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 0625, 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.
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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