Compare masses and weights using a balance
Use equal-arm balance comparisons at one location and distinguish them from force-meter readings.
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
- Recognise a balance's level and unbalanced states.
- Use the same local field for compared samples.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What must be shared when equal local weights are used to infer equal masses?
What you will learn
- Describe how a balance compares weights and masses.
- Explain why equal local weights imply equal masses.
Compare under common conditions
An equal-arm beam balance compares the downward weights on its two pans. With the balance correctly zeroed and level, placing an unknown sample on one pan and known reference masses on the other allows a comparison. At the same location, both sides experience the same gravitational field strength, so equal weights imply equal masses.
Reference masses of 100 g, 100 g and 50 g balancing a sample give sample mass 250 g, or 0.250 kg. The sample's gravitational weight at 9.8 N/kg is 2.45 N. The mass result and the force result have separate units; the balance comparison does not turn grams into newtons.
Check what each instrument does
Remove loads and check the balance's zero before comparing samples. Keep the pans free to move and prevent either sample touching the bench. Add or remove reference masses until the comparison is level, then sum the actual reference masses rather than counting how many pieces were used.
An electronic balance may infer mass from a sensed support force using calibration, whereas a newton meter is labelled in force units. These instruments are not identical to an equal-arm comparison. A container's mass must be subtracted or tared if the desired result is only the sample mass. A tare does not change the material's physical mass; it changes the reading reference.
Sources for this lesson
Pause and explain
A sample balances 100 g, 100 g and 50 g references. What mass is inferred?
Worked example
A sample balances 100 g + 100 g + 50 g reference masses. Find its mass and weight at g = 9.8 N/kg.
Show the worked solution
- Sum reference masses: 250 g = 0.250 kg.
- Equal balance compares equal weights in the same field.
- Sample weight = 0.250 × 9.8 = 2.45 N.
Answer 0.250 kg; 2.45 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.
A sample balances 100 g + 100 g + 50 g. Find mass in kg and weight at 9.8 N/kg.
Give me a hint
Sum the references, convert, then calculate gravitational force.
Compare my reasoning
- Total mass is 250 g.
- Convert to 0.250 kg.
- W = 0.250 × 9.8 = 2.45 N.
0.250 kg; 2.45 N.
Look for these in your work
- Sum reference values.
- Keep mass and force units separate.
An empty container has mass 42 g. With a sample it balances 100 g + 20 g + 10 g. Find the sample mass.
Give me a hint
Subtract the container from the total balanced mass.
Compare my reasoning
- Total mass is 130 g.
- Sample mass = 130 − 42.
- Sample mass is 88 g.
88 g.
Look for these in your work
- Sum all references.
- Remove the container contribution.
Two objects balance each other on equal arms. One is twice the volume of the other. Does the balance establish equal volume or equal mass?
Give me a hint
The comparison responds to weight, not occupied space.
Compare my reasoning
- The local weights balance.
- At common g this gives equal mass.
- Different volumes are compatible with different densities, so equal volume is not established.
Equal mass at the same field strength; not necessarily equal volume.
Look for these in your work
- Explain the mass inference.
- Keep volume separate.
Common mistakes
- Add mass values, not the count of reference pieces.
- A pan touching the bench spoils the comparison.
- Subtract the container when finding sample mass.
What can you explain now?
A sample balances 200 g and 20 g reference masses. What is its mass?
Compare with the explanation
220 g.
At the same local field, balanced equal-arm weights imply equal masses.
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Make it stick
Describe a balance comparison, a zero check and a container-mass correction.
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.