Combine forces along the same straight line
Add signed force contributions and state the resultant magnitude and direction.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Add positive and negative quantities.
- Identify forces acting on the same chosen object.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
With right positive, what sign does a leftward force have?
What you will learn
- Determine collinear resultants for two or more forces.
- Keep direction signs and force units consistent.
Choose one positive direction
For forces along one straight line, choose a positive direction and add signed values. On one object, 14 N right, 6 N left and 4 N left give resultant 14 − 6 − 4 = 4 N right. Do not add all magnitudes as though opposite directions were identical.
All included arrows must describe forces on the same chosen object. An object's pull on another object belongs to a different body's diagram and cannot be added as though it were an extra force on the first. The collinear method also does not apply unchanged to perpendicular forces; those need a vector method.
Translate the sign back into a direction
With right positive, 5 N right and 12 N left give −7 N, meaning magnitude 7 N left. With upward positive, 45 N up and 50 N down give −5 N, meaning 5 N downward. A resultant is not just the largest individual force; it represents their signed combined effect.
A zero sum means no resultant force on the chosen object. It does not mean each individual force disappeared, or that the object must be stationary. The next lesson connects that result to an unchanged velocity in the selected reference frame.
Sources for this lesson
Pause and explain
For 14 N right and 6 N plus 4 N left, which is the resultant?
Worked example
One object has forces 14 N right, 6 N left and 4 N left. Find its resultant.
Show the worked solution
- Choose right positive.
- Add 14 − 6 − 4 = +4 N.
- The resultant is 4 N right.
Answer 4 N right.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Combine 14 N right, 6 N left and 4 N left on one object.
Give me a hint
Choose a positive direction before adding contributions.
Compare my reasoning
- Right is positive.
- 14 − 6 − 4 = 4 N.
- The positive result is rightward.
4 N right.
Look for these in your work
- Include every stated force.
- Give magnitude and direction.
One body has 5 N right and 12 N left. Another has 45 N upward and 50 N downward. Give each resultant.
Give me a hint
Treat the two chosen bodies separately.
Compare my reasoning
- First sum, right positive: 5 − 12 = −7 N.
- Second sum, up positive: 45 − 50 = −5 N.
- Resultants are 7 N left and 5 N down.
7 N left; 5 N downward.
Look for these in your work
- Keep each body's forces together.
- Translate negative signs to directions.
Two forces of 8 N act at right angles. Can the collinear subtraction rule prove their resultant is zero? Explain.
Give me a hint
Opposite directions on one line are different from perpendicular directions.
Compare my reasoning
- The forces do not act along the same line.
- Equal magnitudes are not opposite vectors here.
- Use a vector method; the resultant is not zero.
No; perpendicular forces do not cancel as equal opposite collinear forces.
Look for these in your work
- Check the method's direction condition.
- Avoid cancelling perpendicular vectors.
Common mistakes
- Add signed contributions, not all magnitudes.
- Select forces on one object.
- State the direction of a non-zero resultant.
What can you explain now?
With 45 N upward and 50 N downward, what is resultant?
Compare with the explanation
5 N downward.
Using upward positive gives forty-five minus fifty, so the resultant is downward.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Draw three forces on one line, find their signed sum and translate its sign into a direction.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.