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Weight v Mass

Weight and Mass -Let Confusion Abound

Although engineers might like to believe that this subject is clearly defined, there is still confusion surrounding the definitions of mass and weight. You would think it was simple – the definition states:, “The mass of any object represents the quantity of the material it contains ; it is independent of physical changes such as gravity, temperature etc.”

The international unit of mass is the kilogram and is defined as the mass of the International Prototype Kilogram which is held at the International Bureau of Weights and Measures ( B.I.P.M). The kilogram is now the only physical artifact used for establishing a fundamental unit. A number of authorized copies are held by laboratories around the world (the UK holds number 18 and the US number 20). From these, reference and working kilogram standards are held by Weights and Measures authorities.

Unfortunately through common misusage, standards of mass are referred to as weights.

The term ‘weight’ is ambiguous and is used to describe both mass and force. Although the SI system clearly differentiates between mass and force, with no reference to the term weight, weighing has, through common usage, become the accepted term for the determination of mass in all walks of life. One possible reason is that ‘mass’ is a noun whereas ‘weight’ is derived from the verb ‘to weigh’ giving it far more flexibility in use. In fact weighing determines the apparent mass of an object, ignoring the effects of air buoyancy

Unlike mass, weight varies with geographic location due to changes in the value of g. Gravity is greater at the poles than at the equator and decreases with increase in altitude and the effect of gravity at any given location can be calculated using the following formulae

g = 9.806 32 – 0.025 86 x cos 2ø + 0.000 03 x cos 4ø m/sec2 (latitude)-0.000 002 93 x h m/sec2 (altitude)

where ø = degrees latitude and h = height in metres above sea level.

Therefore scales which work by measuring the gravitational force on an object rather than comparing one mass with another are technically only correct if calibrated and used at the same location. A legal for trade weighing instrument would be regarded as being sensitive to variations in gravity if, as a result of a change in location, a change of greater than the absolute value of the maximum permissible error (applicable on verification) occurred for any load applied.

For a Class III instrument having 3000 e, verified in London and subsequently moved to Edinburgh an additional error in the performance of the instrument would result due to the increase in the value for gravity.

Latitude change London to Edinburgh is approximately equal to 485 km

Error (assuming no change in altitude) is approximately equal to 1.1 e at maximum capacity

The consequence of the change due to gravity is that the instrument will have used up more than a third of the positive error allowance in relation to the in service allowance.

The change due to gravity is proportional; therefore the error at 500 e would be approximately 0.18 e and at 2000 e approximately 0.74 e.

If the instrument already had a significant linearity or hysteresis error on initial verification then the instrument might be close to being outside the error allowance at the m.p.e change points i.e. 500 e and 2000 e, although still within the in-service allowance.

Do things weigh less on the moon?

Yes and no!

If a scale which measures weight is calibrated on earth and transported to the moon, then a 1 kg mass placed on the scale on the moon’s surface will appear to weigh approximately 160 g.
However, if this same scale is now calibrated on the moon’s surface using the same 1 kg mass, then, when 1 kg is placed on the scale, the scale will register 1 kg.

Check how much you would weigh on the different planets by visiting www.solarviews.com

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