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 | 1.4x10^{26} 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 | 2x10^{30} 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} |

Problems

Estimate:

(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)

Estimate:

(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)