Calculate weight mass and gravitational field strength
Rearrange W = mg and convert mass units before substituting.
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
- Rearrange a product equation.
- Convert grams to kilograms.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which equation finds mass from W and g?
What you will learn
- Use W = mg, m = W/g and g = W/m.
- Choose the supplied value of g and retain physical units.
Use field strength with mass
Gravitational field strength is gravitational force per unit mass: g = W/m. Rearranging gives W = mg. Where g is 9.8 N/kg, each kilogram has gravitational weight 9.8 N. A 0.650 kg sample therefore has W = 0.650 × 9.8 = 6.37 N.
If the mass is given in grams, divide by one thousand before using g in N/kg. For 750 g at 9.8 N/kg, W = 0.750 × 9.8 = 7.35 N. Using 750 directly would overstate the weight by a factor of one thousand.
Rearrange for the requested quantity
To find mass from a measured stationary weight of 24 N at g = 10 N/kg, use m = W/g = 2.4 kg. To find field strength when a 0.30 kg object has weight 2.4 N, use g = 2.4/0.30 = 8.0 N/kg. State which quantity is being calculated before selecting an equation.
Use the value of g supplied in the problem. Near Earth's surface it is approximately 9.8 N/kg, but a question may explicitly use 10 N/kg or give another location's value. Substituting 9.8 regardless of the question changes its stated model. The units provide a useful check: kg × N/kg leaves N, and N divided by N/kg leaves kg.
Sources for this lesson
Pause and explain
A 750 g object is at g = 9.8 N/kg. What is its weight?
Worked example
Find the weight of a 650 g sample where g = 9.8 N/kg.
Show the worked solution
- Convert 650 g to 0.650 kg.
- W = mg = 0.650 × 9.8.
- Weight = 6.37 N.
Answer 6.37 N.
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.
Calculate the weight of 650 g at 9.8 N/kg.
Give me a hint
Convert the mass to kg before multiplying by g.
Compare my reasoning
- 650 g = 0.650 kg.
- 0.650 × 9.8 = 6.37.
- Use the weight unit N.
6.37 N.
Look for these in your work
- Convert mass correctly.
- Use a force unit.
A body has weight 24 N where g = 10 N/kg. Find mass, then the weight of a 750 g sample at 9.8 N/kg.
Give me a hint
Use division for the first quantity and multiplication for the second.
Compare my reasoning
- First mass = 24/10 = 2.4 kg.
- Second mass = 0.750 kg.
- Second weight = 0.750 × 9.8 = 7.35 N.
2.4 kg; 7.35 N.
Look for these in your work
- Choose the correct rearrangement.
- Use each problem's g value.
A 0.30 kg object has stationary weight 2.4 N. Infer g and predict the weight of 0.75 kg at the same location.
Give me a hint
Find force per kilogram, then scale it to the new mass.
Compare my reasoning
- g = 2.4/0.30 = 8.0 N/kg.
- Use the same field for the new object.
- W = 0.75 × 8.0 = 6.0 N.
8.0 N/kg; 6.0 N.
Look for these in your work
- Infer the local field.
- Keep the same-location assumption.
Common mistakes
- Convert mass to kg when g is in N/kg.
- Use the supplied field strength.
- Weight is not measured in N/kg; field strength is.
What can you explain now?
An object weighs 24 N where g = 10 N/kg. What is its mass?
Compare with the explanation
2.4 kg.
Divide gravitational force by force per kilogram.
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Make it stick
Write all three rearrangements and check their units before calculating a new example.
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.