This document discusses various methods of measuring force, including using scales, balances, elastic elements, and pressure-based sensors. It describes how equal-arm beam balances, unequal-arm scales, pendulum scales, spring scales, cantilever beams, proving rings, and hydraulic load cells operate to measure force based on principles such as moment equilibrium, elastic deformation, and fluid pressure changes. Examples of applications for various force measurement techniques are also provided.

1. Force measurement
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2. introduction
Force maybe defined as a that produces resistance or
obstruction to any moving body, or changes the
motion of a body, or tends to produce these effects.
Force is usually measured by applying it to a
calibrated device which resists the force and
indicates or records its magnitude.
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3. Methods of measuring force
• The unknown force may be measured by following
methods:-
1. Balancing the unknown force against known
gravitational force due to standard mass. Scales and
balances works based on this principle.
2. Applying unknown force to an elastic member and
measuring the deflection on calibrated force scale
or the deflection may be measured by using a
secondary transducers. i.e. Spring scale, cantilever
beam, Providing ring, Strain gauge load cell.
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4. Continue…
3. Translating the force to a fluid pressure and then
measuring the resultant pressure and then
measuring the resultant pressure. Hydraulic and
pneumatic load cells works on this principle.
4. Applying force to known mass and then measuring
the resulting acceleration.
5. Balancing a force against a magnetic force which is
developed by interaction of magnet and current in
coil.
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5. Scales and balances
In this session we conclude following topics:-
1. Equal arms beam balance scale
2. Even or equal arms balance scales
3. Pendulum scale
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6. Equal arms beam balance scale
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• As shown in figure equal arm beam balance scale
operates on the principle of moment comparison.
• The moment produced by the unknown mass or force
is compared with that produced by a gravitational force
due to known standard mass.
• When null balance is obtained the two weights or
forces are equal.
• For null balance w1l1= w2l2. If equal arms l1 = l2.
∴ w1 = w2.
• This types of instruments generally used in physics and
chemistry labs to measure the unknown weights.
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8. Even or unequal arms balance scale
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The main dis advantage of equal arms balance scale is
requires a set of weights at least as heavy as the heaviest
load to be measured.
There are two arms in that system 1st is load arm which is
associated with unknown load and other is power arm
which is associated with known weights.
In this scale known weight can be decreased by
increasing length of load arm, hence heavier load can be
measure with help of small known mass and large arm.
For null balance ,
w1*length of power arm = w2*length of load arm
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10. Pendulum scale
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The pendulum scale is deflection type instrument in
which the unknown weight is converted to a torque
that is then balanced by the torque of a fixed
standard mass arranged as pendulum.
When the unknown weight is applied to the load rod,
sectors tend to rotate due to tension in loading
tubes, and consequently the counter weight wc
swing out.
The motion of the equilibrium are attained when the
moment due to counter weights is becomes same as
moment due to ap
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The motion of the equalizer bar is converted into an
angular movement of the indicator by a rack and
pinion arrangement.
The deflection of the pointer is calibrated in terms of
applied force.
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13. Elastic force meter
The elastic elements (spring, rod, cantilever,
simply supported beam, ring, bellows,
diaphragm etc.) can be used for measurement
of force directly or indirectly through
displacement of elastic limit.
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14. Spring scale
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As shown in figure spring scale, the unknown weight
is suspended from a hook.
The deflection of spring with respect to weight is
read on the scale in terms of the weight.
The scale is calibrated on the basis of the spring.
𝐹 = 𝑘. 𝑥,
𝑤ℎ𝑒𝑟𝑒 𝑘 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠 𝑜𝑓 𝑠𝑝𝑟𝑖𝑛𝑔, 𝑥deflection, F is
load
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16. Cantilever beams load cell
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It is the simplest type of load cell of force
measurement. It measures force based on principle
as ‘bending moment developed in the beam is
proportional to applied force’ to the end of beam.
The deflection at free end is given by
4𝐹𝑙3
𝛿 =
𝐸𝑏𝑡3
The strain at fixed end is given by
6𝐹𝑙
𝜀 =
𝐸𝑏𝑡3
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18. Proving ring
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Scientists and engineers often use proving rings as a
way to measure force.
The devices are made using a ring of metal with a
spring-like consistency.
Inside the ring there is a screw attached to a dial
with measurements on it and a plate that vibrates
after being struck with something.
The contraption in the center works to show the
ring's diameter after it has been compressed or
stretched, which produces a reliable force
measurement that
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20. Hydraulic force meter
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The cell uses conventional piston and cylinder
arrangement.
The piston is placed in a thin elastic diaphragm.
The piston doesn't actually come in contact with the
load cell.
Mechanical stops are placed to prevent over strain of
the diaphragm when the loads exceed certain limit.
The load cell is completely filled with oil.
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When the load is applied on the piston, the
movement of the piston and the diaphragm
arrangement in an increase of oil pressure which in
turn produces a change in the pressure on a Bourdon
tube connected with the load cells.
Because this sensor has no electrical components, it
is ideal for use in hazardous areas.
Typical hydraulic load cell applications include
result tank, bin and hopper weighing.
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