure clockwise: 037°.
The tip-to-tail method gives the same answer: draw the second force starting from the tip of the first, then join the start to the finish. The workbook answers use this triangle. Use whichever you find easier.
⚠ Trap — bearings
A bearing is measured clockwise from North and always has three figures: 037°, not 37°. Measuring the angle from the horizontal (53°) is the most common way to drop this mark.
One force → two components (resolving)
A force acting at an angle does two jobs at once. Splitting it into two components at right angles shows you how much of it does each job.
- Draw the force to scale at its angle.
- Make a right-angled triangle: draw a line along one direction (e.g. horizontal) from the start, and a line at right angles to it from the tip of the force.
- Measure the two shorter sides and convert with the scale. The force is the long side (the hypotenuse), so each component is always smaller than the force.
| Situation | The useful component | Why |
|---|---|---|
| Pulling a suitcase, cart or sledge by a handle at an angle | horizontal (along the ground) | only this part moves it along; the vertical part just lifts it |
| An object on a slope | weight down the slope | this part makes it slide; the part into the slope is balanced by the normal contact force |
Lower the handle and the horizontal component grows. Make the slope steeper and the component down the slope grows.
Balanced forces on a vector diagram
If an object is in equilibrium (the forces are balanced), drawing all its forces tip to tail makes a closed shape: you end up back where you started, so the resultant is zero. For three forces that's a closed triangle.
The answer that gets the marks
Using a scale of 1 cm = ___ N, the resultant is ___ cm long, so the
resultant force is ___ N on a bearing of ___° (clockwise from North).
state the scale measure, then convert direction, three figures
🗣 Words to use in a written answer
Tick each one off as you use it.
How to write it in the exam
A boat's engine gives a thrust of 20 kN north. The wind pushes it with 15 kN east. Using a scale of 1 cm = 5 kN, draw a scaled vector diagram to find the resultant force on the boat. (4 marks)
Thrust: 20 ÷ 5 = 4 cm north. Wind: 15 ÷ 5 = 3 cm east. Complete the parallelogram; the diagonal measures 5.0 cm, so the resultant = 5 × 5 = 25 kN on a bearing of 037°.
A person pulls a suitcase with a force of 100 N along a handle at 37° to the horizontal. Using a scale of 1 cm = 20 N, find the component of the force along the ground. (3 marks)
Draw 100 ÷ 20 = 5 cm at 37°. Drop a vertical line from the tip to the horizontal. The horizontal side measures 4.0 cm, so the force along the ground = 4 × 20 = 80 N. (The vertical component is 3 cm = 60 N.)
A box of weight 50 N rests on a slope at 30° to the horizontal. Using a scale of 1 cm = 10 N, find the component of its weight acting down the slope.
Draw the weight 5 cm straight down. Draw a line parallel to the slope from the start, and a line at right angles to the slope from the tip of the weight. The side along the slope measures 2.5 cm, so the component down the slope = 2.5 × 10 = 25 N.
Two tugs pull a ship with forces of 30 kN each. The ropes are 60° apart. Using 1 cm = 10 kN, find the resultant force.
Each force is 3 cm, drawn 60° apart from the same point. The diagonal of the parallelogram measures 5.2 cm, so the resultant = 5.2 × 10 = 52 kN, pointing straight between the two ropes. Not 60 kN: forces at an angle don't simply add.
✅ Check your answer has all 4 parts
A scale written down · arrows drawn with a ruler and protractor · a measured length converted with the scale, with its unit · a direction (three-figure bearing, or which component you measured).
📘 Now do it in your workbook
Draw your own scaled vector diagram and a force split into components, then the boat (resultant and bearing) and the suitcase (force along the ground) exam questions.
AQA GCSE Physics Workbook · FORCES · page 5✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this topic.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Watch both scale drawings being done step by step, with a ruler and protractor, then the two workbook questions on page 5 filled in.
Watch both scale drawings being done step by step, with a ruler and protractor, then the two workbook questions on page 5 filled in. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook page above cover every mark.
Now put it into practice
Page 5 of the Forces workbook is free: a scaled vector diagram, a force resolved into components, and two exam-style questions.
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