# Dependence of size on method of measurement

##### Demonstration

This introduces students to the idea that the value of a measurement depends on the nature of that measurement.

#### Apparatus and materials

Rope or belt, 1.5 m

Metre rule

#### Procedure

a Use the rope or belt as a tape measure, putting it around a student's waist.

b Remove the rope. Lay it straight and, with the aid of the metre rule, find the circumference of the waist.

c Invite students to calculate the diameter.

d As a thought experiment only, ask what the diameter would be if a wire were used instead of the rope ' particularly if the wire were pulled tight like that used to cut cheese!

#### Teaching notes

1 Though students may think this experiment trivial, it starts an important idea. The idea that a measured result may depend on the way it was obtained is fundamental to operational physics. Neither atoms nor students' waists are 'hard': their size will depend on the energy involved in making the measurement.

2 The estimates for molecules or atoms lying side by side, or loosely attached to other atoms, or making mild collisions like those between air molecules, are approximations to reality.

With sufficiently violent collisions, one atom moves right through the electron structure of another. Scientists lose track of the lightweight electrons and see a collision in which there seems to be only a nucleus with a diameter 10 000 times smaller. Nuclear collisions are not restricted to alpha particles or other charged projectiles. Neutral atoms endowed with the same large energy will make the same kind of nuclear collisions. (Though it is difficult to accelerate uncharged particles and produce violent collisions between them.)

Thanks to Leon Firth for suggesting improvements to the teaching notes.

This experiment was safety-checked in December 2006