Calculate weight in a gravitational field
Distinguish mass from weight and use the local gravitational field strength to calculate the force on a mass.
Section 3 · Dynamics
AS Level · Cambridge International Physics 9702, 2025–2027 syllabus, Topic 3. These original explanations and practice support theory study; they do not establish supervised practical competence or replace timed assessment and teacher review. Drag is treated qualitatively, and coefficient of restitution is outside this syllabus section.
Before you begin
- Use vectors and signed values consistently, and distinguish mass from weight.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which unit is used for weight?
What you will learn
- Describe weight as the effect of a gravitational field on mass
- Recall and use W = mg
- Distinguish weight from mass and use correct units
Mass and weight describe different properties
Mass is a property of an object and is measured in kilograms. Weight is the gravitational force acting on that mass. In a gravitational field of strength g, the magnitude of the weight is W = mg.
The direction of weight is toward the source of the gravitational field. The field strength is force per unit mass, measured in N kg⁻¹, which is equivalent to m s⁻². Weight is a force and is measured in newtons.
Use the field strength given for the location
The mass stays the same when an object moves to a different gravitational field, while its weight can change because g changes. Use the value of g supplied in the question and keep units through the substitution.
In a free-fall model, the object's acceleration is g when gravity is the only force. If another force also acts, such as drag or a support force, use the resultant force to find acceleration rather than setting it equal to g.
Pause and explain
What changes when the same object is moved to a weaker gravitational field?
Worked example
A 3.0 kg instrument is on a planet where g = 4.0 N kg⁻¹. Find its weight.
Show the worked solution
- Use the local value of g given for the planet.
- W = mg = 3.0 × 4.0.
- Weight is a force, so report newtons and the field direction.
Answer 12 N toward the planet.
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.
Find the weight of a 0.80 kg sample where g = 10 N kg⁻¹.
Give me a hint
Multiply mass by field strength and report a force.
Compare my reasoning
- Use W = mg.
- W = 0.80 × 10 = 8.0.
- Attach the unit N.
8.0 N toward the planet.
Look for these in your work
- Correct relationship
- Substitution and arithmetic
- Force unit included
An astronaut has mass 70 kg on a moon where g = 1.6 N kg⁻¹. Find the astronaut's weight there.
Give me a hint
Use the moon's field strength, not an Earth value.
Compare my reasoning
- W = mg.
- W = 70 × 1.6.
- State the result in newtons.
112 N toward the moon.
Look for these in your work
- Local g used
- Product calculated
- Weight unit correct
A 2.0 kg sensor weighs 18 N on a world. Calculate the field strength and state what would happen to the sensor's mass if it were moved elsewhere.
Give me a hint
Rearrange W = mg and separate mass from weight.
Compare my reasoning
- g = W/m = 18/2.0.
- The field strength is 9.0 N kg⁻¹.
- Mass is a property of the sensor and remains 2.0 kg when moved.
g = 9.0 N kg⁻¹; the sensor's mass remains 2.0 kg in another location, though its weight may change.
Look for these in your work
- Equation rearranged
- Field-strength unit correct
- Mass distinguished from weight
Common mistakes
- Giving weight in kilograms
- Using Earth's field strength when another value is supplied
- Assuming an object always accelerates at g even when other forces act
What can you explain now?
Which unit is used for weight?
Compare with the explanation
N
Weight is a force.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why can the same object have a different weight while keeping the same mass?
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.