Connect gravitational field strength with free-fall acceleration
Recognise N/kg and m/s² as equivalent units for g while keeping force distinct from acceleration.
Exam scope and assessment notes
Core and Extended · Physics 0972, 2026–2028, section 1.3. Mass is measured in kg; weight is a gravitational force measured in N. Use W = mg or g = W/m with the field strength stated in the question. A balance can compare weights and hence masses at the same location. Written method exercises support supervised practical learning but do not demonstrate practical competence. Written practice is self-checked; cumulative assessment and human subject-teacher review remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
Before you begin
- Recall near-Earth free-fall acceleration.
- Use weight = mass × field strength.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Is 19.6 N a force or an acceleration?
What you will learn
- Relate g = W/m to ideal free-fall acceleration.
- Distinguish weight changes from acceleration changes.
One local g, two equivalent unit descriptions
At a location with gravitational field strength 9.8 N/kg, ideal free-fall acceleration is 9.8 m/s². In SI units one newton is one kg·m/s²; dividing it by kg leaves m/s². Thus N/kg and m/s² are equivalent unit forms for g, not values requiring a factor of one thousand.
The meanings still differ from weight. A 2 kg object at g = 9.8 N/kg has gravitational force 19.6 N; its ideal gravitational acceleration is 9.8 m/s², not 19.6 m/s². Multiplying by mass gives a force rather than another acceleration.
Mass affects force but not this free-fall rate
In a uniform field of 4.0 N/kg, objects of 1 kg and 3 kg have weights 4 N and 12 N. In the gravity-only model each has free-fall acceleration 4.0 m/s². The greater force on the larger mass does not imply a three-times-larger gravitational acceleration.
Air resistance or other forces can change the actual acceleration. A stationary object supported on a table has weight but no changing velocity; support contributes an upward force. Do not infer an object's actual acceleration from gravitational weight alone unless the free-fall assumptions apply.
Pause and explain
Two different masses fall without resistance in the same uniform field. How do their gravitational accelerations compare?
Worked example
In a field of 4.0 N/kg, compare the weights and ideal free-fall accelerations of 1 kg and 3 kg.
Show the worked solution
- Weights are 1 × 4 = 4 N and 3 × 4 = 12 N.
- The local g has equivalent value 4.0 m/s².
- Both free-fall accelerations are 4.0 m/s² downward without other forces.
Answer Weights 4 N and 12 N; both ideal accelerations 4.0 m/s² downward.
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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.
Convert g = 9.8 N/kg into acceleration units and find the weight of 2 kg.
Give me a hint
Keep force and acceleration as separate results.
Compare my reasoning
- N/kg has equivalent unit m/s².
- The ideal acceleration is 9.8 m/s².
- W = 2 × 9.8 = 19.6 N.
9.8 m/s²; weight 19.6 N.
Look for these in your work
- Use the unit equivalence.
- Do not multiply acceleration by mass and keep acceleration units.
At g = 4.0 N/kg, find the weights of 1 kg and 3 kg and their ideal free-fall accelerations.
Give me a hint
Use W = mg for forces and g itself for the ideal acceleration.
Compare my reasoning
- Weights are 4 N and 12 N.
- The same field strength corresponds to 4.0 m/s².
- Both accelerations are 4.0 m/s² downward.
4 N and 12 N; both 4.0 m/s² downward.
Look for these in your work
- Scale weight with mass.
- Keep the free-fall condition.
A 2 kg object rests on a table at g = 9.8 N/kg. Is its actual acceleration 9.8 m/s²? Explain.
Give me a hint
The object is supported rather than freely falling.
Compare my reasoning
- Its gravitational weight is 19.6 N downward.
- The table's support balances that force in this stationary setup.
- Actual acceleration is zero; the local g remains 9.8 m/s².
No; actual acceleration is zero because support balances weight.
Look for these in your work
- Include the support force.
- Separate local g from total acceleration.
Common mistakes
- Weight and acceleration have different units.
- A larger gravitational force does not by itself imply larger free-fall g.
- Support or resistance changes the total-force situation.
What can you explain now?
What acceleration-unit value corresponds to 8 N/kg?
Compare with the explanation
8 m/s².
N/kg and m/s² are equivalent units for g.
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Make it stick
Explain why two masses can have different weights and the same gravity-only acceleration.
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