Spark image

Estimation - Approximate sizes and values

It is always a good idea to be able to estimate the size of a quantity, so that when you work out a problem or finish an experiment you have a rough idea of what sort of value you might expect. Physicists use the phrase "the right order of magnitude" to mean a number in the right sort of range. For example finding the time of swing of a one metre pendulum as 1.2 s and not 12 s, the specific heat capacity of water as 4500 Jkg-1 K-1 and not 45 000 Jkg-1 K-1, or working out that the refractive index of an air-glass interface is 1.4 and not 0.4. As you may have read earlier all these numbers would be meaningless without their correct units so you must not forget to include them.

The following is a list of some quantities followed by a list of estimations for you to carry out yourselves: (N.B no answers are given for the estimates!)

Distance from Earth to the most distant quasar known 1.4x1026 m
Diameter of proton 1.3x10-15 m
Radius of the Earth 6400 km
Mass of a human 50-100 kg
Mass of the Sun 2x1030 kg
Volume of a human head 3 litres
Refractive index of glass 1.5 (air/glass interface)
Resiostance of a metre of constantan wire a few ohmas
Resistance of a metre of copper wire a few thousandths of an ohm
Specific heat capacity of water 4200 Jkg-1

(a) the mass of a sparrow
(b) the volume of your bedroom at home
(c) the volume of one of your friends
(d) the force needed to tear a piece of paper
(e) the temperature of a hot bath
(f) the frequency of wing beat of a fly (Hz)

© Keith Gibbs