Unit 9

MASS AND WEIGHT MEASUREMENT

1. Practice reading the following words.

What are the units of mass and weight measurement? What do you know about mass and weight measuring devices? Discuss in groups.

3. Look at the pictures below. Find the picture which shows:

equal arm balance, spring scale, torsion balance, beam balance, strain gage load cell, laboratory balances.

Picture 1 Picture 2 Picture 3

Picture 4 Picture 5 Picture 6

Read and translate text A.

TEXT A

Mass and weight are often used interchangeably; however, they are different. Mass is a quantitative measure of inertia of a body at rest. As a physical quantity, mass is the product of density and volume. Weight or weight force is the force with which a body is attracted toward the Earth. Weight force is determined by the product of the mass and the acceleration of gravity.

M=V´D

where

M= mass

V= volume

D= density

Note: In most books, the symbol for density is the Greek letter r.

W=M´G

where

W = weight

G = gravity

The embodiment of units of mass are called weights; this increases the confusion between mass and weight. In the International System of Units (SI), the modernized metric measurement system, the unit for mass is called the kilogram and the unit for force is called the newton. In the United States, the customary system the unit for mass is called the slug and the unit for force is called the pound. When using the U.S. customary units of measure, people are using the unit pound to designate the mass of an object because, in the United States, the pound has been defined in terms of the kilogram since 1893.

Weighing Instruments

Weighing is one of the oldest known measurements, dating back to before written history. The equal arm balance was probably the first instrument used for weighing. It is a simple device in which two pans are suspended from a beam equal distance from a central pivot point. The standard is placed in one pan and the object to be measured is placed in the second pan; when the beam is level, the unknown is equal to the standard. This method of measurement is still in wide use throughout the world today.

A balance is a measuring instrument used to determine the mass of an object by measuring the force exerted by the object on its support within the gravitational field of the Earth. One places a standard of known value on one pan of the balance. One then adds the unknown material to the second pan, until the gravitational force on the unknown material equals the gravitational force on the standard. This can be expressed mathematically as:

S´G=U´G

where

S= mass of the standard

G= gravity

U= mass of the unknown

Given the short distance between pans, one assumes that the gravitational forces acting on them are equal. Another assumption is that the two arms of the balance are equal.

Since the gravitational force is equal, it can be removed from the equation and the standard and the unknown are said to be equal. This leads to one of the characteristics of the equal arm balance as well as of other weighing devices, the requirement to have a set of standards that allows for every possible measured value. The balance can only indicate if objects are equal and has a limited capability to determine how much difference there is between two objects.

Probably, the first attempt to produce direct reading balances was the introduction of the single pan substitution balance. A substitution balance is, in principle, similar to an equal arm balance. The object to be measured is placed in the weighing pan; inside the balance are a series of calibrated weights that can be added to the standard side of the balance, through the use of dials and levers. The standard weights can be added and subtracted through the use of the balance’s mechanical system, to equal a large variety of weighing loads. Very small differences between the standard weights and the load are read out on an optical scale.

The spring scale is probably the least expensive device for making mass measurements. The force of gravity is once again used as the reference. The scale is placed so that the unknown object is suspended by the spring and the force of gravity can freely act on the object. The elasticity of the spring is assumed to be linear and the force required to stretch it is marked on the scale. When the force of gravity and the elastic force of the spring balance, the force is read from the scale, which has been calibrated in units of mass. Capacity can be increased by increasing the strength of the spring. However, as the strength of the spring increases, the resolution of the scale decreases. This decrease in resolution limits spring scales to relatively small loads of no more than a few kilograms. There are two kinds of springs used: spiral and cantilevered springs.

The torsion balance is a precise adaptation of the spring concept used to determine the mass indirectly. The vertical force produced by the load produces a torque on a wire or beam. This torque produces an angular deflection. As long as the balance is operated in the linear range, the angular deflection is proportional to the torque. Therefore, the angular deflection is also proportional to the applied load. When the torsion spring constant is calibrated, the angular deflection can be read as a mass unit. Unlike the crude spring scales, it is possible to make torsion balances capable of measuring in the microgram region. The torsion element could be a band, a wire, or a string.

The beam balance is probably the next step in accuracy and cost. The beam balance uses the same principle of operation as the equal arm balance. However, it normally has only one pan and the beam is offset. A set of sliding weights are mounted on the beam. As the weights slide out the beam, they gain a mechanical advantage due to the inequality of the distance from the pivot point of the balance. The weights move out along the beam until the balance is in equilibrium. Along the beam, there are notched positions that are marked to correspond to the force applied by the sliding weights. By adding up the forces indicated by the position of each weight, the mass of the unknown material is determined. Beam balances and scales are available in a wide range of accuracy’s load capacities. Beam balances are available to measure in the milligram range and large beam scales are made with capacities to weigh trucks and trains. Once again, the disadvantage is that as load increases the resolution decreases.