Saturday, March 24, 2012

Measurements of mass and of time

Now we continue with our last discussion about .

Comparison between mass and weight

  • The mass of a body

  • The mass of a body is the quantity of matter it contains ( more details: Equivalence of mass and energy), and the basic SI unit of mass is the kilogram. The standard kilogram is the mass of a certain cylindrical piece of platinum-iridium alloy kept at Sevres.

  • Its various multiples and submultiples are given below:

  •     1 ton (t) = 1000 (kg)

  •     1 kg       = 1000 gram (g)

  •     1   g       = 1000 milligrams (mg)

  •     1 mg      = 100000 micrograms (µ g )

    The kilogram was originally intended to be equal to the mass of 1000 cubic centimeters (cm³ ) of pure water at the temperature of its maximum density, 4 °C. But a slight error was made at the time and the kilogram is actually equal the mass of 1000.028 cm³ of water ( details are near the bottom of this post).

  • The weight of a body

  The weight of a body is the force it exerts on anything which supports itNewton second law of motion- and, normally, it exerts this force owing to the fact that it is itself being attracted towards the earth by the force of gravity.

  In everyday conversation the distinction between mass and weigh is relatively unimportant: a butcher, for example, who had not studied physics would doubtless be surprised if a housewife who had done so, asked him what was the mass of her week-end joint.

     In science, however, we must be careful to distinguish between them- mass and weight-. Formerly this was done by adding the word “weight”.

Thus, the weight of a body of mass 5 kg would be written 5 kg wt. At the present time, it is more usual to use the word “force” instead of “weight”. Hence, we now say 5 kilogram force or : weight = mass × acceleration due to gravity ( mg ) = 5 × 9.8 = 49 Newton.

Measurement of mass. The laboratory balance

    Since weight is proportional to mass, we can measure the mass of a body by comparing the earth’s pull on it with the pull on a standard mass.

For this purpose we use a beam-balance and a box of “weights”. Strictly speaking, these weights ought to be called “standard masses”.common-balance-diagram

   The balances used in laboratories differ from those used in shops in that they are more sensitive. This means that they respond to much smaller changes of weight in the pans.

The bearings of the beam and scale-pan stirrups are made either of agate ( a very hard, semiprecious stone) or synthetic sapphire.

The beam is pivoted about an agate knife-edge resting on agate planes, while the stirrups have V-shaped agates resting on knife-edges at the end of the beam.

Bearings of this type posses very little friction, and so the beam swings freely without sticking. Also, the accuracy of the balance is improved, since the sharpness of the knife-edges ensures that the distances between the stirrup bearings and the beam bearing remain constant as the beam swings.

  Naturally, the knife-edges are fragile and are easily blunted if the balance is jolted. Hence, when the balance is out of use, or before anything is placed on or removed from the pans, the beam is brought to rest by turning the arrestment handle or knob. This lowers the centre bearing and brings the knife-edges out of contact with their planes.

The image above shows the main features of an ordinary laboratory balance. However, some are fitted with rider or chain attachments for reading fractions of gram.

The balancing screws at the ends of the beam occasionally require adjustment to allow for changes in the mass of the pans brought about by cleaning water.

How to use a balance

  Before attempting to weigh something, the leveling screws at the base of the balance must be adjusted until the plump-line hangs centrally through its ring.

If the beam is now raised, the pointer should swing through equal numbers of divisions on either side of the central mark.

If it fails to do so, the balancing screws may need slight adjustment, but first make sure that the stirrups have not been displaced.

   The object to be weighed should always be placed in the left-hand pan. Even the cleanest fingers are slightly greasy, and so forceps are always used for handling weights.

Having found a weight which is slightly less than the weight of the object, extra weights are added in decreasing order of magnitude until the pointer swings equal numbers of divisions on either side of the central mark.

Beginners soon learn that random choice of weights is a waste of time. Do not forget to lower the beam every time before weights are added to or removed from the pan. To set the beam swinging, a pan may be gently fanned with the hand.

  Having completed the weighing, write down the result and then check it carefully before replacing weights in the box. Do not try to weigh hot objects and always wipe the outside of a bottle or beaker containing liquid before placing it on the pan.

Volume of liquids

  The volume of a liquid is measured in liters. The liter has had an unfortunate history.

  The liter is 1000 cubic centimeters ( cm³ ) and, when the standard platinum-iridium kilogram was constructed in 1889, it was intended to be the mass of 1 liter of pure water at the temperature of its maximum density, 4 °C.

  The liter was then officially defined as the volume of 1 kg of pure water at 4 °C. This is where the trouble began. In 1907, careful experiments showed that a slight error had been made in constructing the standard kilogram. It was found to be the mass of 1000.028 cm³ of water.

Consequently, as defined above,

   1 liter = 1000.028 cm³

   At the time it was decided to leave the matter as it stood and to divide the liter in 1000 equal parts called milliliters (ml) so that,

    1 cm³ = 0.999972 ml

  Scientists thereupon began to use burettes and other liquid-measuring vehicles calibrated in ml instead of cm³.

  In 1964, the General Conference of Weights and Measures redefined the liter as equal to 1000 cm³. This means that the liter is, by its new definition, related directly to the meter and not the kilogram.

  However, vessels calibrated in ml are likely to continue in use for some time but except for very accurate analytical work we may assume that 1 ml = 1 cm³.

  The image below shows a selection of graduated vessels in common use.


The measuring cylinder is for measuring or pouring out various volumes of liquid; the measuring flask and pipette for getting fixed predetermined volumes.

The burette delivers any required volume up to its total capacity, usually 50 ml, and is long and thin to increase its sensitivity. Burette divisions generally represent 0.1 ml, but measuring cylinders may be graduated at 1, 5 or 10 ml intervals according to size.

  Readings on all these instruments are always taken at the level of the bottom of the meniscus or curved surface of the liquid. Mercury is an exception, as its meniscus curves downwards. Care should be taken to place the eye correctly so as to avoid parallax error ( that was discussed in the previous post).

When taking readings, the pipette and burette must be upright and the cylinder and flask must stand on a horizontal bench, otherwise errors may arise from tilting.

Measurement of time: the cesium atomic clock

  Everyone knows that a day is divided into 24 hours, each containing 60 minutes of 60 seconds each. At first, water clocks were used and later on mechanical clocks were made to measure time in these units.

Until recent years the accurate measurement of time has not been easy. For reasons which we need not discuss ( for now), the length of the day varies throughout the year, so that an average value has to be taken.

  At the Royal Greenwich Observatory there are a number of very accurate clocks which are checked daily against astronomical observations. These clocks are similar to ordinary electric clocks but are controlled by the vibrations of quartz crystals.

These quartz clocks are themselves checked by the cesium atomic clock at the National Physical Laboratory.

   The atomic clock is too complex a device to be described in detail, but briefly it is a radio transmitter giving out short waves - about 3 cm long-, the frequency of which is controlled by energy changes in gaseous cesium atoms.

The great advantage here is that the frequency ( in other words, the number per second) of the changes is constant and not subject to error.

  By using a cesium clock time intervals can now be measured with an error of not more than one second in 3000 years! This is so much better than results obtained by astronomical observations alone, so in 1967, the second was redefined as the time interval occupied by 9192631770 cycles of a specified energy change in the cesium atom.

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