Page 121 - Instrumentation Reference Book 3E

7 Measurement of force

C. S. BAHRA and J. PAROS

7.1 Basic concepts employed in their design, limitations, and use. It
is not intended to give a too detailed description
If a body is released, it will start to fall with an of mathematical and physical concepts, but
acceleration due to gravity or acceleration of free enough information to allow an interested reader
fall of its location. We denote by g the resultant to read further.
acceleration due to attraction of the earth upon
the body and the component of acceleration due 7.2 Force measurement
to rotation of the earth about its axis. The value methods
of g varies with location and height and this
variation is about 0.5 per cent between the equa-
tor and the poles. The approximate value of g is Force measurement methods may be divided into
9.81 mls’. A knowledge of the precise value of g is two categories, direct comparison and indirect
necessary to determine gravitational forces acting comparison. In a direct comparison method, an
on known masses at rest, relative to the surface of unknown force is directly compared with a gravi-
the earth, in order to establish practical standards tational force acting on a known mass. A simple
of force. Practical standards of dead-weight cali- analytical balance is an example of this method.
An indirect comparison method involves the use
bration of force-measuring systems or devices are
based on this observation. of calibrated masses or transducers and a sum-
It is necessary to make a clear distinction mary of indirect comparison methods is given
between the units of weight-measuring (mass- below:
measuring) and force-measuring systems. The
weight-measuring systems are calibrated in kilo- (a) Lever-balance methods.
grams while the force-measuring systems are in (b) Force-balance method.
newtons. Mass, force, and weight are defined as (c) Hydraulic pressure measurement.
follows: (d) Acceleration measurement.
(e) Elastic elements.
Mass. The mass of a body is defined as the
quantity of matter in that body and it remains Note that the lever-balance methods include
unchanged when taken to any location. The unit examples of both direct and indirect compari-
of mass is the kilogram (kg). sons, but to maintain continuity of information,
Force. Force is that which produces or tends to
produce a change of velocity in a body at rest or they are described under one heading.
in motion. Force has magnitude, direction, and a
point of application. It is related to the mass of a 7.3 Lever-balance methods
body through Newton’s second law of motion
which gives: force = mass x acceleration. 7.3.1 Equal-lever balance
Unit of force. In the International System of
units, the unit of force is the newton (N) and it is A simple analytical balance is an example of an
that force which when applied to a mass of one equal-lever balance, which consists of a “rigid” beam
kilogram, gives it an acceleration of one meter per pivoted on a knife-edge, as shown in Figure 7.1. An
second per second (m/s2). unknown force F1 is compared directly with a
Weight. Weight F of a body of mass m at rest known force F’. When the beam is in equilibrium
relative to the surface of the earth is defined as the the sum of moments about the pivot is zero.
force exerted on it by gravity: F = mg, where g is Fla - F2a = 0
the acceleration due to gravity.
The main purpose of this chapter is to review .’. F1 = F2
the most commonly used force measurement This type of balance is mainly used for weighing
methods and to discuss briefly the principles chemicals. It gives direct reading, and can weight