Determine field strength from weight-mass data
Interpret force-per-mass ratios and a weight-versus-mass gradient.
Section P1.3 · Mass and weight
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Calculate a straight-line gradient.
- Interpret N/kg as force per unit mass.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What unit results from a weight–mass gradient?
What you will learn
- Calculate g from measured or supplied weight and mass pairs.
- Use a graph gradient to compare gravitational fields.
Use paired readings
For original illustrative data at one location, masses 0.20, 0.40 and 0.60 kg have stationary weights 1.96, 3.92 and 5.88 N. Each ratio W/m is 9.8 N/kg. The agreement is consistent with the same gravitational field strength for all three samples.
For a supervised measurement, check a force meter's zero, measure the supported stationary weight, and determine mass separately with a suitable balance. A force meter's reading during acceleration is not automatically the gravitational weight. Record headings with quantity and unit, then examine repeated readings and any zero offset before inferring a field.
The graph gradient has physical meaning
Plot W in N vertically and m in kg horizontally. For W = gm at constant g, a straight line through the origin has gradient g. Using separated points, (5.88 − 1.96)/(0.60 − 0.20) = 9.8 N/kg. The gradient divides a force difference by a mass difference, not square counts on differently scaled axes.
Real readings may scatter, so use an appropriate best-fit line rather than connecting every point as a jagged path. A non-zero intercept can suggest a zero error or another unaccounted force; do not simply divide every offset reading by mass and call the resulting variation a changing field. These exercises interpret data; they do not certify an experiment as performed.
Sources for this lesson
Pause and explain
A W-versus-m line runs through (0.20,1.96) and (0.60,5.88) in kg and N. What is g?
Worked example
Find the gradient between (0.20 kg, 1.96 N) and (0.60 kg, 5.88 N).
Show the worked solution
- Weight change = 3.92 N.
- Mass change = 0.40 kg.
- Gradient = 3.92/0.40 = 9.8 N/kg.
Answer 9.8 N/kg.
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.
Use weights 1.96,3.92,5.88 N at masses 0.20,0.40,0.60 kg to infer g.
Give me a hint
Calculate a ratio for each matched data pair.
Compare my reasoning
- 1.96/0.20 = 9.8 N/kg.
- 3.92/0.40 and 5.88/0.60 also equal 9.8.
- The data are consistent with g = 9.8 N/kg.
9.8 N/kg for all three pairs.
Look for these in your work
- Keep readings paired.
- Use force-per-mass units.
Another W-versus-m line contains (0.10 kg,0.80 N) and (0.50 kg,4.00 N). Find its gradient.
Give me a hint
Use changes in both physical coordinates.
Compare my reasoning
- Force change = 3.20 N.
- Mass change = 0.40 kg.
- Gradient = 8.0 N/kg.
8.0 N/kg.
Look for these in your work
- Subtract endpoints.
- Interpret the gradient as g.
A force meter adds a constant +0.20 N offset to every weight. Explain why small-mass W/m ratios are especially distorted and suggest a correction.
Give me a hint
The same added force is divided by different masses.
Compare my reasoning
- Measured W/m = g + 0.20/m.
- The extra term is larger for smaller m.
- Check and correct the meter zero before collecting data; examine the line's intercept.
The offset has a larger per-kg effect at small mass; correct the zero and check the intercept.
Look for these in your work
- Explain the mass-dependent effect.
- Address the systematic offset.
Common mistakes
- Check that the vertical quantity is weight, not mass.
- A gradient uses coordinate differences.
- A force-meter zero error can distort W/m ratios.
What can you explain now?
If 0.30 kg has weight 2.4 N, what is field strength?
Compare with the explanation
8.0 N/kg.
The gravitational force per unit mass is 2.4/0.30.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Sketch W against m, label the gradient unit and explain what a zero offset would change.
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.