Estimating Physical Quantities
Estimating Physical Quantities
- Some exam questions ask for a reasonable estimate of an everyday quantity. No measuring is possible; you must build the answer from values you already know.
- An estimate should have the correct order of magnitude (the correct power-of-ten scale) and a sensible unit. It is not expected to be a precise measurement.
? m s⁻¹? cm³? AValues to remember
- Memorise a few standard values. Almost every estimate question is built from them.
| Everyday quantity | Value to remember |
|---|---|
| mass of an adult | 70 kg |
| height of an adult | 1.7 m |
| walking speed | 1 m s⁻¹ |
| motorway car speed | 30 m s⁻¹ |
| density of water | 1000 kg m⁻³ |
| g (free-fall acceleration) | 9.81 m s⁻² (≈ 10) |
| weight of an apple | ≈ 1 N |
| thickness of a sheet of paper | ≈ 0.1 mm |
Making an estimate
Near Earth, a quick estimate is weight in N ≈ mass in kg × 10. You will learn the full force relation later.
- Pick the standard values the quantity needs.
- Combine them with a simple formula (weight = , mass = density × volume, volume = length × width × height).
- Round to one figure and compare powers of ten.
Worked example
Smallest case: the weight of an adult
Choose the best estimate: 7×10⁰, 7×10², 7×10⁴ or 7×10⁶ N.
- Take the mass of an adult: .
- Weight is a force: .
- Nearest choice: .
Answer
(9702/12/O/N/25 Q1)
Your turn9702/11/O/N/24 Q4 · 1 mark · adapted
Estimate the volume of one page of an examination paper in mm³. Choose from 60, 600, 6000 or 60 000 mm³.
Show worked answer
- A page is about 300 mm long and 210 mm wide. Paper is about 0.1 mm thick.
- Volume: .
Answer
Start from familiar values, combine them with the correct relation, then check the unit and order of magnitude.
Common mistake
Estimating the wrong quantity. Weight is in newtons, so multiply the mass by . Writing 70 N (forgetting ) or 700 kg (a mass, not a weight) is wrong either way.