Explain weight as the effect of a gravitational field
Compare one mass in different fields without treating a changed weight as lost matter.
Extended only (Supplement); Physics 0625, 2026–2028, section 1.3. Weight is the effect of a gravitational field on a mass. Keep the mass fixed when comparing different fields and state the weight direction. These examples use the supplied local field strengths rather than assuming Earth’s value everywhere. Written practice is self-checked
Before you begin
- Use W = mg.
- Distinguish mass from weight.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantity stays fixed when an intact object is moved between fields?
What you will learn
- Describe gravitational weight as a field acting on mass.
- Compare force magnitude and direction in different local fields.
A field determines force per kilogram
A gravitational field gives a gravitational force to an object with mass. Its local strength g is force per unit mass, and its direction is the direction of that force. A 2.0 kg object in fields of 9.8 N/kg and 1.6 N/kg has weights 19.6 N and 3.2 N respectively. Moving the intact object does not remove any matter.
The weight ratio equals the field-strength ratio when mass is unchanged: 3.2/19.6 = 1.6/9.8. Its weight acts toward the local attracting body in each case. The diagram compares magnitudes schematically; the two bodies' locations and sizes are not drawn to an astronomical scale.
Keep the condition for the comparison explicit
If the mass changes as well, a weight comparison alone cannot establish the change in g. Calculate W/m for each case. A 1 kg object at 9.8 N/kg and a 2 kg object at 4.9 N/kg both weigh 9.8 N, even though their masses and field strengths differ.
A zero gravitational field would give zero gravitational weight to a non-zero mass in this model. Conversely, a zero support-force reading during free fall does not by itself prove a zero gravitational field; gravity can still cause the motion. Distinguish actual gravitational force from a scale's support-force reading rather than calling all zero readings absence of mass.
Pause and explain
The same 2 kg object moves from 9.8 to 1.6 N/kg. What is its new mass and weight?
Worked example
The same 2.0 kg object moves from g = 9.8 N/kg to g = 1.6 N/kg. Find both weights and identify the unchanged quantity.
Show the worked solution
- First weight = 2.0 × 9.8 = 19.6 N.
- Second weight = 2.0 × 1.6 = 3.2 N.
- Mass stays 2.0 kg if the object remains intact.
Answer 19.6 N and 3.2 N; mass remains 2.0 kg.
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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.
Compare weights of the same 2.0 kg object at 9.8 and 1.6 N/kg.
Give me a hint
Hold mass fixed and change only the local field.
Compare my reasoning
- At 9.8 N/kg, weight is 19.6 N.
- At 1.6 N/kg, weight is 3.2 N.
- Mass stays 2.0 kg.
19.6 N; 3.2 N; mass unchanged.
Look for these in your work
- Use both fields.
- Keep the object intact.
A 1 kg object at 9.8 N/kg and a 2 kg object at 4.9 N/kg are compared. Find their weights and explain whether equal weight implies equal mass.
Give me a hint
Calculate each product before drawing a conclusion.
Compare my reasoning
- First weight is 9.8 N.
- Second weight is also 9.8 N.
- Their masses differ because the fields differ.
Both 9.8 N; equal weight here does not imply equal mass.
Look for these in your work
- Use each local g.
- State why the equal-field condition matters.
An object has mass 0.80 kg and gravitational weight 6.4 N. Another intact 0.80 kg object is in a field half as strong. Find that field and weight.
Give me a hint
Infer the first field, halve it, then use the unchanged mass.
Compare my reasoning
- First g = 6.4/0.80 = 8.0 N/kg.
- Half-strength field is 4.0 N/kg.
- New weight = 0.80 × 4.0 = 3.2 N.
4.0 N/kg; 3.2 N.
Look for these in your work
- Infer force per mass.
- Scale weight with the changed field.
Common mistakes
- Do not change mass just because g changes.
- Equal weight at different fields need not mean equal mass.
- A support-force reading is not always gravitational weight.
What can you explain now?
At g = 1.6 N/kg, what is the weight of 2.0 kg?
Compare with the explanation
3.2 N toward the attracting body.
Multiply mass by local field strength and specify the gravitational direction.
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Make it stick
Explain why weaker gravitational weight does not mean an intact object has lost mass.
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