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Quantities and estimates Cambridge International AS & A Level Physics revision

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In plain words

Every measurement in physics is a number and a unit together: "5" means nothing, "5 metres" does. And a good physicist can make a sensible guess at the size of almost anything, which is the quickest way to spot an answer that has gone wrong.

Three things to know

  1. A physical quantity has a numerical magnitude and a unit. Leave the unit off and the answer is incomplete.
  2. Values worth knowing: an adult has a mass of about 70 kg; an apple about 0.1 kg (so it weighs about 1 N); a car about 1000 kg; a room is about 3 m high; walking speed is about 1.5 m/s; sound travels through air at about 340 m/s.
  3. To estimate something, pick sensible values, round them, and work to one significant figure. Getting the right power of ten is what matters.

Worked example

Estimate the kinetic energy of a sprinter.

  1. Mass about 70 kg; top speed about 10 m/s.
  2. Kinetic energy = ½mv² = ½ × 70 × 10².
  3. = 3500 J, so about 4 kJ.

Tips and tricks

  • In a multiple-choice estimate the options usually differ by factors of ten, so you only need the right power of ten.
  • Check every final answer against common sense. A car with a mass of 15 kg, or a person running at 300 m/s, means a slip somewhere.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Quantities and estimates: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. Which is the best estimate of the mass of an apple?
    • 1 g
    • 100 g (the answer)
    • 1 kg
    • 10 kg

    Its weight is about 1 N.

  2. Which is the best estimate of the height of a door?
    • 0.2 m
    • 2 m (the answer)
    • 20 m
    • 200 m

    A little taller than an adult.

  3. Which is the best estimate of the time between the heartbeats of a person at rest?
    • 0.01 s
    • 0.1 s
    • 1 s (the answer)
    • 10 s

    About 60 to 80 beats a minute.

  4. Which is the best estimate of the wavelength of visible light?
    • 5 × 10⁻¹⁰ m
    • 5 × 10⁻⁷ m (the answer)
    • 5 × 10⁻⁴ m
    • 5 × 10⁻² m

    Visible light runs from about 400 nm to 700 nm.

  5. A student writes the length of a bench as "4.2". What is missing?
    • the unit (the answer)
    • the direction
    • the prefix
    • the uncertainty

    A number with no unit doesn't say what was measured.

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